In this appeal from the district court’s grant of a writ of habeas corpus, we are confronted by a crime that is now nearly forty years old and the problems that arise when a defendant is re-tried decades after an initial conviction. Petitioner-Appellee Albert Woodfox, an inmate in the Louisiana State Penitentiary at Angola, Louisiana, was originally convicted in 1973 for the murder of prison guard Brent Miller. His conviction was eventually overturned in state court post-conviction proceedings, but the State re-indicted him and proceeded to a second trial in 1998. By that time many of the witnesses had died and physical evidence had been lost. The State and the defense were both forced to present the prior recorded testimony of witnesses from the first trial.
Not surprisingly, the jury was presented with two portrayals of Woodfox, one as a hardened offender who advocated 'racial violence and force against the prison officials, and a second as a protector of weaker inmates and an advocate for prison reform who was targeted and framed for the crime due to his political activism. Although presented both with witnesses who swore that Woodfox was the killer and other witnesses who swore he had an alibi, the jury resolved the matter in favor of the State and again convicted Woodfox of murder. That conviction is the subject of the instant federal habeas proceeding.
The district court held that Woodfox’s 1998 trial counsel rendered ineffective assistance in several respects. It held that counsel should have objected on confrontation grounds to the reading of the 1973 testimony from inmate Hezekiah Brown, who provided an eyewitness account incriminating Woodfox and who had died before the 1998 trial. The court believed the prior testimony was inadmissible because prior to the first trial, the State had suppressed information showing that Brown may have been lying about prom*783ises from prison officials in return for his testimony. The district court also faulted counsel for failing adequately to investigate or to object to other physical and testimonial evidence. The State of Louisiana, acting through the Respondent-Appellant Warden Burl Cain, appeals.
We conclude that Woodfox’s confrontation-based argument about Brown is precluded from federal review because it was not adequately exhausted in state court, and that it also fails on the merits. As we explain below, we conclude that the deferential standard of review applied to state habeas decisions under the Antiterrorism and Effective Death Penalty Act mandates that we REVERSE the district court’s judgment.
I. Factual and Procedural Background
In 1972, the Louisiana State Penitentiary was a segregated institution prone to violence and harsh living conditions. The record suggests that stabbings occurred among the inmate population on a regular basis. Homosexual rape was prevalent, as was the presence of so-called “gal-boys,” inmates who acted like women in homosexual relationships and who were traded as slaves by stronger, predator inmates. The social and political unrest of the early 1970s that was common in the entire country added to the tension of an already hostile prison environment. The relevance of all these facts to this case will become clear later in this opinion. Albert Woodfox was an inmate at the penitentiary serving a fifty-year sentence for armed robbery.
The prison’s medium security area included four dormitory groups (each with four dormitories), known as Pine, Hickory, Walnut, and Oak, that housed inmates in a barracks-like setting. Woodfox lived in the Hickory 4 dorm. Brent Miller, a young, well-liked prison guard, was one of two correctional officers assigned to the four Pine dormitories. The prison at that time was understaffed with correctional officers, and inmates often conducted themselves with a minimal number of guards supervising them. For example, prisoners in medium security were allowed a certain amount of autonomy in deciding whether or not to remain in their dorms or to go to breakfast in the dining hall.
On April 17, 1972, Miller stayed behind in the dorm area while fellow correctional officer Paul Hunt escorted the inmates from Pine down the “walk” to the dining hall for breakfast. The inmates were initially unable to gain entrance to the dining hall because the inmate servers refused to serve breakfast in protest of the hours they were required to work. The disturbance was known as a “buck.” The prisoners were held out of breakfast while the warden attempted to resolve the buck. Some inmates returned to their dormitories, others remained outside. After the grievance was resolved, a second call to chow was made.
Sometime between 7:30 a.m. and 8:00 a.m., while all this was going on, Miller entered the Pine 1 dormitory where inmate Hezekiah Brown kept a small coffee pot. Brown typically remained in the dorm for breakfast and often shared coffee with the guards. Upon returning from breakfast a short time later, Correctional Officer Hunt found Miller’s body lying in a pool of blood in the anteroom of the dorm. Miller had been stabbed 32 times.
The prison immediately went into lock-down. Correctional officers began searching the dormitory area and found a homemade prison knife covered with wet blood hidden in a vent underneath Pine 1. Officers called in the West Feliciana Parish Sheriffs Department and the state police. A physical examination of the crime scene yielded four finger prints that were found by dusting the dorm wall by the water *784cooler near Miller’s body. An apparent bloody finger print was also visible on the door frame. Prison officials coordinated an investigation with the Sheriffs Department, which commenced questioning of several hundred inmates who were in the prison yard or near the scene at the time of the murder.
Sheriff Bill Daniel and Deputy Thomas Guerin conducted much of the questioning of individual prisoners in the prison’s clothing room as the inmates waited for hours in line outside. They eventually questioned Woodfox, who denied any knowledge of the murder and claimed he was eating breakfast at the time. Sheriff Daniel testified that he seized Woodfox’s clothing — including a green jacket, blue pants, and brown shoes — because of small, suspicious stains that might have been blood. Daniel bagged these items for evidence and sent them to the state police crime lab for further examination. A state criminologist testified that a small stain on the jacket was found to be human blood but there was an insufficient amount to determine the blood type. The small stains on the pants and shoe were also determined to be blood, but the quantity was so small that the State’s expert could not determine if it was human or animal blood. This was significant because Wood-fox worked in the kitchen, where he could have come into contact with animal blood. Further, neither the fingerprints on the wall nor the bloody print found at the scene was matched to Woodfox or any other person at the prison.
The State’s case against Woodfox was built largely on eyewitness testimony. The most damaging information came from Hezekiah Brown, who testified at Woodfox’s first trial in 1973. Because Brown was deceased by the time of the second trial in 1998, his prior testimony was read into the record. Brown was a 66-year-old inmate who had previously been on death row but had his sentence commuted to life prior to the events described herein. He initially told investigators on April 17, 1972, that he knew nothing about the murder and claimed to have an alibi placing him in the blood plasma unit at the time of the crime. Brown was questioned a second time on April 19, however, and gave a very different story.
Brown testified at the 1973 trial that he was in the Pine 1 dorm when Miller came in to have coffee and sat down on Brown’s bed, which was the closest bunk to the door. As Brown was plugging in the coffee pot, he heard scuffling behind him. He looked up and saw four inmates had entered: Woodfox, Herman Wallace, Gilbert Montegut, and Chester Jackson. Brown testified that the men held handkerchiefs over their faces but that he was able to recognize them. Woodfox suffers from a skin condition that causes blotching and rendered him identifiable.
According to Brown, Woodfox grabbed Miller from behind, lifted him up off the bed, and stabbed him in the back with a knife. He testified that the other inmates also grabbed Miller and began “jugging on him.” As they repeatedly stabbed Miller, the inmates pulled him into the small lobby area at the front of the dorm where they left him as they fled out the door.
Brown testified that he was terrified the inmates were also going to kill him. As he watched Miller dying on the floor, Brown, who was black, believed it imperative that he not be present when the white guard was found. He followed the fleeing inmates out the door but soon realized he was still wearing his pajamas. He therefore returned to change his clothes and then went to the blood plasma unit to establish an alibi.
Sheriff Daniel testified that after Brown gave his second statement, he prepared *785arrest warrants for Woodfox, Wallace, Montegut, and Jackson. Wallace was convicted after Woodfox’s first trial, and Jackson pleaded guilty to manslaughter. Montegut was acquitted, however.
How prison officials came to interview Brown the second time and the circumstances under which he incriminated Woodfox were disputed at trial. Brown averred in his 1973 testimony that he did not know how prison officials knew that he had information about the murder but that no one threatened him or made promises in return for his testimony. At the 1998 trial, Warden C. Murray Henderson testified that he had promised to protect Brown from inmate retribution if he provided information and to help Brown with a pardon application. As discussed in greater detail below, the Warden’s testimony is not entirely clear as to what was said and when, but the Warden did apparently promise some assistance before Woodfox’s first trial. Brown was never questioned about the Warden’s promises because defense counsel in 1973 did not know about them. In any event, Henderson also testified that he was led to Brown by another inmate who lived in the Pine 1 dorm, Leonard “Specs” Turner.
Turner was due to be released from his state sentence on the day after the murder. Henderson knew that Turner had not gone to breakfast on the morning of the killing and threatened to stop Turner’s parole if he did not tell what he saw in Pine 1. According to Henderson, Turner said that he did not see anything but that Brown was in the dorm and must have seen what had occurred.
The State called Turner as a witness at the 1998 trial. He testified that he was in the dorm and saw Miller come in but that he left about five minutes later and saw nothing. He did not remember telling Henderson that Brown had been present. Turner also did not remember having a meeting with Captain C. Ray Dixon the night before his release, and he denied telling Dixon that he saw Woodfox kill Miller.
The State later called Dixon, who testified that Turner often acted as his informer about events on the yard and that he spoke with Turner about Miller’s killing the night before Turner was released. Dixon said Warden Hayden Dees told him that Warden Henderson wanted Dixon to speak with Turner before Turner left the prison. According to Dixon, Turner wanted to keep his involvement secret and did not want to testify or sign any statements. Dixon testified that Turner told him what he knew about the murder and that Dixon wrote down what Turner said. Dixon identified an unsigned statement as being in his handwriting, but he had no independent recollection of what Turner had told him. Dixon was permitted to read from the statement to impeach Turner. The statement indicated that Turner said he saw Woodfox enter Pine 1 wearing a black cap and holding a handkerchief. Turner said Woodfox grabbed Miller in a “mugger hold” from behind and stabbed him as the other inmates helped in the struggle. The trial court gave a limiting instruction that the statement should be considered only to discredit Turner and should not be considered as evidence that the statement was true.
The State also introduced other testimony in support of Brown’s account of the murder. First, the State called Joseph Richey, a former inmate at Angola who had lived in Pine 4 dorm across the walk from Pine 1. Richey testified that after the buck in the dining hall he went back to this dorm and slept for about an hour. After he awoke he saw Miller enter Pine 1 while Richey was brushing his teeth. Because he wanted to resume a previous *786conversation with Miller about Viet Nam, Richey began to leave his dorm. From his doorway, he saw Turner leave Pine 1 at a fast pace. Richey then observed Woodfox leave Pine 1 also at a fast pace and bump into a trash cart that was being pushed down the walk by another inmate named Fess Williams. Woodfox was not wearing a hat or gloves. Richey saw Montegut, Wallace, Jackson and then Brown exit the dorm, and he initially thought they were going to chow. He noticed that Brown, who was wearing pajamas, turned and went back in the dorm, and then came out again wearing his clothes and headed toward the kitchen. He thought this was unusual because Brown usually did not go to breakfast. Richey proceeded to Pine 1 where he saw Miller’s body. When he saw all the blood, Richey thought the inmates had gone to get medical help for Miller, and he waited on the side of the Pine dorm smoking a cigarette.
Richey testified that when he was first interviewed about the murder he gave a “generic” answer about seeing Miller and waiting for help to arrive, but that about a month later he was interviewed again by Warden Dees and Captain Dixon and that he gave a statement identical to his testimony. On cross-examination, defense counsel questioned Richey about that prior statement, pointing out that, unlike his trial testimony, Richey had said that the four inmates actually passed him as he was entering the Pine 1 dorm and looked like they expected Richey to “walk into something.” Richey testified that his previous statement contained errors made by the typist, who confused the questions being asked with his answers. He also testified that the statement was later revised but that he signed it without reading it.
The State also presented previously recorded testimony from inmate Paul Fobb. As with Brown, Fobb testified at the 1973 trial but had died prior to the 1998 re-trial. His previous testimony was also read into the record. Fobb had severe vision problems due to glaucoma in his left eye and an accident with a cotton stick that rendered him blind in his right eye. Fobb claimed, however, that he could see well enough in April 1972. Fobb first testified that during that month he had witnessed a confrontation between Miller and Woodfox where Miller had ordered Woodfox out of the Pine dorm area because Woodfox did not live there. About a week before Miller was killed, Fobb heard Woodfox say that Miller was “always messin’ with him.” Woodfox then said that he “had fifty years” and “ain’t gonna be kicked,” and he threatened “to fix that little bitch.” Fobb continued that on the Sunday before the murder he heard Woodfox and others plotting to stage the buck so that the guards would be distracted and leave the walk, leaving only one guard in each dormitory area. On the morning of April 17, Fobb was on his way to the blood plasma unit when he saw Woodfox enter Pine 1. Fobb testified that he saw Woodfox exit the dorm five to ten minutes later and throw a rag into the Pine 4 dorm. He said he was “stunned” at seeing Woodfox. Although Fobb identified Woodfox leaving Pine 1, he testified on cross-examination that he did not see anyone else.
The State presented further evidence to suggest a motive for Woodfox in the killing. First, James Stevens, who was the Director of Prison Classifications in 1972, testified that a woman had been removed from Woodfox’s approved visitor list after prison officials intercepted a letter Wood-fox had written to the woman stating that “all correctional officers were pigs and that all white races should be killed.” John Sinquefield, the state prosecutor who prosecuted Woodfox in 1973, also testified about an encounter he had with Woodfox in a New Orleans courtroom where Wood-*787fox purportedly raised his shackled hands to spectators and said, “I want all of you to see what these racist, facist pigs have done to me.” Finally, the State presented a letter Woodfox had written after he was accused of Miller’s murder in which he spelled the word “America” with three “k”s.
While the State painted Woodfox as a violent and militant offender, the defense theory was that Woodfox was singled out by prison officials because of his political activism in the Black Panther Party and his efforts to obtain prison reform, especially in the protection of victims of sexual predation. His theory was that prison officials rushed to judgment because he and the other accused inmates were perceived as “troublemakers.” Woodfox elicited testimony from Warden Henderson, who had come to Angola from out of state with designs for prison reform, that established prison officials, such as Warden Dees, resented his presence, were opposed to court orders for reform, and did not conduct a non-biased investigation of Miller’s murder. Woodfox suggested that Warden Dees had immediately made up his mind about who had committed the murder and confined him and the other three suspects in immediate “lockdown.” His theory was that prison officials such as Dees “put words” in the mouths of the inmates who incriminated him.
Woodfox presented as an alibi witness the 1973 trial transcript of Everett Jackson, an inmate who said Woodfox was with him at breakfast. He also presented live testimony from Clarence Sullivan, an inmate who worked in the kitchen and said he saw Woodfox at the dining hall. Sullivan admitted he had never told anyone about this until speaking with defense counsel prior to trial, however, because at the time in 1972 he had been planning an escape and did not want to get involved. Woodfox further presented a transcript of the 1973 testimony of Fess Williams, who denied seeing anyone come out of Pine 1 and denied that Woodfox had bumped into his trash cart that morning, thereby contradicting the testimony of Richey.
Woodfox also testified in his own behalf. He contended that after the buck in the dining hall he went to breakfast between 7:30 a.m. and 7:50 a.m. He claimed that after eating he went with Everett Jackson to get some legal papers and returned to his own dorm in Hickory 4 between 8:15 a.m. and 8:30 a.m. when all the inmates were ordered out onto the walk for questioning. He claimed that prison officials seized his clothes. Contrary to the testimony of Sheriff Daniel that Woodfox was wearing a green jacket, blue pants, and brown shoes that were bagged and labeled for evidence, Woodfox testified that he was wearing blue jeans, a grey sweatshirt, and rubber boots that he wore because he worked in the kitchen. He testified that the clothing was simply thrown into a pile in the corner. Woodfox also testified that the prison administration was blatantly racist, that Sheriff Daniel had pointed a gun at his head and threatened to shoot him, and that the State’s witnesses lied because of their hatred of him for trying to stop the sexual attacks at the prison. He claimed that both Brown and Richey were sexual predators, although there was no evidence corroborating this testimony.
The jury found Woodfox guilty of murder, and he was sentenced to a mandatory term of life in prison without the benefit of parole, probation, or suspension of sentence. Woodfox unsuccessfully appealed his conviction through the state appellate process. He subsequently filed a timely state application for post-conviction relief, raising numerous claims of error. The state trial court initially denied the petition without obtaining a response from the *788State. The Louisiana First Circuit Court of Appeal granted a writ of review, however, and remanded with instructions that the trial court obtain an answer to the application from the prosecution. The State thereafter filed its response, and the trial court again denied the application. The trial court held that the application was without merit, and it also adopted the State’s response as its written reasons for denial. The state appellate court and the Louisiana Supreme Court both denied applications for writs without written opinions.
Woodfox then timely filed the instant petition pursuant to 28 U.S.C. § 2254. The magistrate judge issued a report recommending that relief be granted on several grounds. The magistrate judge determined first that counsel rendered ineffective assistance by failing to object to the admission of Brown’s 1973 testimony at the 1998 trial. The magistrate judge reasoned that Woodfox’s 1973 counsel was unable to question Brown about promises made to him by Warden Henderson because the State had suppressed that information, and therefore the admission of the testimony in 1998 violated the Confrontation Clause. The magistrate judge also determined that Woodfox’s trial counsel had been ineffective for (1) failing to object to testimony by former prosecutor John Sinquefield vouching for Brown’s demeanor and credibility when testifying at the 1973 trial; (2) failing to investigate and obtain expert witnesses to test the bloodstained clothing or review the tests performed by the State’s expert; (3) failing to obtain an expert to evaluate the bloody print found at the murder scene and to verify or refute the conclusion of the State’s expert that the print might be a palm print rather than a finger print; (4) failing to investigate and present medical evidence concerning witness Paul Fobb’s blindness that would have discredited Fobb’s testimony; and (5) failing to object to the State’s referral to inadmissible hearsay statements contained in a prior statement of Chester Jackson. The magistrate judge determined that the foregoing deficiencies of Woodfox’s counsel prejudiced the defense and undermined confidence in the outcome of the 1998 trial. The magistrate judge therefore recommended that Woodfox’s conviction be vacated and the case remanded to the state court.1
The district court adopted the magistrate judge’s report and granted the writ of habeas corpus. The State now appeals. It contends that the district court, through adoption of the magistrate judge’s report, failed to afford the state habeas proceedings the proper measure of deference and incorrectly determined that trial counsel rendered ineffective assistance.2
II. Standard of Review
On review of the district court’s grant of habeas relief, we review issues of *789law de novo and findings of fact for clear error. Fratta v. Quarterman, 536 F.3d 485, 499 (5th Cir.2008). A claim of ineffective assistance of counsel presents a mixed question of law and fact. Richards v. Quarterman, 566 F.3d 553, 561 (5th Cir. 2009). If the district court’s findings of fact are not clearly erroneous, we will independently apply the law to the facts as found by the district court. Id.
Woodfox’s § 2254 petition is governed by the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA). The AEDPA requires that federal courts defer to a state court’s adjudication of a claim if the claim has been adjudicated on the merits in the state court proceedings unless the state court decision was (1) “contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court,” or (2) “was based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding.” 28 U.S.C. § 2254(d).
A state court decision is “contrary to” federal precedent if it applies a rule that contradicts the governing law set forth by the Supreme Court or if it involves a set of facts that are materially indistinguishable from a Supreme Court decision but reaches a result different from that Court’s precedent. Woodward v. Epps, 580 F.3d 318, 325 (5th Cir.2009). “A state court unreasonably applies clearly established federal law as determined by the Supreme Court if it identifies the correct governing principle established by the Supreme Court, but unreasonably applies that principle to the facts of the case.” Rogers v. Quarterman, 555 F.3d 483, 488-89 (5th Cir.2009). An unreasonable application of federal law is different from an incorrect or erroneous application of the law. Id. (citing Williams v. Taylor, 529 U.S. 362, 409-10, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)). “The question under AEDPA is not whether a federal court believes the state court’s determination was incorrect but whether that determination was unreasonable — a substantially higher threshold.” Schriro v. Landrigan, 550 U.S. 465, 473, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007). Furthermore, we review for objective reasonableness the state court’s ultimate legal decision, not necessarily the state court’s opinion and legal reasoning for its ultimate decision. Neal v. Puckett, 286 F.3d 230, 246 (5th Cir.2002) (en banc).
III. Discussion
The State argues that the district court failed to apply the AEDPA’s heightened deferential standard of review to Wood-fox’s ineffective assistance claims. It notes that the court reviewed de novo Woodfox’s claim regarding counsel’s failure to challenge the 1998 indictment and testimony of Brown on Confrontation Clause grounds, and then carried that standard of review forward when considering Woodfox’s remaining claims. We agree that the district court failed to apply the proper degree of deference to the state court’s denial of relief on Woodfox’s confrontation-based claim, but we pause first to consider the threshold issue whether Woodfox properly exhausted that claim for relief. See Nobles v. Johnson, 127 F.3d 409, 419 (5th Cir.1997) (“A state prisoner normally must exhaust all available state remedies before he can apply for federal habeas relief.”). We raise this issue sua sponte because, as discussed further below, we conclude that the State has not expressly waived it. See Tigner v. Cockrell, 264 F.3d 521, 526 n. 3 (5th Cir.2001).
A. Ineffective assistance for failing to raise a confrontation objection 1. Exhaustion
A federal court may not grant habeas relief unless “the applicant has ex*790hausted the remedies available in the courts of the State.” 28 U.S.C. § 2254(b)(1)(A). Exhaustion requires that the prisoner “have fairly presented the substance of his claim to the state courts.” Nobles, 127 F.3d at 420. “Determining whether a petitioner exhausted his claim in state court is a case- and fact-specific inquiry.” Moore v. Quarterman, 533 F.3d 338, 341 (5th Cir.2008) (en banc). Therefore, in order to determine whether Wood-fox properly exhausted his confrontation-based claim, it is necessary to examine in detail Woodfox’s federal claim compared with his state claim.3
Woodfox’s federal § 2254 petition characterized his claims as ineffective assistance. He specifically challenged counsel’s failure to contest on confrontation grounds the admission of Brown’s 1973 testimony at the 1998 trial. Woodfox’s theory was that the State suppressed the fact that Warden Henderson promised to help Brown get a pardon in return for his testimony, thereby denying Woodfox the opportunity to impeach Brown in 1973 and rendering the reading of that prior testimony inadmissible in 1998. Woodfox, who was represented by counsel in both federal and state court, argued the claim in federal court this way:
Brown’s prior testimony runs far afoul of the requirements of the [Confrontation [CJlause, not only because the jury was unable to assess his demeanor firsthand, but because Mr. Woodfox was unable to impeach and otherwise cross examine this critical witness regarding, among other things, the promise of a pardon made to him by the head warden in exchange for his testimony. Counsel’s failure to pursue this challenge to retrial cannot be defended. Because the trial court would have had no choice but to uphold such a challenge, prejudice is established.
Woodfox’s claim thus presented a hybrid of Brady/Giglio principles4 and an inadequate opportunity for cross-examination, layered within an ineffective assistance claim.
In his state court application for post-conviction relief, which is voluminous and disjointed, Woodfox focused on the perceived unfairness of being subjected to a re-trial after the passage of so many years because of the intervening death of several witnesses and the loss of physical evidence. Woodfox presented fifty pages of discussion of his version of the “facts,” broken into subsections dealing with particular trial witnesses. With respect to Hezekiah Brown, Woodfox discussed Brown’s 1973 testimony and its alleged deficiencies. He stated that “[sjince the 1996 death of Brown — and with him, the opportunity for Mr. Woodfox to meaningfully cross-examine him — a vast amount of impeachment evidence has come to light.” He then spent several pages discussing the Warden’s promise to Brown, letters the Warden wrote on Brown’s behalf after the 1973 trial, the alleged incentives Brown later *791received, and the testimony and out-of-court statements of other witnesses suggesting that Brown “was a liar” and unworthy of belief. Woodfox concluded: “Brown’s testimony, with its contradictions and his inability to answer numerous key questions, is highly dubious. When coupled with the impeachment evidence ... it is simply unbelievable.” Woodfox did not argue that counsel was ineffective for failing to challenge on confrontation grounds the reading of Brown’s testimony in 1998, focusing instead on the alleged unreliability of Brown’s testimony.
Woodfox then presented 90 pages of specific “claims for relief,” none of which asserts that counsel failed to object to Brown’s 1998 testimony. Instead, Wood-fox’s state application (1) cites and discusses the general principles of Brady, Giglio, and Kyles v. Whitley, 514 U.S. 419, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995); (2) asserts that had he not been denied certain exculpatory evidence (unrelated to Brown), “he could have refuted the State’s case at every turn”; and (3) argues that counsel should have sought to quash the indictment because the 21-year delay between indictments denied him due process and confrontation, in part because of the intervening death of Brown.
As the district court noted, this last argument appears akin to a speedy trial claim. Woodfox’s state habeas application asserted that the 1998 trial counsel was ineffective for failing to quash the 1998 indictment, noting that more than 20 years had passed since the first indictment. The argument reads as follows:
[Counsel] should have filed a motion to quash the indictment on this ground. The delay between the first and second indictment was 21 years. The length of this delay is presumptively oppressive given the fact that Mr. Woodfox was in state custody. The reason for the delay was the failure of the state to bring his case before a legal grand jury. The delay of more than two decades has adversely affected his defense. The key witness against him, Hezekiah Brown, died before trial, as did Paul Fobb. Evidence could not be found and was thus unavailable for defense testing. Because of counsel’s failure to challenge the indictment, Mr. Woodfox’s rights to Due Process and Confrontation could not be honored. His conviction must be reversed.
(Emphasis added).
Although Woodfox mentioned the Confrontation Clause, he presented no coherent argument on confrontation, and this paragraph does not resemble the claims Woodfox made in his § 2254 petition about counsel’s ineffectiveness as l’elated to Brown. The various assertions that Woodfox did make in the state application about Brown, confrontation, and his own counsel are interspersed and separated by many pages. Then at page 139 of his state application, Woodfox sets out among a laundry list of claims — without discussion or analysis — the bald statement that his “rights to due process and to confrontation were violated by the admission of transcripts of prior testimony of Hezekiah Brown.”
We cannot conclude from the foregoing that Woodfox’s state application fairly raised the distinct issue of whether his 1998 counsel should have objected to Brown’s testimony on the ground that his 1973 counsel was denied a fair opportunity to cross-examine and impeach Brown on the Warden’s promise. All Woodfox did was present general principles of law and present information that might permit an inference of such a claim. Although he presented to the state court the concepts of Brady/Giglio and the mere suggestion that he was unable to effectively cross-*792examine Brown in 1973, he made no effort to join the law with the facts of the case.
“It is not enough that all the facts necessary to support the federal claim were before the state courts or that a somewhat similar statelaw claim was made.” Anderson v. Harless, 459 U.S. 4, 6, 103 S.Ct. 276, 74 L.Ed.2d 3 (1982) (internal citations omitted). “Rather, the petitioner must afford the state court a ‘fair opportunity to apply controlling legal principles to the facts bearing upon his constitutional claim.’ ” Bagwell v. Dretke, 372 F.3d 748, 755 (5th Cir.2004) (quoting Anderson, 459 U.S. at 6, 103 S.Ct. 276). Woodfox’s state application did not afford such an opportunity to the state court without that court first having to surmise and infer the basis for Woodfox’s ineffective assistance claim. In addition, Wood-fox was proceeding with counsel. Although we liberally construe pro se pleadings, we do not afford such latitude to pleadings prepared by counsel.5 See United States v. Gonzalez, 592 F.3d 675, 680 n. 3 (5th Cir.2009); Beasley v. McCotter, 798 F.2d 116, 118 (5th Cir. 1986). We therefore conclude that Wood-fox’s confrontation-based ineffective assistance claim is unexhausted and procedurally barred from federal review. See Hatten v. Quarterman, 570 F.3d 595, 605 (5th Cir.2009).
As noted above, we have raised the exhaustion issue sua sponte, which we have the authority to do provided that the State has not waived it. See Tigner, 264 F.3d at 526 n. 3; Clinkscale v. Carter, 375 F.3d 430, 436-37 (6th Cir.2004); 28 U.S.C. § 2254(b)(3) (“A State shall not be deemed to have waived the exhaustion requirement or be estopped from reliance upon the requirement unless the State, through counsel, expressly waives the requirement.”). Although the State indicated in its answer to the § 2254 petition in the district court that Woodfox’s claims were exhausted, we do not find an express waiver in light of the State’s briefing of the issue.
“The touchstone for determining whether a waiver is express is the clarity of the intent to waive.” Carty v. Thaler, 583 F.3d 244, 256 (5th Cir.2009) (quotation marks and citation omitted), cert. denied, - U.S. -, 130 S.Ct. 2402, 176 L.Ed.2d 923 (2010) (No. 09-900). In Carty, we noted with approval a Sixth Circuit decision that found waiver based on “ ‘counsel’s conduct during the district court proceedings,’ ” which had “ ‘manifested a clear and unambiguous intent to waive’ ” exhaustion. Id. at 257 n. 9 (quoting D Ambrosio v. Bagley, 527 F.3d 489, 497 (6th Cir.2008)). We held that the State waived the exhaustion issue in Carty because its motion for summary judgment in the district court showed that it treated all the relevant claims as exhausted. Id. at 257; see also Bledsue v. Johnson, 188 F.3d 250, 254 (5th Cir.1999) (holding exhaustion expressly waived when the State admitted in its answer to the federal habeas petition that the prisoner had “sufficiently exhausted his state remedies”). We have also held that there was no “express waiver” where the State indicated *793that it merely “believed” the prisoner had exhausted his claims, although we concluded this was the equivalent of failing to assert the defense of non-exhaustion. McGee v. Estelle, 722 F.2d 1206, 1213 (5th Cir.1984) (en banc).
The State’s answer to Woodfox’s federal habeas petition stated that “on October 11, 2006, petitioner filed these timely and exhausted claims in the present petition for writ of habeas corpus.” (emphasis added). The State made an identical statement in its memorandum in support of its answer. However, in the body of its memorandum addressing the ineffective assistance claim surrounding Brown’s testimony, the State argued that Woodfox was actually making a new argument. The State first asserted that in the state habeas application Wood-fox had “limited his argument [about counsel’s failure to challenge the indictment] to the fact that twenty-one years between the first and second indictments as well as evidence that had been lost was presumptively oppressive and had a prejudicial [effect on] his defense.” The State subsequently argued that:
In this present claim, petitioner expands on the fact that the second trial jury was unable to assess Hezekiah Brown’s demeanor first hand, that petitioner was unable to impeach Brown and otherwise cross examine this “critical” witness regarding such issues as a pardon offer made by the warden. As a result of this new argument, petitioner then comes to the new conclusion that a trial court “would have had no choice but to uphold such a challenge” and prejudice [from counsel’s ineffectiveness] is thereby established.
(Emphasis added). By characterizing Woodfox’s argument as a new claim in its district court brief, the State hardly made a clear and unambiguous waiver of exhaustion.6 At most, it simply failed to assert non-exhaustion as a defense. We therefore hold that we are not precluded from raising exhaustion sua sponte and finding that Woodfox’s claim is procedurally barred.
Woodfox may not obtain federal relief on the unexhausted claim. If a prisoner fails to exhaust state remedies and the court to which the prisoner would be required to present his claims in order to meet the exhaustion requirement would now find the claims procedurally barred due to the prisoner’s own procedural default, “federal courts are barred from reviewing those claims.” Sones v. Hargett, 61 F.3d 410, 416 (5th Cir.1995). To overcome the procedural bar on nonexhaustion, Woodfox must “demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law, or demonstrate that failure to consider the claims will result in a fundamental miscarriage of justice.” Coleman v. Thompson, 501 U.S. 722, 750, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991); see Ries v. Quarterman, 522 F.3d 517, 523-24 (5th Cir.2008).
We find no basis for cause for failing to exhaust the claim in state court, especially since Woodfox was represented by counsel in the state habeas proceedings. See In re Goff, 250 F.3d 273, 276 (5th Cir.2001) (“[I]neffective assistance of counsel in a post-conviction proceeding cannot serve as cause to excuse procedural default in a federal habeas proceeding.”). We likewise see no basis to find a miscarriage of justice for not reviewing the claim. A claim of a miscarriage of justice is limited to a claim of “actual innocence,” which *794requires the prisoner to establish through new and reliable evidence “that it was ‘more likely than not that no reasonable juror would have convicted him in the light of the new evidence.’ ” Fairman v. Anderson, 188 F.3d 635, 644 (5th Cir.1999) (quoting Schlup v. Delo, 513 U.S. 298, 327, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995)). The “new” evidence upon which Woodfox’s claim rests is the Warden’s promise to assist Brown with his pardon application. This evidence does not establish that no juror would have convicted Woodfox. In fact, the 1998 jury convicted Woodfox despite the revelation of Warden Henderson’s promise. We therefore conclude that Woodfox cannot overcome the procedural bar of non-exhaustion.
Even assuming arguendo that Woodfox adequately presented his confrontation-based ineffective assistance claim in his state habeas application, we find that the district court erroneously granted federal habeas relief. To address the district court’s grant of habeas relief on the confrontation claim, we must determine whether the state court adjudicated the claim on the merits, thereby requiring the application of AEDPA deference, and if so, whether the state court’s adjudication was contrary to or an unreasonable application of federal law.
2. AEDPA deference
The AEDPA’s deferential standard is afforded to a state court decision only when the state court adjudicated the petitioner’s claims on the merits. See 28 U.S.C. § 2254. This is akin to asking whether the state court decision was “ ‘substantive or procedural.’ ” Mercadel v. Cain, 179 F.3d 271, 274 (5th Cir.1999) (quoting Green v. Johnson, 116 F.3d 1115, 1121 (5th Cir.1997)). In the instant case, the Louisiana Supreme Court denied Woodfox’s application for supervisory writs with a one-word denial. See State v. Woodfox, 937 So.2d 850 (La.2006). “When faced with a silent or ambiguous state habeas decision, the federal court should ‘look through’ to the last clear state decision on the matter.” Jackson v. Johnson, 194 F.3d 641, 651 (5th Cir.1999). The last clear state court decision of any substance to address Woodfox’s claims was the state trial court’s decision denying Woodfox’s habeas application. That decision, in turn, also adopted the State’s answer to Wood-fox’s application. We must therefore decide whether the state habeas court’s decision and adoption of the State’s response was an adjudication on the merits because it was a “substantive” decision subject to the AEDPA deferential standard of review, or whether it was a “procedural” decision to which deference does not apply. See Mercadel, 179 F.3d at 274.
The state court’s “decision” in this case actually comprised two documents, a “Judgment” and a statement of “Written Reasons.” The “Judgment” denied Wood-fox’s entire habeas application. It stated that Woodfox’s claims had been “fully addressed” by the State’s response and that “[a] review of the record of these proceedings, as well as the answer, indicates that there is no need to hold an evidentiary hearing in these proceedings. For written reasons this day adopted and assigned, the Court finds that the allegations are without merit and the Application may be denied without the necessity of any further proceedings.”
A separate, undated document captioned “Written Reasons” stated that “Petitioner,” meaning Woodfox, bears the burden of proof to show he is entitled to habeas relief. It cited La.Code Crim. P. art. 930.2, and then stated that “[i]n light of such burden of proof, the Court has fully considered the application, the answer, and all relevant documents and has determined *795that Petitioner has failed to carry his burden of proof.” The document continued, “In determining that Petitioner’s application should be denied, the Court, moreover, adopts the State’s Response to Application for Post Conviction Relief as the written reasons for the Court’s decision.”
The district court decided that the state trial court, through its adoption of the State’s opposition to Woodfox’s post-conviction relief application, failed to address Woodfox’s Due Process and Confrontation Clause contentions respecting the reading of Brown’s 1973 testimony at the 1998 trial. This purported failure by the state court to address the claim led the district court to conclude that de novo review applied rather than the AEDPA’s deferential standard. We disagree with the district court’s assessment.
First, the State’s response to Woodfox’s state habeas application mirrored the structure of Woodfox’s petition. It first discussed generally Woodfox’s factual assertions about the various trial witnesses, and it then discussed the specific legal claims. In the first part of the State’s brief in a section captioned “Hezekiah Brown,” the State said: “What is very interesting is that, although there is discussion of the testimony of Hezekiah Brown included in the Statement of Facts portion of the application, there is no mention of it in the Claims for Relief section.” The State then went on to indicate how important Brown’s testimony was and that even if Woodfox disagreed with the verdict, it was reasonable for the jury to choose to believe the State’s witnesses. This directly responded to Woodfox’s attack on Brown’s credibility. In the second part of its response, the State addressed inter alia Woodfox’s specific claims of ineffective assistance of counsel. Although it did not discuss Brown again, the State set forth the correct legal standard under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), for evaluating ineffective assistance claims and issued a blanket denial “that any of Wood-fox’s claims allege deficient performance on the part of counsel.” (Emphasis added). The state court’s judgment and written reasons, along with the incorporated State response, thus show that the state trial court issued a merits-based adjudica-, tion of all of Woodfox’s claims, including the claim about Brown’s testimony.7
Lest there be any doubt, we have adopted a three-part test to decide whether a state court’s decision was an adjudication on the merits when that decision is unclear. We consider the following:
*796(1) what the state courts have done in similar cases; (2) whether the history of the case suggests that the state court was aware of any ground for not adjudicating the case on the merits; and (3) whether the state courts’ opinions suggest reliance upon procedural grounds rather than a determination on the merits.
Mercadel, 179 F.3d at 274.
Besides stating that Woodfox’s claims had no merit and that it would adopt the State’s response, the state court here cited La.Code Crim. P. art. 930.2. That provision provides simply that “[t]he petitioner in an application for post conviction relief shall have the burden of proving that relief should be granted.” The Louisiana Supreme Court has cited article 930.2 in other cases when a petitioner failed to carry his burden on the merits of the case. See State v. LeBlanc, 937 So.2d 844, 844 (La. 2006) (citing art. 930.2 after stating that petitioner failed to show he pleaded guilty involuntarily); State v. Berry, 430 So.2d 1005, 1013 (La.1983) (citing art. 930.2 because petitioner’s claim that the jury was not furnished with a copy of aggravating and mitigating circumstances was “unsubstantiated and therefore without merit”). But the court has also cited that provision when a petitioner failed to meet his burden on some procedural point. See State v. Russell, 887 So.2d 462 (La.2004) (citing art. 930.2 because petitioner failed to carry his burden of proof that post-conviction application was timely filed). Therefore, consideration of what the state courts have done in other cases, by itself, is not dispositive of whether the state court’s citation to article 930.2 in this case was substantive or procedural. But when considered in light of the other factors, we think it is clear that the state court decided all of Wood-fox’s claims on the merits.
The second factor of the Mercadel test, whether the history of the case suggests that the state court was aware of any ground for not adjudicating the case on the merits, fails to show any such awareness. In Barrientes v. Johnson, 221 F.3d 741, 779 (5th Cir.2000), we held that this factor supported a conclusion that the state court adjudicated the merits where the State’s response to the habeas petition in state court attacked the claims on the merits rather than arguing the procedural point of waiver. We “surmised” that the state court was not put on notice by the State’s response that the claim was waived. Id. Similarly here, the State made no argument to put the state court on notice of any procedural defect in Woodfox’s state application.8 Instead, the State presented only merits-based arguments under the Strickland standard and, as noted above, denied that any of the ineffective assistance claims showed deficient performance by counsel. Furthermore, Woodfox conceded in his § 2254 petition in the district court that the state court had ruled on the merits of his claims, specifically stating that “the claims raised in this petition[, other than the grand-jury claim, which was raised on direct appeal,] were presented by Mr. Woodfox in his state postconviction application, and all claims were rejected on the merits.” Therefore, the history of the case suggests the state court adjudicated the merits.
The final prong of the three-part inquiry, “whether the state courts’ opinions sug*797gest reliance upon procedural grounds rather than a determination on the merits,” further tips the scale in favor of finding a merits-based adjudication. The state court’s judgment stated that the “record,” as well as the State’s response, indicated no need for a hearing and that “the allegations are without merit.” (Emphasis added). Similarly, the state court’s written reasons stated that the court had considered “the application, the answer, and all relevant documents” before concluding that Woodfox failed to meet his burden of proof. The court then stated that “moreover” it would adopt the State’s response to Woodfox’s application. “Moreover” means “[i]n addition thereto, also, furthermore, likewise, beyond this, beside this,” Black’s Law Dictionary 1009 (6th ed.1990), or “in addition to what has been said.” Merriam-Webster’s Collegiate Dictionary 755 (10th ed.2002). In other words, the state court reviewed all relevant documents in the record of the proceedings, including the State’s answer, and found no merit to any of Woodfox’s claims. In addition to this conclusion, the court adopted the reasoning of the State’s response. There is simply no indication in the state court adjudication that suggests a reliance on any procedural vehicle rather than the merits to deny relief.9
Moreover, AEDPA deference applies to a state court adjudication even when the state court gives no indication whatsoever as to the reasons for the decision. See Schaetzle v. Cockrell, 343 F.3d 440, 443 (5th Cir.2003) (“Because a federal habeas court only reviews the reasonableness of the state court’s ultimate decision, the AEDPA inquiry is not altered when, as in this case, state habeas relief is denied without an opinion.”); Henderson v. Cockrell, 333 F.3d 592, 598 (5th Cir.2003) (“AEDPA’s standards apply, however, when the state’s highest court rejects a claim without giving any indication of how or why it reached that decision.”). If we would accord AEDPA deference to a state court decision that contained no explanation for its denial of relief, we are hard pressed to deny such deference to a state court’s decision indicating that the claims were without merit but also adopting the State’s response to the habeas application. We therefore conclude that, assuming Woodfox properly exhausted his confrontation-based ineffective assistance claim concerning Hezekiah Brown’s testimony, the state court’s denial of relief was an adjudication on the merits to which we must afford AEDPA deference.
Turning to the merits of Woodfox’s claim, we must next determine whether the state court’s denial of relief was contrary to or an unreasonable application of clearly established federal law as established by the Supreme Court. See § 2254(d)(1).
3. Application of AEDPA deference to the merits
At Woodfox’s 1973 trial, Hezekiah Brown testified in response to questioning from the State that he had not been promised any incentives in return for his testimony, other than protection from other inmates.10 During his 1973 cross-examination, Brown denied making certain state*798ments to defense counsel and indicated that defense counsel was the only person to have made any promises to help Brown.11 Brown’s direct and cross-examination were read to the jury in 1998. As part of his defense, Woodfox called Warden Henderson, who testified about interviewing Brown a few days after the murder. When Brown incriminated Woodfox at this interview, he had been moved to the “dog pen,” a minimum security area used to house the prison’s hunting dogs and to also house trustees and inmates under protection. Henderson testified that he promised to “protect” Brown and that he “later” promised to support Brown’s pardon application, although Henderson could not recall when he made that promise. When asked about Brown’s testimony in 1973 that nothing had been promised to him, Henderson said, “Well nothing was promised to him to begin with, but we told him, you know, we would protect him and try to help him any way we could after he, you know, cracked the case for us.” Id. at 1964 (emphasis added). When asked whether promises were made “before [Brown] testified,” Henderson said, “That’s right.” Defense counsel also had Henderson identify letters that were later written on Brown’s behalf in support of a pardon application.12
The foregoing testimony, although equivocal as to what promises were made *799to Brown, is the basis upon which the district court held that the admission of Brown’s 1973 testimony violated the Confrontation Clause because Brown could not be questioned about the Warden’s promise, and that the failure of Woodfox’s 1998 trial counsel to raise an objection was deficient performance. We disagree with the district court.
In order to find that the state court’s denial of relief was contrary to clearly established federal law, we must conclude that a potential Brady/Giglio violation in 1973 that suppressed information contradicting Brown’s testimony rendered that testimony inadmissible at the second trial, and that Woodfox’s 1998 counsel was objectively unreasonable for failing to raise a confrontation objection even though the jury was aware of the impeaching information at the second trial. Although the merits of Woodfox’s claim thus concern the intersection of Brady/Giglio with Confrontation Clause jurisprudence, the overarching legal principle is the familiar ineffective assistance standard of Strickland. Under that standard, the petitioner bears the burden to show that counsel’s performance fell below an objective standard of reasonableness and that the deficiency prejudiced the defense. See Strickland, 466 U.S. at 687-88, 104 S.Ct. 2052. Our review of counsel’s performance is highly deferential, and counsel’s conduct is presumed to fall within a wide range of reasonable professional assistance. Id. at 689, 104 S.Ct. 2052; Soffar v. Dretke, 368 F.3d 441, 471 (5th Cir.2004). The petitioner must show that counsel “made errors so serious that he was not functioning as the ‘counsel’ guaranteed to the defendant under the Sixth Amendment.” Strickland, 466 U.S. at 687, 104 S.Ct. 2052. To establish prejudice, the petitioner must show a reasonable probability that, but for counsel’s deficient performance, the result of the proceedings would have been different. Id. at 694, 104 S.Ct. 2052. “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Id. A failure to establish either deficient performance or prejudice defeats the claim. Id. at 697, 104 S.Ct. 2052.
The performance of Woodfox’s 1998 trial counsel hinges on the objective reasonableness of counsel’s failure to raise a confrontation-based objection to Brown’s 1973 testimony. This requires examination of the controlling law for confrontation-based claims. The Supreme Court’s Confrontation Clause jurisprudence was changed significantly when the Court decided in Crawford v. Washington, 541 U.S. 36, 53-55, 124 S.Ct. 1354, 158 L.Ed.2d 177 (2004), that testimonial statements from an unavailable witness may not be introduced at trial without a prior opportunity for cross-examination, irrespective of any exceptions for hearsay. Crawford is not relevant to our consideration, however, because it was decided after Woodfox’s 1998 trial and it does not apply retroactively. See Whorton v. Bockting, 549 U.S. 406, 409, 127 S.Ct. 1173, 167 L.Ed.2d 1 (2007). Instead, defense counsel’s performance must be judged based on the law that was in existence at the time of the trial. See Paredes v. Quarterman, 574 F.3d 281, 287 (5th Cir.2009). At the time of Woodfox’s 1998 trial the admission of Brown’s testimony was governed by the Supreme Court’s decision in Ohio v. Roberts, 448 U.S. 56, 100 S.Ct. 2531, 65 L.Ed.2d 597 (1980).
The Confrontation Clause of the Sixth Amendment guarantees a criminal defendant the right “to be confronted with the witnesses against him.” U.S. Const. amend. VI. In Roberts, the Supreme Court held that the admission of a hearsay statement will not violate the Confrontation Clause if the witness is unavailable and the statement “bears ‘adequate indicia of reliability.’ ” 448 U.S. at 66, 100 S.Ct. *8002531; United States v. Avants, 367 F.3d 433, 445 (5th Cir.2004). This indicia of reliability is present if the statement “falls within a firmly rooted hearsay exception” or if it is shown to possess “particularized guarantees of trustworthiness.” Roberts, 448 U.S. at 66, 100 S.Ct. 2531. There is no question but that sworn testimony, such as Brown’s, given at a prior hearing where the defendant had an opportunity to cross-examine the now-unavailable witness, ordinarily meets the Roberts test for admission under a firmly rooted exception to hearsay. See id. at 68, 100 S.Ct. 2531 (noting “the established rule that prior trial testimony is admissible upon retrial if the declarant becomes unavailable”); see also Fed.R.Evid. 804(b)(1); La.Code Evid. Ann. art. 804(B)(1).
Woodfox, of course, not only had an opportunity to cross-examine Brown in 1973 but he did so, questioning Brown at length about Brown’s version of the events and testing his memory about what he saw.13 It is well-established that “previously cross-examined prior trial testimony ... has [been] deemed generally immune from subsequent confrontation attack.” Roberts, 448 U.S. at 72-73, 100 S.Ct. 2531; see also Mancusi v. Stubbs, 408 U.S. 204, 213, 92 S.Ct. 2308, 33 L.Ed.2d 293 (1972) (“At least since the decision of this Court in Mattox v. United States, 156 U.S. 237, 15 S.Ct. 337, 39 L.Ed. 409 (1895), prior-recorded testimony has been admissible in appropriate cases.”).
The crux of Woodfox’s claim is that the suppression of Warden Henderson’s promises to Brown denied him the opportunity for cross-examination. When asked at oral argument for authority in support of a holding that the possibility Brown lied in 1973 means that his prior testimony could not be used at all in the second trial after Brown was dead, Woodfox’s counsel conceded that he had no authority directly on point and relied on the general principles of cases like Roberts. We must uphold the state court’s decision denying Woodfox’s claim unless it is contrary to federal law as articulated in the clear holdings of the Supreme Court. See Thaler v. Haynes, — U.S. ——, 130 S.Ct. 1171, 1173, — L.Ed.2d-(2010) (“A legal principle is ‘clearly established’ within the meaning of [§ 2254(d)(1)] only when it is embodied in a holding of this court.”); Williams v. Taylor, 529 U.S. 362, 412, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000) (“[A]s the statutory language makes clear ... § 2254(d)(1) restricts the source of clearly established law to this Court’s jurisprudence.”); Moore v. Cockrell, 313 F.3d 880, 881 (5th Cir.2002) (“Clearly established federal law refers to the holdings, as opposed to the dicta, of [the Supreme] Court’s decisions as of the time of the relevant state-court decision.”) (internal quotation and citation omitted). We find no clear answers in the Supreme Court’s jurisprudence, however.14
*801The Court has suggested that while generally immune from an attack at a subsequent trial, prior recorded testimony might be challenged as inadmissible if counsel was prevented or limited in engaging in meaningful cross-examination. See Roberts, 448 U.S. at 71, 100 S.Ct. 2531 (noting that counsel there had not been “ ‘significantly limited in any way in the scope or nature of his cross-examination’ ”) (citation omitted); see also Magouirk v. Warden, 237 F.3d 549, 553-54 (5th Cir. 2001) (holding that admission of prior recorded testimony violated the Confrontation Clause because defendant “was unable to conduct any cross-examination” due to trial court’s erroneous sustaining of prosecution objections). Yet, the Court has also suggested that not all limited cross-examination violates the Confrontation Clause. See Delaware v. Fensterer, 474 U.S. 15, 20, 106 S.Ct. 292, 88 L.Ed.2d 15 (1985) (emphasizing that while the Confrontation Clause guarantees an opportunity for cross-examination, it does not guarantee “cross-examination that is effective in whatever way, and to whatever extent, the defense might wish”).
Woodfox contends that the Confrontation Clause afforded counsel a firm basis to object in this case because defense counsel lacked an opportunity for cross-examination on the critical matter of Brown’s credibility in light of the alleged promises from the Warden. But any deficiency in the 1973 cross-examination was due to the State’s alleged Brady violation in suppressing information. We have found no Supreme Court authority for the proposition that a Brady violation impacting a defendant’s prior cross-examination of a witness, in which- counsel otherwise took full advantage in questioning, renders that prior testimony per se inadmissible at a subsequent trial. Therefore, we cannot conclude that the state court’s denial of relief on such a basis is unreasonable. “[I]t is not an unreasonable application of clearly established Federal law for a state court to decline to apply a specific legal rule that has not been squarely established by th[e Supreme] Court.” Knowles v. Mirzayance, — U.S. —, 129 S.Ct. 1411, 1419, 173 L.Ed.2d 251 (2009) (internal quotation marks and citations omitted).
In the absence of a specific rule from the Court governing the situation at hand, we must ask whether it was nevertheless deficient performance under the broader Strickland standard for counsel not to have pressed the objection. But “because the Strickland standard is a general standard, a state court has even more latitude to reasonably determine that a defendant has not satisfied that standard.” Id. at 1420. This court’s review is therefore “doubly deferential” to the state court adjudication. Id.; see also Wooten v. Thaler, 598 F.3d 215, 222 (5th Cir.2010).
Under this deferential review, we cannot fault the state court for denying relief. In hindsight, it may be easy to say defense counsel could have argued that the State’s suppression of Warden Henderson’s promise to Brown denied Woodfox an opportunity to adequately cross-examine Brown in 1973. But we must eliminate the distorting effects of hindsight, see Strickland, 466 U.S. at 689, 104 S.Ct. 2052, and keep in *802mind both counsel’s perspective at the time and the alleged precipitating Brady violation. In 1998, the Supreme Court had already said that previously recorded trial testimony was virtually unchallengeable. See Roberts, 448 U.S. at 72-73, 100 S.Ct. 2531; Mancusi, 408 U.S. at 213, 92 S.Ct. 2308. Moreover, the remedy for a Brady violation typically is a new trial at which the previously excluded evidence is admitted. See Monroe v. Blackburn, 748 F.2d 958, 960 (5th Cir.1984) (noting that the new trial remedy for a Brady violation occurs because the defendant’s right to a fair trial has been prejudiced by the suppression of evidence); United States v. Beasley, 576 F.2d 626, 630 (5th Cir.1978) (a violation of the constitutional standard of fairness under Brady requires a new trial if after conviction it is learned that suppressed evidence creates a reasonable doubt as to guilt that did not previously exist); see also United States v. Davis, 578 F.2d 277, 280 (10th Cir.1978) (assuming a Brady violation occurred “the most an invocation of Brady could accomplish would be the ordering of a new trial in which the withheld information is fully disclosed”); United States v. Coleman, 862 F.2d 455, 458-59 (3d Cir.1988) (“The awarding of a new trial to remedy a Brady violation insures that the defendant will be able to make full use of the exculpatory evidence during the subsequent proceeding.”).
In the instant case, the 1998 jury knew about Warden Henderson’s discussions with Brown. Counsel took advantage of that information at the second trial by closely questioning Henderson about the circumstances of Brown’s testimony. Counsel also introduced documentary evidence showing that Warden Henderson attempted to make good on his promise of assistance to Brown by writing various letters in support of Brown’s pardon application, by authorizing the prison to pay for Brown’s pardon notice, and by providing Brown periodically with cigarettes while Brown was incarcerated. In short, the impeachment evidence that Woodfox contends was suppressed in 1973 was presented along with other documentary impeachment evidence to the 1998 jury. Woodfox may not have been able to ask Brown about the promise in 1998, but after reviewing the trial transcript we are convinced that the jury knew Brown allegedly had an incentive to lie, and it is not unreasonable to conclude that defense counsel did not render constitutionally deficient performance by failing to pursue a confrontation objection.
Up to this point, we have assumed for the sake of the discussion that the Warden’s testimony was impeachment evidence under Brady and that the State suppressed the Warden’s purported promise to Brown. Although we see no evidence in the record that the State knew at the time of the 1973 trial about any inducements made by prison officials to Brown, the State’s subjective intent is not determinative. See Brady, 373 U.S. at 87, 83 S.Ct. 1194 (due process is violated by suppression of material evidence irrespective of the good faith or bad faith of the prosecution). Nevertheless, we also pause to note that it is not clear from our review of the record that there was a Brady violation.15 First, Warden Henderson’s testimony was equivocal. He testified that nothing was *803promised to Brown initially, other than protection, and that Brown was not told the Warden would assist with the pardon application until Brown “cracked the case.” This is consistent with Brown’s testimony that nothing was promised to him. The Warden did agree with defense counsel that promises were made before Brown testified, but this testimony, which was also elicited by defense counsel, was internally inconsistent. Warden Henderson further specifically testified that he did not consider his discussions with Brown “sinister” and that no one ever suggested to Brown that he identify Woodfox as being involved in the murder.
Moreover, even assuming that Henderson’s testimony could impeach Brown, this court has previously recognized that there can be no viable Brady claim when allegedly suppressed evidence was available to the defendant through his own efforts. Rector v. Johnson, 120 F.3d 551, 558 (5th Cir.1997) (holding that to state valid Brady claim habeas petitioner must demonstrate inter alia that “discovery of the allegedly favorable evidence was not the result of a lack of due diligence”); United States v. Marrero, 904 F.2d 251, 261 (5th Cir.1990) (finding no Brady claim where defendant could have discovered exculpatory information by interviewing witnesses). Woodfox called Warden Henderson at the 1998 trial to testify about his interaction with Brown after the murder. If Warden Henderson was willing to testify in 1998, it is not clear why Woodfox could not have also presented the same testimony at the 1973 trial.
In sum, the issue of counsel’s ineffectiveness for failing to object on confrontation grounds in 1998 to the admission of Brown’s 1973 testimony was not raised in Woodfox’s state habeas application in a manner that gave the state court a fair opportunity to rule on it. We do not liberally construe pleadings prepared by counsel, and we hold the issue is unexhausted and not properly before us. In the alternative, assuming that the issue was properly presented in state court, we conclude that the state court’s decision was an adjudication of the merits requiring AEDPA deference. Under that deferential standard, there is no basis in clearly established Supreme Court holdings for the conclusion that an unavailable witness’s prior recorded testimony is inadmissible under the Confrontation Clause because a post-trial revelation of Brady/Giglio impeachment evidence shows that the witness may have lied, and defense counsel was ineffective for not objecting on that ground even though the impeachment evidence was before the second jury. We therefore cannot find that the denial of habeas relief on Woodfox’s claim was unreasonable or contrary to federal law. This is so even if we were to conclude from our own independent analysis that the denial was erroneous. See Williams, 529 U.S. at 412, 120 S.Ct. 1495 (“[A]n unreasonable application of federal law is different from an incorrect or erroneous application of federal law.”) (emphasis in original). For this reason, we are compelled by the deferential standard under the AEDPA to conclude that Wood-fox’s ineffective assistance claim must fail and the district court’s judgment must be reversed.
A Due process
In its discussion of counsel’s ineffectiveness relating to Brown’s testimony, the district court held that counsel was deficient for failing to challenge the indictment “on Confrontation Clause and Due Process grounds.” The court reasoned that counsel should have sought to quash the indictment because, with the passage of time since the 1973 trial, physical evidence had been lost and several witnesses had died. *804The court noted that Woodfox’s counsel failed to object that the bloodstained clothing could not be located for testing or that counsel would be unable to cross-examine not only Brown but also Paul Fobb and state criminologist Carl Cobb, whose prior recorded testimony was also presented at the 1998 trial. Woodfox also urges in his appellate brief that counsel rendered deficient performance for failing to move to quash the indictment. We disagree.
Although the Due Process Clause limits the time after an offense within which the State may indict the accused, the defendant must meet a two pronged test to show a due process violation. See Avants, 367 F.3d at 441. The defendant must show that pre-indictment delay “ ‘was intentionally brought about by the government for the purpose of gaining some tactical advantage over the accused in the contemplated prosecution or for some other bad faith purpose’; and ‘the improper delay caused actual, substantial prejudice to his defense.’ ” Id. (quoting United States v. Crouch, 84 F.3d 1497, 1523 (5th Cir.1996) (en banc)). Here, there is no indication in the record, nor is there any claim by Woodfox, that prosecutorial misconduct caused the delay in Woodfox’s second indictment. Indeed, Woodfox’s conviction on the original 1972 indictment was set aside by the state courts in 1992, and the State wasted little time in re-indicting him in 1993. There was therefore no basis for a due process objection to the indictment.
Furthermore, with respect to the lost clothing, defense counsel did file a motion to compel its production and also argued to the trial court a motion to quash the indictment based on the absence of the physical evidence. We do not see what more counsel could have done and find no deficient performance concerning the clothing. As for the testimony of Fobb and Cobb, both witnesses testified under oath at the first trial and were subject to unfettered cross-examination. Their testimony was therefore admissible. See Roberts, 448 U.S. at 72-73, 100 S.Ct. 2531. We conclude that counsel was not deficient for failing to seek to quash the indictment on the grounds identified by the district court.
B. Failure to object to testimony from former prosecutor
The district court also granted Woodfox habeas relief due to counsel’s failure to object to the testimony of former prosecutor John Sinquefield, who prosecuted Woodfox in the 1973 trial. Sinquefield testified at the second trial immediately after the State read Brown’s 1973 testimony into the record. The State called him purportedly to explain certain gestures Brown had made during his testimony at the first trial. Defense counsel objected to the State’s attempt to bolster Brown’s testimony with Sinquefield. The court overruled the objection but gave a limiting instruction that the jury was to be the sole evaluator of witness credibility. During the course of questioning, Sinquefield volunteered the following about Brown:
Hezekiah Brown testified in a good, strong voice, he was very open, he was very spontaneous, he answered questions quickly, and he was very fact specific. He didn’t have to hesitate and think about his answers, but if you got something wrong, he would stop you, even to the extent in one part of his testimony, I think he — he stopped and corrected me that he said, now, you know, wait, this wasn’t Woodfox just by hisself, there were others involved. He would even stop you if you tried to put more on Mr. Woodfox than he thought Mr. Woodfox did. He was very open, very quick. He testified, he didn’t hesitate, he testified very clearly and I was *805proud of the way he testified. I thought it took a lot of courage.
Although defense counsel had objected earlier, he did not specifically object to the foregoing testimony.
On direct appeal of his conviction, Wood-fox argued that Sinquefield’s testimony was improper. The Louisiana First Circuit Court of Appeal was troubled that Sinquefield was allowed to give his opinions about Brown. The court found no reversible error, however, because the testimony had been unresponsive to the prosecutor’s questions and Woodfox did not specifically object to that portion of it. The court further held, however, that even if Woodfox’s prior objection to Sinquefield’s testimony adequately preserved the issue, any overzealousness on the part of Sinquefield did not rise to reversible error given the trial court’s limiting instruction.
Woodfox naturally raised in his state habeas application and in his § 2254 petition the claim that trial counsel was ineffective for failing to object to Sinquefield’s testimony. The state habeas court, through adoption of the State’s answer, held inter alia that Woodfox failed to allege any actual prejudice.
Woodfox maintains in this appeal that defense counsel was ineffective for not objecting to the testimony. Like the state appellate court, we too are troubled by that aspect of Sinquefield’s testimony wherein he exclaimed how “proud” he was of Hezekiah Brown and that Brown’s testimony “took courage.” This is the kind of testimony ordinarily found to be improper. See United States v. Corona, 551 F.2d 1386, 1389 (5th Cir.1977) (reversing conviction on direct appeal where, among many other improper comments to the jury, prosecutor stated that he was “kind of proud” of the witness). A prosecutor’s vouching for the credibility of witnesses improperly suggests to the jury (1) that evidence not presented at trial but known to the prosecutor supports the charges against the defendant so that the conviction is not based only on evidence presented to the jury, and (2) that the prosecutor’s opinion, which carries an imprimatur of the State, should be trusted over the jury’s own view of the evidence. United States v. Young, 470 U.S. 1, 18-19, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985).
Nevertheless, we do not find that the state court’s denial of relief on this claim was unreasonable or contrary to clearly established federal law. As noted above, the state appellate court on direct appeal held that even if the issue was preserved, reversal was not warranted because of the trial court’s limiting instruction. If there was no reversible error, there could be no ineffective assistance claim because defense counsel’s failure to object could not have caused prejudice.
The state appellate court’s analysis was not unreasonable. A prosecutor’s improper comments may be subject to harmless error analysis. See Young, 470 U.S. at 12, 105 S.Ct. 1038 (prosecutor’s comments “must be examined within the context of the trial to determine whether the prosecutor’s behavior amounted to prejudicial error”); United States v. Carey, 589 F.3d 187, 193 n. 4 (5th Cir.2009) (reviewing claim of improper vouching by prosecutor for plain error but noting that error was also harmless); Hughes v. Quarterman, 530 F.3d 336, 347 (5th Cir.2008) (holding that a curative instruction may reduce risk of prejudice to defendant from prosecutor’s improper remark). Here, Sinquefield’s testimony was volunteered and was relatively isolated in the context of the trial as a whole. The trial court also gave a limiting instruction. See Richardson v. Marsh, 481 U.S. 200, 211, 107 S.Ct. 1702, 95 L.Ed.2d 176 (1987) (“[JJuries are *806presumed to follow their instructions.”). Improper prosecutorial remarks are constitutionally unfair only if they are persistent and pronounced, or if the evidence is so weak that no conviction would have occurred but for the remarks. Hughes, 530 F.3d at 347. Sinquefield’s comments were not pervasive, and the jury had sufficient evidence from which to disbelieve Brown if it so chose. The jury resolved the credibility determination against Woodfox, and we do not believe the comment from Sinquefield likely tipped the balance.
Moreover, defense counsel did attempt to object to improper bolstering by Sinquefield at the commencement of the testimony. Although the state appellate court held the objection insufficient to preserve error, it is apparent that counsel was not simply sitting idly by during the testimony, and we are not convinced the jury would not have convicted Woodfox but for counsel’s failure to object a second time. Therefore, Woodfox has not shown that but for counsel’s alleged error the results of the proceeding would have been different.
We stress again that the issue before us is not whether we would have ruled differently, or even whether Woodfox has made the necessary showing under Strickland; rather, the issue is whether the state court’s decision that Woodfox has not made that showing was unreasonable. See Gonzales v. Quarterman, 458 F.3d 384, 390 (5th Cir.2006) (citing Busby v. Dretke, 359 F.3d 708, 717 (5th Cir.2004)). We conclude that the state court’s decision that there was no reversible error from Sinquefield’s testimony was not an unreasonable application of clearly established federal law, which in turn means it was not an unreasonable application of clearly established federal law for the state court to find no prejudice from defense counsel’s failure to object. We therefore reverse the district court’s grant of habeas relief for this claim.
C. Failure to investigate
The district court granted Woodfox habeas relief on three claims related to defense counsel’s failure to investigate prior to the 1998 trial. These claims involved the bloodstained clothes that Sheriff Daniel seized from Woodfox in 1972, the bloody print found at the scene of the murder, and evidence of witness Paul Fobb’s blindness.
“[C]ounsel has a duty to make reasonable investigations or to make a reasonable decision that makes particular investigations unnecessary.” Strickland, 466 U.S. at 691, 104 S.Ct. 2052. Any decision by counsel not to investigate is assessed for reasonableness under all the circumstances, with a heavy measure of deference to counsel’s judgment. Id. “In assessing counsel’s investigation, we must conduct an objective review of their performance, measured for reasonableness under prevailing professional norms, which includes a context-dependent consideration of the challenged conduct as seen from counsel’s perspective at the time.” Wiggins v. Smith, 539 U.S. 510, 523, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (internal quotation marks and citations omitted). The reasonableness of an investigation involves “not only the quantum of evidence already known to counsel, but also whether the known evidence would lead a reasonable attorney to investigate further.” Id. at 527, 123 S.Ct. 2527. Bearing these principles in mind, we consider each of Wood-fox’s claims in turn.
1. Bloodstained clothing
The State presented testimony from Carl Cobb, a supervisor at the State Police Crime Lab, who testified at Woodfox’s *8071973 trial about blood stains on the clothing that Sheriff Daniel seized from Wood-fox. According to Cobb, stains on the three items of clothing were all found to be blood, but the sample size on two items (the pants and shoe) were too small to determine whether the blood was human or animal. The third item (a jacket) was found to contain human blood, but again the sample was too small to determine anything else. Cobb testified that the presence of blood was determined by use of a benzidine test, while the origin of the blood (human or animal) was tested with a pricipitin test. Because Cobb had died by the time of the second trial in 1998, the State read Cobb’s testimony into the record. In 1973, defense counsel stipulated to Cobb’s qualifications as an expert and conducted little cross-examination.
The district court faulted the 1973 defense counsel for failing to ask Cobb about the testing methodologies and procedures, the experience and competency of the state crime lab personnel, or the chain of custody of the clothing. The district court held that in light of these problems with the 1973 eross-examination, trial counsel in 1998 should have objected to the introduction of the testimony or obtained his own expert evidence to counter Cobb’s opinions.
We do not find counsel ineffective for failing to object to the introduction of Cobb’s prior recorded testimony. Cobb was under oath at the 1973 trial and defense counsel had ample and unrestricted opportunity to cross-examine him. Because he was dead and unavailable in 1998, the testimony was admissible. See Roberts, 448 U.S. at 68, 100 S.Ct. 2531. The district court suggested Woodfox could have obtained expert evidence to show that Cobb’s opinions were inadmissible as scientifically unreliable. See, e.g., State v. Foret, 628 So.2d 1116, 1121-22 (La.1993) (discussing requirements for admission of expert scientific testimony); see also Daubert v. Merrell Dow Pharms., Inc., 509 U.S. 579, 113 S.Ct. 2786, 125 L.Ed.2d 469 (1993). But Woodfox stipulated at the 1973 trial to the expert’s qualifications. Perhaps the 1973 counsel was ineffective for doing so, but that is not a claim properly before us in this case. Further, Wood-fox cites no authority, let alone clearly established authority from the Supreme Court, that prior trial testimony from an expert, whose qualifications were stipulated to by the defendant, is rendered inadmissible because a contemporary expert at a second trial may disagree with the first expert’s methods or conclusions. Viewing the matter from counsel’s perspective in 1998, the prior recorded testimony of the now-unavailable witness was admissible. Counsel also knew that the testimony was at best inconclusive because the purported blood on the clothing was not matched to the victim, Woodfox, or anyone else. We perceive no constitutional deficiency in failing to object to the admission of Cobb’s testimony under these circumstances. Of course, counsel could still have attacked Cobb’s conclusions with his own expert witnesses at the second trial, which we consider next.
Woodfox maintains in this appeal, consistent with the district court’s opinion, that counsel was ineffective for failing to obtain his own experts to discredit Cobb by showing that the testing procedures used in 1973, specifically the benzidine and precipitin tests, were inadequate or scientifically invalid for determining the presence of blood on the clothing. Woodfox points to two expert witnesses from whom he obtained declarations in 2002 during the post-conviction state habeas proceedings that demonstrated purported deficiencies in Cobb’s testimony and testing methodology. The district court also relied in large *808part on the existence of these experts’ declarations for its finding that 1998 counsel rendered ineffective assistance.
At bottom, Woodfox’s claim is one of uncalled witnesses. Claims that counsel failed to call witnesses are not favored on federal habeas review because the presentation of witnesses is generally a matter of trial strategy and speculation about what witnesses would have said on the stand is too uncertain. See Alexander v. McCotter, 775 F.2d 595, 602 (5th Cir.1985). For this reason, we require petitioners making claims of ineffective assistance based on counsel’s failure to call a witness to demonstrate prejudice by “nam[ing] the witness, demonstrating] that the witness was available to testify and would have done so, set[ting] out the content of the witness’s proposed testimony, and showing] that the testimony would have been favorable to a particular defense.” Day v. Quarterman, 566 F.3d 527, 538 (5th Cir.2009). This requirement applies to both uncalled lay and expert witnesses. Id.
Woodfox presented the declarations from the expert witnesses to cast doubt on the State Police Crime Lab’s 1973 findings by criticizing the benzidine and precipitin tests and explaining how advanced testing procedures, such as DNA testing, should have been performed in 1998. Although the experts declared as part of the state habeas proceeding that if called to testify they could testify competently to the matters contained within the declarations, they did not state that the experts were available to testify at trial in 1998 and would have done so, or that they would have testified to the same extent as their opinions presented in the declarations. See id. This is not a matter of formalism. In Day, we addressed very similar circumstances. The petitioner there presented an expert affidavit in post-conviction proceedings rebutting the opinions of the State’s experts, but he failed to show the expert was available to testify at trial and would have done so. We stressed that the petitioner’s claim of uncalled expert witnesses was therefore subject to “the exact problem of speculation that the Fifth Circuit seeks to avoid by requiring the prejudice showing set forth [above].” Id. In other words, we have no evidence beyond speculation that in 1998 defense counsel could have found and presented an expert witness who would have testified as he claimed in his post-conviction applications. See id.
Moreover, we find that Wood-fox’s claim fails for other reasons. First, “[t]he scope of a defense counsel’s pretrial investigation necessarily follows from the decision as to what the theory of defense will be.” Soffar, 368 F.3d at 443. Here, the theory of the defense was that the clothing seized by Sheriff Daniel and tested by the State did not belong to Woodfox, who consistently denied that the clothes were his and so testified at trial. Although counsel could have sought experts to challenge Cobb’s scientific testimony about the blood, we do not find that failure to do so was unreasonable in light of Woodfox’s adamant insistence that he wore other clothes.16
*809Second, we do not find Cobb’s testimony so crucial to the State’s case that defense counsel’s failure to obtain a blood expert caused Woodfox prejudice in the Strickland sense. The sample sizes on the three items of clothing were so small that Cobb could not determine conclusively whether the purported blood was even human on two of them. The testimony at trial was that the crime scene was very bloody, and counsel was able to reasonably argue that with all of the blood at the scene the jury should have expected to see bloody items positively traceable to the killer but that there were no such items. Woodfox also worked in the prison kitchen, which provided still another reasonable explanation for the presence of blood or other substances on the clothing. In short, the absence of a rebuttal blood expert did not affect other avenues for mitigating the physical evidence.
Furthermore, with respect to the finding that blood on the jacket seized from Wood-fox was human, Cobb indicated that this result was obtained from the precipitin test. One of Woodfox’s experts agreed that a precipitin test can be used to determine whether blood is human or animal, but he averred that the test can be unreliable and a false positive could result if it were not performed properly. The expert opined that further detail should have been included in the State’s lab reports in order to determine how the test was conducted and that additional confirmatory testing should have been done in 1998. But the expert did not opine that there was any indication that the State had performed the test incorrectly, and of course further testing could not be conducted because the clothing was no longer available. The expert opinion was therefore speculative. Cf. Greiman v. Thalacker, 181 F.3d 970, 974 (8th Cir.1999) (petitioner failed to show ineffective assistance for failing to object to State’s expert rebuttal witness where a reasonable jury would have accepted conclusions of State’s experts over the speculative opinions of the defendant’s experts).
Finally, there was still evidence from other witnesses placing Woodfox at the scene and identifying him as the killer. In order to establish prejudice, Woodfox was required to show more than a mere possibility that counsel’s errors could have affected the outcome of the trial. See United States v. Drones, 218 F.3d 496, 501 (5th Cir.2000). He was required to establish a reasonable probability. We cannot conclude from all the circumstances that there is a reasonable probability that but for counsel’s failure to call a blood expert to rebut Cobb’s testimony, the jury would not have convicted Woodfox.17
2. Bloody print
In 1973, the State presented at the first trial testimony from Steven Leddell, who *810was employed by the Louisiana State Police and who participated in the investigation after the murder. Leddell testified that he examined the crime scene and located a bloody fingerprint on the door to the Pine 1 dorm, which he photographed. Leddell explained' that although the print was identifiable, it did not match the fingerprints on file for either Woodfox or any of the other defendants charged in the case. Relying on the exculpatory nature of this prior testimony, defense counsel at the second trial in 1998 argued in his opening statement to the jury that, although a bloody fingerprint was found at the scene, there would be no evidence at trial linking that fingerprint to Woodfox.
The State then presented testimony from Carol Richard, a State Police fingerprint examiner, who testified for the first time that she thought the print, previously long believed to be a fingerprint, was actually a palm print. The exculpatory nature of the print would be affected if it was from a palm instead of a finger because Richard testified that no comparisons had been made between anyone’s palm prints and the print found at the scene. Therefore Woodfox would no longer be positively excluded as the source of the print.
Defense counsel objected to Richard’s testimony on the basis of undue surprise because all along the State had represented the print was from a finger. The trial court overruled the objection. The court held that rather than simply rely on the expert opinion from 1973, Woodfox could have obtained his own expert to independently examine the print and either confirm or refute the State’s experts. Wood-fox subsequently presented as part of his defense the prior testimony of Leddell, who, like so many other witnesses, was no longer available for the second trial.
The district court here held that defense counsel rendered ineffective assistance for failing to investigate and obtain a fingerprint expert. The court noted that the state trial court had even discussed the fact that funds were available for the court to appoint an expert. The district court reasoned that if defense counsel had consulted his own expert rather than rely on the 1973 testimony of Leddell, counsel could have known before trial whether the print was from a finger or palm and been prepared to refute Richard’s testimony. The district court also noted that Woodfox presented in both his state habeas application and his § 2254 petition a declaration from a fingerprint expert, who disagreed with Richard and opined that the print was from a finger, specifically a thumb, rather than a palm. Assuming the print was from a palm, however, the expert also compared the print to Woodfox’s palm prints and concluded there was no match.
We disagree with the district court’s finding of ineffective assistance. First, as with his claims respecting the failure to call experts to evaluate the testing of the bloody clothes, Woodfox has not shown that his fingerprint expert was available to testify at the 1998 trial. The claim of failing to present an expert witness is therefore unavailing. See Day, 566 F.3d at 538.
Second, after eliminating the distorting effects of hindsight, we find no deficiency in counsel’s performance. Counsel knew in 1998 that the 1973 expert had given sworn testimony that the bloody print was a fingerprint and that it matched neither Woodfox nor anyone else charged in the case. Counsel could have obtained an expert to confirm that opinion, but had he done so counsel also risked potentially uncovering damaging information depending on what the retained expert found. Counsel was thus faced with a dilemma: he could do nothing in the face of evidence that did not inculpate Woodfox and in fact *811exculpated him, or he could retain an expert who possibly might disagree with the prior sworn testimony. “Counsel’s decision not to pursue evidence that could be ‘double-edged in nature [was] objectively reasonable and therefore does not amount to deficient performance.’ ” Drones, 218 F.3d at 501 (quoting Lamb v. Johnson, 179 F.3d 352, 358 (5th Cir.1999)) (other citations omitted).
It is axiomatic that the State bears the burden of proof in any criminal case, and a defendant need prove nothing. See United States v. Manetta, 551 F.2d 1352, 1357 (5th Cir.1977). Unless there was some reason for counsel to reasonably doubt that the bloody print was a fingerprint, which is not apparent from the record, we see no deficiency in counsel’s decision to hold the State to its burden and to rely on the prior sworn testimony that in no way inculpated Woodfox.
In support of its decision that counsel rendered deficient performance by failing to obtain an expert, the district court relied largely on the Sixth Circuit’s decision in Richey v. Bradshaw, 498 F.3d 344 (6th Cir.2007). The court there held that counsel for a defendant convicted of arson rendered ineffective assistance because he did not conduct a reasonable investigation or adequately consult experts to test the State’s scientific evidence that a fire was caused by the use of accelerants. We find Richey and other similar cases cited in the district court’s opinion inapposite because they concerned expert opinions from government witnesses that inculpate the defendant. But here the State’s previously presented expert provided testimony that tended to exonerate Woodfox. Counsel’s duty is to reasonably investigate or make a reasonable decision that no further investigation is necessary. See Strickland, 466 U.S. at 691, 104 S.Ct. 2052. Given the information known to counsel at the time, we see no reason for counsel to have believed further investigation of the bloody print was necessary. See Wiggins, 539 U.S. at 527, 123 S.Ct. 2527.
Finally, we also conclude that the absence of a fingerprint expert did not cause Woodfox prejudice that warrants habeas relief. The district court held that a fingerprint expert could have provided support for the theory that the print was a fingerprint, and not a palm print, so that the print retained some exculpatory value. But although the print-as-a-palm-print theory may have reduced the print’s exculpatory nature, it did not eliminate it altogether. Counsel argued to the jury in his opening statement that there was no bloody print evidence linking Woodfox to the crime scene. That remained true even if the print was a palm print because no match was made to Woodfox. Even after Richard’s testimony the jury was left to wonder why the print was not tested against Woodfox’s prints. Richard testified that palm prints were not routinely included on a prisoner’s fingerprint card at Angola, and that the print was not sufficiently detailed to run it through the State’s automated fingerprint database, which went online in 1988. However, defense counsel elicited testimony from Richard that the print was identifiable and could be compared manually with other prints. Thus, even accepting Richard’s testimony that the print came from a palm, it did not inculpate Woodfox, and it likely would have caused the jury to wonder why the State did not manually compare it with Woodfox’s prints. Furthermore, defense counsel presented the prior testimony of Leddell as part of the defense case, which contradicted Richard’s testimony. Although Richard testified about the improvement and evolution of fingerprint examination since the first trial in 1973, the *812jury was still presented with two State witnesses who gave contrary opinions.
We conclude from the totality of the circumstances that the state court’s denial of habeas relief on the claim that counsel should have retained a fingerprint expert was not an unreasonable application of clearly established federal law.
3. Paul Fobb’s blindness
Finally, the district court also found defense counsel ineffective in 1998 for failing to investigate evidence to discredit inmate Paul Fobb, who testified in 1973 that he saw Woodfox enter the Pine 1 dormitory and then throw a rag into the Pine 4 dorm. Fobb’s testimony from the first trial was read into the record because he, too, was dead by the time of the second trial. The district court reasoned that defense counsel in 1998 should have presented Fobb’s medical records and/or consulted with experts about the records in order to demonstrate that Fobb’s severe visual impairments rendered it unlikely for him to have seen what he claimed. The court also found that counsel rendered deficient performance by failing to make further efforts to locate another inmate, Clarence Franklin, who had testified at the first trial that Fobb did not see well and would stumble over things. Because the State refused to stipulate that Franklin was unavailable in 1998, the trial court refused to allow defense counsel to read Franklin’s prior testimony into the record.
We conclude that Woodfox failed to demonstrate that counsel was ineffective for failing to pursue further evidence of Fobb’s vision problems because the jury was well-aware of Fobb’s limited eyesight from other evidence. During Fobb’s direct examination by the State, Fobb himself conceded that he had no vision in his right eye and had severe glaucoma in his left eye. Although Fobb claimed that he could see well enough at the time of the murder in April 1972, defense counsel extensively cross-examined Fobb about his vision. Counsel established that Fobb had been completely blind in his right eye since 1967. Counsel also elicited testimony from Sheriff Daniel that Fobb was considered to be legally blind. Joseph Richey also testified on direct examination that Fobb was going blind. Counsel further asked Warden Henderson about Fobb’s condition, but Henderson was unaware of it.18 Counsel argued to the jury both in opening and closing statements that Fobb was blind. The question of Fobb’s credibility due to vision problems was certainly palpable at trial, and additional medical records and testimony concerning Fobb’s vision would have been cumulative to evidence already before the jury. See Skinner v. Quarterman, 528 F.3d 336, 345 n. 11 (5th Cir.2008) (“[A]ny ineffective assistance claim must falter where the evidence to be discovered is so similar and cumulative that failure to find and present it would not prejudice the result.”).
The district court noted that two expert witnesses retained by Woodfox as part of his post-conviction proceedings opined based on a review of Fobb’s medical records that Fobb was “very probably significantly visually impaired” at the time of the murder and that it would have been “impossible” for Fobb to have identified someone 30 to 40 feet away by vision alone. Because there is no indication in the record that these experts were available to testify and would have done so at the 1998 trial, there can be no claim of ineffectiveness for failing to call them as witnesses. See Day, 566 F.3d at 538. Moreover, *813Fobb never testified to the exact distance that he was from Woodfox when he saw Woodfox enter the Pine 1 dorm. We therefore find this evidence not only cumulative but also speculative.
We also note that counsel conceivably could have had a strategic reason for not presenting expert and medical record evidence concerning Fobb’s vision. As part of the defense, counsel called Gary Gremillion, who in 1981 became the prison’s Classification Administrator, to testify about Fobb’s release on a medical furlough in 1974. The examination of Gremillion also showed that Fobb was blind, but defense counsel elicited Gremillion’s view that Fobb did not meet the usual requirements for a medical furlough, at least under the policies in effect when Gremillion became Classification Administrator. Counsel intimated through Gremillion that Fobb was given special treatment in return for his testimony against Woodfox. This was consistent with the overall defensive strategy evident at trial to show that prison officials framed Woodfox and induced the testimony against him. But counsel arguably could not overemphasize Fobb’s blindness through the medical records because then it might look like Fobb deserved the furlough. Instead, counsel suggested that Fobb’s testimony was “bought and paid for.” While counsel did not ignore Fobb’s vision, he also presented evidence to suggest that the State essentially- bribed Fobb. We do not find such a trial strategy to have rendered the trial fundamentally unfair. See Martinez v. Dretke, 404 F.3d 878, 885 (5th Cir.2005) (“A conscious and informed decision on trial tactics and strategy cannot be the basis for constitutionally ineffective assistance of counsel unless it is-so ill chosen that it permeates the entire trial with obvious unfairness.”) (internal quotation marks and citation omitted).
Furthermore, we believe the absence of additional evidence about Fobb does not rise to the level of prejudice under Strickland given that Hezekiah Brown and Joseph Richey also placed Woodfox at the scene of the murder. In light of this evidence, and our discussion above, we cannot conclude that but for counsel’s failure to further discredit Fobb’s eyesight there is a reasonable probability that the jury would not have convicted Woodfox. See Strickland, 466 U.S. at 694, 104 S.Ct. 2052...
D. Failure to object to hearsay testimony
Woodfox argued in the state and district courts that his trial counsel was ineffective for failing to object to the State’s questioning of three witnesses that elicited hearsay responses about statements made by Chester Jackson. Jackson, who did not testify in Woodfox’s first trial, pleaded guilty to manslaughter in connection with Miller’s murder and then testified in 1974 against co-defendants Herman Wallace and Gilbert Montegut. In 1998, the State sought pre-trial approval to use Jackson’s 1974 testimony as evidence in Woodfox’s second trial because Jackson had died in the interim. The Louisiana First Circuit Court of Appeal ruled that the prior testimony was inadmissible hearsay because Woodfox never had an opportunity to cross-examine Jackson. Despite this ruling, Woodfox contends, and the district court agreed, that the State impermissibly elicited hearsay testimony about an incriminating statement Jackson gave to prison officials during the murder investigation.
The testimony at issue came from Sheriff Daniel, Warden Henderson, and Deputy Warden Lloyd Hoyle. Because of their similarity, we first consider the testimony of Daniel and Henderson. During questioning of Sheriff Daniel about the investí*814gation of Miller’s murder, the State established that officials took a statement from Jackson on April 19, two days after the murder and after Daniel had obtained the statement from Hezekiah Brown identifying Woodfox as the killer. The prosecution asked whether Daniel had “aequire[d] any information from Chester Jackson that changed [his] mind about issuing an arrest warrant” for Woodfox. Daniel responded negatively.
The State similarly cross-examined Warden Henderson, who had been called by Woodfox, about the investigation. Henderson stated that Hezekiah Brown had incriminated Woodfox, Wallace, and Jackson, and that prison officials decided to confront Jackson because he was the “weakest of the three.” Jackson then gave his statement. When Henderson began to state what Jackson had said, defense counsel immediately objected. The prosecutor instructed Henderson not to say what Jackson told him, but asked “did you get any information from Chester Jackson that contradicted what Hezekiah Brown had told you about Albert Woodfox’s involvement in this case.” Like Daniel, Henderson also responded negatively. Woodfox contends that defense counsel should have objected to Daniel’s and Henderson’s testimony.
Under the Louisiana rules of evidence, an investigating officer may be permitted to refer to statements made to him by other persons involved in the case without it constituting hearsay if it explains his own actions during the course of an investigation and the steps leading to the defendant’s arrest. See State v. Watson, 449 So.2d 1321, 1328 (La.1984); State v. Edwards, 406 So.2d 1331, 1349 (La.1981). This hearsay exception has limits, however, and generally will not include an “explanation” that “involves a direct assertion of criminal activity against the accused.” State v. Hearold, 603 So.2d 731, 737 (La. 1992).
The district court held that the questioning of Daniel and Henderson indirectly elicited the substance of Jackson’s statement. Woodfox contends on appeal that the testimony readily revealed that Jackson had stated that Woodfox participated in the murder. Under this reasoning, the testimony about Jackson’s statement would fall outside of the “explanation” exception for hearsay because it would constitute a direct out-of-court accusation by Jackson against Woodfox. We conclude, however, that the testimony plainly did not reveal what Jackson said. It merely demonstrated that during the course of the investigation, Daniel and Henderson did not learn anything to change their minds about what Hezekiah Brown told them. This is unlike State v. Wille, 559 So.2d 1321 (La. 1990), where the Louisiana Supreme Court held that an investigating officer’s testimony about statements from witnesses improperly revealed the substance of accusatory hearsay assertions against the defendant. The court noted that the investigator there was careful not to say that the witnesses told him the defendant killed the victim, but he did say that the witnesses led him to conclude that the defendant was the prime suspect and to believe that the defendant was responsible for the crime. Id. at 1332 n. 8. That is not true here, where Brown had already incriminated the defendant and neither Daniel nor Henderson stated that Jackson named Woodfox or led them to believe Woodfox was involved. For all the jury knew from Daniel’s and Henderson’s testimony, Jackson might have said nothing at all about Woodfox. Therefore, we conclude that it is not unreasonable to find that counsel was not deficient for failing to object to the testi*815mony, which otherwise helped explain the course of the investigation.19
Woodfox’s claim about Deputy Warden Lloyd Hoyle’s testimony requires a little more discussion, but we conclude that the state court’s denial of relief with respect to that claim was also not unreasonable. Woodfox’s defensive strategy throughout the trial was to show that prison officials targeted Mm after the murder and framed him for the crime because he was considered to be a troublemaker and a political activist. He claimed that he was immediately placed in lockdown status as part of a biased investigation and that prison officials influenced the other inmates to lie about his involvement in the murder. In support of this theory, defense counsel called Deputy Warden Hoyle and repeatedly asked Hoyle about whether the pace of the investigation had been too quick and whether Hoyle believed people were blamed who were not involved. He sought agreement from Hoyle that Wood-fox was already a suspect on April 17, the day of the murder, before officials had even interviewed anyone. When Hoyle’s responses did not support Woodfox’s theory, defense counsel asked the following questions:
Defense counsel: If I told you that— that Mr. Woodfox was formally charged by a grand jury in this matter two and a half weeks after the incident, would that refresh your recollection?
Hoyle: No it wouldn’t refresh my recollection at all, cause I heard his name mentioned on the nineteenth.
Defense counsel: Okay. But, that was the first time you — you heard his name mentioned.
Hoyle: That’s the only time I heard his name mentioned, by one of the perpetrators who was with him.
Defense counsel: Okay. But, that was on the nineteenth?
Hoyle: That was on the nineteenth, at the A Building.
Defense counsel then tendered Hoyle for cross-examination, and the prosecutor immediately asked the following:
Prosecutor: Mr. Hoyle, you — was the nineteenth, that statement that you’re talking about, was that the statement— was that Chester Jackson?
Hoyle: That was a prelude to the statement of Chester Jackson.
Prosecutor: And was that the only statement that you were present for, during the first couple of days?
Hoyle: I didn’t even stay for the statement, basically. I stayed for the minute that a certain convict walked into that interrogation room and admitted Ms role in the thing, and named Woodfox, and Wallace as the perpetrators of that stabbing. I couldn’t stand even to be in the room with that pair. I left.
The district court held that defense counsel was ineffective for failing to object to this testimony because it directly revealed Jackson’s hearsay statement that implicated Woodfox. The State contends that the testimony was admissible as relevant to explain the investigation’s progress and also to rebut Woodfox’s conspiracy theory defense. We agree that because the statement directly accused Woodfox, the mere fact that it explains the progression of the investigation “may not be used as a passkey to bring before the jury the substance of the out-of-court information *816that would otherwise be barred by the hearsay rule.” Hearold, 603 So.2d at 737. That does not end the matter, however, because although an investigating official’s testimony explaining his conduct almost always has only marginal relevance and will generally be inadmissible when it reveals accusatory hearsay statements, the Louisiana Supreme Court has indicated that the conduct of an investigating officer will sometimes need to be explained. Wille, 559 So.2d at 1331 n. 7. To be sure, such a necessity will occur “ ‘only in rare instances,’ ” id. (citation omitted), and requires “some unique circumstances in which the explanation of purpose is probative evidence of a contested fact....” Hearold, 603 So.2d at 737. We think the instant case presents the kind of rare instance contemplated by the Louisiana Supreme Court.
Defense counsel’s direct examination of Hoyle put at issue the circumstances under which Woodfox became a suspect, particularly when and how Hoyle first heard Woodfox was suspected. Counsel clearly suggested that Woodfox was targeted from the start on the investigation. Hoyle’s testimony directly contradicted that theory. It was therefore probative of a contested issue at trial, and we cannot say an objection from counsel would have been sustained. See id.; see also State v. Guy, 669 So.2d 517, 525 (La.Ct.App.1996) (holding that testimony about informant’s tip was not inadmissible where inter alia the propriety of the officer’s actions was made relevant by the defense’s theory that informant was unreliable and was paid to fabricate testimony against defendant). Furthermore, information learned by investigators during the course of an investigation will often have an “impermissible hearsay aspect as well as a permissible nonhearsay aspect,” at which point “the issue of relevancy becomes significantly interrelated with the hearsay issue.” Wille, 559 So.2d at 1331. The court is required to “balance the need of the evidence for the proper purpose against the danger of improper use of the evidence by the jury.” Id. This balancing question is an issue for the state court applying state law. On habeas review we will defer to a state court’s interpretation and application of state law because we search only for violations of federal law. See Fierro v. Lynaugh, 879 F.2d 1276, 1278 (5th Cir. 1989).
Woodfox argues that the testimony from Daniel, Henderson, and Hoyle did not refute his trial defense because it did not explain why prison officials initially decided to question Jackson, nor did it reveal that Jackson made allegations that he was beaten during questioning. But Woodfox could have brought out this information himself, and he makes no allegation that counsel was ineffective for not doing so. Because Woodfox put the propriety of the investigators’ conduct at issue in his direct examination as part of his reasoned trial strategy, and Hoyle’s testimony provided an explanation of the conduct, we conclude that defense counsel was not ineffective for failing to object.
We also agree with the State that Woodfox failed to show prejudice under Strickland from counsel’s alleged deficiency in failing to object to the testimony of these witnesses. As noted above, neither Daniel nor Henderson revealed the substance of Jackson’s statement. And while Hoyle testified that Jackson incriminated Woodfox, this hearsay testimony was cumulative of testimony from Hezekiah Brown and Joseph Richey. Because the testimony was cumulative of other evidence, we cannot hold that but for counsel’s failure to object the results of the trial would have been different. See Strickland, 466 U.S. at 694, 104 S.Ct. 2052; *817see also United States v. Allie, 978 F.2d 1401, 1408-09 (5th Cir.1992) (holding on direct appeal that improper admission of hearsay evidence that was merely cumulative constituted harmless error). We therefore hold that it was not an unreasonable application of clearly established federal law for the state court to conclude that Woodfox failed to show his counsel was ineffective for failing to object to the testimony.
IV. Conclusion
This was not a perfect trial, and certainly the jury’s task was complicated by the great lapse in time between the crime and the trial, which resulted in the deaths of many witnesses, the loss of memory, and the loss of physical evidence. Those issues are not uncommon when a defendant is subject to a second prosecution after an earlier successful appeal. Nevertheless, we must keep in mind only the clear legal issues presented by the case and the very deferential scope of review of a state habeas court’s decision, which limits our review to reasonableness, not whether we think the state court decision was merely incorrect or erroneous. Under that deferential standard, and for the foregoing reasons, we conclude that the district court erred in its conclusion that counsel rendered constitutionally ineffective assistance.20 We therefore VACATE the district court’s judgment and REMAND for resolution of *818the only remaining issue relating to the selection of the grand jury foreperson.
VACATED and REMANDED.
. In the alternative, the magistrate judge concluded that Woodfox’s § 2254 petition presented a prima facie case of discrimination in the selection of the grand jury foreperson but that an evidentiary hearing would be necessary to allow the State an opportunity to present rebuttal evidence. In light of her conclusions with respect to Woodfox's ineffective assistance claims, the magistrate judge did not conduct a hearing, and instead recommended that the matter be referred for a hearing if the district court disagreed with the magistrate judge’s resolution of those claims. The ruling on discrimination in the grand jury foreperson selection has not been appealed and is not before us.
. Because the district court adopted the magistrate judge’s report as its own opinion, we hereinafter refer to the findings and conclusions of the magistrate judge as those of the district court.
. Rather than begin with exhaustion, the dissent considers it as part of an analysis of how the state court resolved Woodfox’s claim, and it asserts that a threshold issue is whether the state court resolved the claim on the merits. See Dissenting op. at 819-20. But exhaustion is of primary import because federal habeas relief may not be granted without it. See Nobles, 127 F.3d at 419; § 2254(b)(1)(A). We assume exhaustion later as part of our alternative analysis of the substantive versus procedural issue in Part III.A.2 below.
. See Brady v. Maryland, 373 U.S. 83, 87, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) (holding that prosecution must produce evidence favorable to the accused that is material to guilt or punishment); Giglio v. United States, 405 U.S. 150, 154, 92 S.Ct. 763, 31 L.Ed.2d 104 (1972) (holding that Brady extends to impeachment evidence).
. The dissent asserts that Woodfox's state habeas application would not have prevented the substance of the claim from being understood. Dissenting op. at 825. The dissent agrees, however, that Woodfox made no coherent argument as to Brown and confrontation. Id. at 823-24. We do not believe the state court would necessarily understand the claim, presented as it was amidst a voluminous, disjointed submission. See Dissenting op. at 823-24. In contrast to the claim about Brown, Woodfox did make specific claims that his counsel was ineffective for failing to object on confrontation grounds to two other witnesses — Carl Cobb and Leonard Turner.
. We note that the dissent agrees that the State has not explicitly waived the exhaustion issue. See Dissenting op. at 819.
. The dissent asserts that the State’s response neither analyzed the Confrontation Clause nor made other legal arguments, and that the argument the state trial court must have embraced was that the issue was not properly presented. Dissenting op. at 821-22. The dissent believes the state trial court therefore based its decision on the independent, but inadequate, state procedural grounds governing the presentation of state habeas claims. See La.Code Crim. Proc. Ann. art. 926(B)(3) & E. The failure of the State to analyze the Confrontation Clause, in our view, is more likely because Woodfox made no coherent Confrontation Clause argument and failed to exhaust the issue. But assuming arguendo that Woodfox adequately raised the issue, the State made no express procedural argument under art. 926, and there is no indication that the state trial court relied on it or another state procedural rule. Even if the state trial court is viewed to have ruled procedurally, it also adopted as part of the State's response the State's blanket denial of all of Woodfox's ineffective assistance claims, which is a merits-based adjudication. When a state court rules alternatively on both procedural grounds and on the merits of a prisoner's claims, the AEDPA deference is still applicable. See Busby v. Dretke, 359 F.3d 708, 721 n. 14 (5th Cir.2004).
. Although the dissent contends that the State's response asserted Woodfox failed to present his claim because it observed that Woodfox had not discussed Brown in the claims for relief section of the state habeas application, we believe that is more akin to the exhaustion issue. We are assuming for purposes of this discussion that Woodfox properly presented his claim in state court.
. Our conclusion that the state court adjudicated the merits of Woodfox's claim is based on our analysis of the entire three-part test under Mercadel, not solely on the state court's finding that Woodfox failed to carry his burden of proof, which the dissent says was simply a "convenient generalization” by the state court. Dissenting op. at 821. Although the dissent also faults our consideration of the word "moreover” in the state trial court’s ruling, we find an adequate basis to believe the state trial court’s adoption of the State's response was in addition to its conclusion that Woodfox’s application lacked merit.
. The questioning as appears in the record was as follows:
*798Prosecutor: Did anybody promise you anything to make you tell the truth?
Brown: Promise me anything?
Prosecutor: Did they?
Brown: No. They didn't threaten me. I sat there a long time; I waited before I could say anything. Nobody promised me nothing.
Prosecutor: All right, now, Hezekiah, because of your triál testimony here today, did you — let me ask you this: You stated that no one from the State promised you anything for this testimony, is that correct?
Brown: That’s right.
Prosecutor: All right, but we did tell you that you would not be put back in the same place at—
Brown: That’s right.
Prosecutor: — The penitentiary?
Brown: They told me that.
Prosecutor: — With Albert Woodfox?
Brown: That's right.
. The cross-examination, in relevant part, shows the following:
Defense counsel: Didn't you tell me that Fess was in the dormitory at the time that Woodfox came in there?
Brown: No. No. I hadn't never told you that. No.
Defense counsel: You absolutely positive?
Brown: I know. I ain't no positive to it. I know I ain’t told you nothin’ about that man.
Defense counsel: All right, you didn’t tell me Fess was over by the ... water cooler?
Brown: No. No. Now, wait a minute man. Let me tell you somethin', I ain't told nothin' that night. You come in there, and you had your pad when I come up there to meet you.
Brown: ... You and me, you sat there and talked for quite a while, and I was explaining my case to you, and I told you then ... I'm sorry that you is in this case, I says. Well, the only thing I can do is tell you that it was a cold blooded murder, and I says, I’m going to meet you on the stand when you- — -that's what I told you there that night. And you said, that I had a good case, and if after — after this was — after this is all over with, you would help me. You remember when you told me that- — when you told me that — told me? You give me your card, remember? Huh? You the onliest somebody that promised to help me, to do somethin’ for me.
. Although defense counsel went to great lengths to show that Henderson helped Brown, virtually all of the documentary evidence post-dated Woodfox’s 1973 trial and could not have been of any benefit to him for the first trial. Further, despite defense counsel’s argument and insinuation that Brown's testimony was "bought and paid for” because of Brown's eventual pardon, the pardon did not occur until 1986, thirteen years after Brown testified.
. Defense counsel attempted to mitigate Brown's incriminating evidence by suggesting that Brown had given defense counsel information contrary to the testimony, and also by eliciting testimony that Brown could not identify Woodfox’s clothing; that Brown did not know if Woodfox got blood on him although there was a lot of blood at the scene; and that Brown did not know which way Woodfox went when he fled. In 1998, counsel tried to further impugn Brown's prior testimony by eliciting the information from Warden Henderson about the promises to help Brown with his pardon application.
. The dissent’s analysis draws from prior opinions of this court, as well as from treatises and a factually-similar case from the supreme court of the State of Pennsylvania. We do not consider these authorities, however, because even if we were to find them persuasive they do not constitute clearly established federal law as articulated by the Supreme Court as required by the AEDPA. See Renico v. Lett, -U.S. -, 130 S.Ct. 1855, 1866, *801176 L.Ed.2d 678 (2010) (court of appeals’ reliance on its own prior precedent was improper because circuit precedent “does not constitute 'clearly established Federal law, as determined by the Supreme Court,’ § 2254(d)(1), so any failure to apply that decision cannot independently authorize habeas relief under AEDPA”); see also Salazar v. Dretke, 419 F.3d 384, 399 (5th Cir.2005) (“[A] decision by this court or one of our sister circuits, even if compelling and well-reasoned, cannot satisfy the clearly established federal law requirement under § 2254(d)(1).”).
. The district court noted that in the case of co-defendant Herman Wallace a state commissioner found a Brady violation because the state suppressed Henderson’s alleged promises to Brown, who had also testified at Wallace’s 1974 trial; however, the state district court rejected the commissioner's recommendation and found no Brady violation, and the Louisiana Supreme Court denied an application for writs. See State v. Wallace, 19 So.3d 4 (La.2009).
. Woodfox's experts suggested that "sloughed off skin cells” and hair obtained from the clothes could have been subjected to DNA testing in 1998 to establish a DNA profile of the habitual wearer of the clothing. In theory, this profile could then have resolved whether or not the clothing belonged to Woodfox. The district court believed that counsel was ineffective for failing to pursue such a course of action. As noted above, however, the clothing had been lost by the time of the trial and therefore was unavailable for testing. We therefore cannot find that defense counsel was ineffective for not having the clothing tested. The same reasoning applies to the experts' opinions that the blood stains should have been subjected to DNA *809testing as well. Counsel could not have tested that which no longer existed.
. Woodfox asserts in his appellate brief that counsel was also ineffective for failing to discredit Cobb’s testimony by presenting evidence of a mid-1970s study conducted by the Department of Justice. Woodfox asserts that the study, which examined 200 crime laboratories around the country, found that "71.2% of laboratories failed,” and that counsel could have used this study to exclude Cobb's testimony as unreliable. This study did not form part of the district court’s decision. Moreover, the study did not make public the results from individual laboratories. It therefore failed to identify any deficiency in the Louisiana State Police Crime Laboratory. We fail to see, therefore, how this speculative evidence would have rendered Cobb's testimony inadmissible, and Woodfox’s conclusory argument is insufficient to support a claim of ineffective assistance of counsel for failing to present the evidence. See Green v. Johnson, 160 F.3d 1029, 1042 (5th Cir.1998).
. Defense counsel further sought to discredit Fobb before the jury by offering psychological reports showing that Fobb was mentally retarded.
. We also note again that with respect to Henderson’s testimony, defense counsel did lodge an immediate objection when Henderson was about to state what Jackson said. This prompted the prosecutor to specifically instruct Henderson not to relate the contents of Jackson’s statement.
. In addition to his ineffective assistance claims, Woodfox raised a Brady claim in his § 2254 petition that the State suppressed investigation notes from Sheriff Daniel that would have impeached the testimony of Joseph Richey and Paul Fobb. The district court did not examine the claim "in any great detail,” but it held that the suppressed notes would have allowed Woodfox to impeach or discredit Richey and Fobb by showing their initial statements differed from their testimony. After carefully examining the trial transcript and the alleged inconsistencies in the investigative notes, we conclude that Wood-fox's Brady claim is unavailing because, despite facial inconsistencies with the testimony, the investigation notes do not satisfy Brady's materiality requirement. See Banks v. Thaler, 583 F.3d 295, 311 (5th Cir.2009) (suppressed evidence is “material” if " ‘there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different’ ”) (quoting United States v. Bagley, 473 U.S. 667, 682, 105 S.Ct. 3375, 87 L.Ed.2d 481 (1985)).
Richey testified on cross-examination that his statements to prison officials were "exactly” as he testified about seeing Woodfox exit the Pine 1 dorm, but that fact was not included in Daniel's note from Richey's initial statement on April 17, 1972. However, Richey also specifically testified that he had given a "generic” answer when he was first questioned. Counsel could have used Richey's own direct testimony to impeach him on his cross-examination that he had given exactly the same statement. Moreover, Richey's testimony alternately referred to statements given to Daniel, Warden Dees, and Captain Dixon on both April 17 and May 16. It is not at all clear from the transcript that when Richey testified that his statements to investigators had always been the same as his testimony, he meant that he discussed Woodfox when he was first interviewed. Such a conclusion is actually contrary to Richey's testimony that he gave only a "generic” answer when first questioned.
Fobb testified at trial that he saw Woodfox enter the Pine 1 dorm, but the investigation notes show that he initially told investigators that he had remained in his dorm on the morning of the killing and that the dorm man could confirm this. Fobb’s initial statement was consistent with Sheriff Daniel's testimony that many of the inmates claimed on April 17 that they lacked any information about the murder. Indeed, it is hardly surprising that Fobb would initially deny seeing anything that morning. Based on our review of the record, we are not convinced that the investigation notes on Richey and Fobb " ‘put the whole case in such a different light as to undermine confidence in the verdict.’" Strickler v. Greene, 527 U.S. 263, 290, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999) (quoting Kyles, 514 U.S. at 435, 115 S.Ct. 1555). Therefore, the state court's denial of habeas relief on the Brady claim was not unreasonable.