Petitioner-Appellant Richard Jordan appeals from the district court’s denial of a certificate of appealability (COA) for ha-beas corpus relief pursuant to 28 U.S.C. § 2254. Jordan was convicted of capital murder committed in the course of a kidnapping and was sentenced to death on four separate occasions. Following the first three convictions, Jordan challenged his death sentence successfully, was retried, and was again re-sentenced to death. In 1991, on remand from the third successful challenge to his sentence, Jordan entered into an agreement with the prosecution to serve a sentence of life imprisonment without parole in exchange for not further contesting his sentence. He nevertheless challenged his sentence, seeking to have it converted to life imprisonment with the possibility of parole. The Mississippi Supreme Court held that the agreement was invalid and remanded for a new sentencing trial. Thereafter, Jordan sought to re-enter into the same plea agreement. The prosecution declined, and instead successfully sought the death penalty for the fourth time in a 1998 sentencing trial. Jordan requests a COA on several claims arising out of that 1998 sentencing. For the reasons that follow, we DENY Jordan a COA on both his prosecutorial vindictiveness claim and his ineffective assistance of counsel claims.
*399In January 1976, Jordan abducted Edwina Marter from her home at gunpoint. Jordan then drove Marter to a secluded area in the woods north of Gulfport, Mississippi. While she was either running away or kneeling, Jordan fatally shot Mar-ter in the back of the head. The following day Jordan was arrested after he picked up the $25,000 ransom he had demanded in exchange for Marter. Jordan has been tried and sentenced to death four times for killing Marter. As the procedural history and testimony offered over the course of these proceedings are relevant to his claims before us in this appeal, we will now recount the history of this case.
A.
Jordan was first tried in 1976. Assistant District Attorney Joe Sam Owen, who figures prominently in Jordan’s current claim of prosecutorial vindictiveness at issue in this appeal, prosecuted the casé along with another attorney. Prior to the trial, defense counsel moved for a psychiatric examination, and Jordan was examined by Dr. Clifton Davis. The intake report from this evaluation stated incorrectly that Jordan was dishonorably discharged from the Army following his service in Vietnam — he was in fact honorably discharged, and it is unclear why the error occurred.1 The psychiatric evaluation report contained other information that Jordan presumably related to the doctor, including Jordan’s version of the kidnapping and murder, in which Jordan reported that an accomplice shot Marter.
According to Dr. Davis, Jordan “explained that the FBI was more or less responsible for [Marter’s] death since they blundered the job in following instructions.” “He comments that he is sorry that she was killed but then shrugged this off by saying ‘better luck next time.’ ” Dr. Davis concluded that Jordan had antisocial personality disorder, a category describing people “in conflict with the mores of society” who “are selfish, callous, irresponsible, impulsive, and unable to feel guilt or to learn from experience and punishment.” Dr. Davis found Jordan competent to stand trial. Dr. Davis did not testify at the 1976 trial, or any trial thereafter, but the expert who later examined Jordan in 1998 relied on Dr. Davis’s reports. David Melton, a sheriffs investigator who investigated the crime scene where Marter’s body was found, testified briefly at the first trial regarding chain of custody. Melton was not questioned about his investigation of the scene.
Under then-existing Mississippi law, Jordan was automatically sentenced to death after being found guilty of capital murder. The Mississippi Supreme Court subsequently mandated bifurcated proceedings in capital murder cases. See Jackson v. State, 337 So.2d 1242 (Miss. 1976) (citing Gregg v. Georgia, 428 U.S. 153, 96 S.Ct. 2909, 49 L.Ed.2d 859 (1976)). As a result, the trial court granted Jordan a new trial with bifurcated guilt and sentencing proceedings.
B.
Owen also served as the lead prosecutor at Jordan’s second trial. Jordan was convicted of capital murder on essentially the same evidence introduced at the first trial. During the sentencing phase, the prosecution offered new evidence to show that *400Jordan shot Marter “execution-style.” Although Investigator Melton did not testify during the guilt phase, the prosecution attempted to introduce testimony from Melton regarding blood spatters that he had observed at the murder scene during the sentencing phase of the trial. Melton was prepared to testify that he had observed blood spatters at the scene that indicated that Marter was kneeling in front of Jordan when she was shot.
The trial court excluded Melton’s testimony because it was not offered during the guilt phase. Dr. William Atchison, the pathologist who conducted Marter’s autopsy, had, however, testified during the guilt phase as to the cause of death and the path of the bullet, which he described as traveling “upward.” Based on that limited testimony as to Marter’s position at the time she was killed, the prosecution was permitted to argue that Marter was on her knees when she was shot. Jordan offered evidence in mitigation, including character testimony from family and friends. Some of Jordan’s witnesses mentioned his military service, and both of his parents testified that he had been honorably discharged.
The jury convicted Jordan and he was again sentenced to death. This court held that the jury was improperly instructed on imposition of the death penalty, granted federal habeas relief setting aside the death sentence (but not the conviction), and afforded Jordan a new sentencing trial. See Jordan v. Watkins, 681 F.2d 1067 (5th Cir.1982).
C.
In 1983, Owen, now an attorney in private practice appearing for the state as special prosecutor, prosecuted the new sentencing trial. Investigator Melton testified that he believed “Marter was standing still when the bullet was fired” based on his blood spatter analysis. According to Melton, Marter was “not moving” and possibly “was on her knees.” Melton testified that he had learned to analyze blood stains at a 1973 seminar taught by Dr. Herbert MacDonnell,2 who Melton indicated was a noted authority in the field of blood stain analysis. Dr. Atchison augmented his 1977 testimony with his opinion that the gun was between thirty inches and four feet from Marter’s head when fired. Dr. Atchison also testified that the trajectory of the bullet suggested that Marter could have been kneeling, with her head bowed, or running away. The defense presented expert testimony suggesting that it was impossible to determine from Dr. Atchi-son’s autopsy report the distance from which Marter was shot.
In mitigation, Jordan testified about his experience serving as a soldier in Vietnam. He stated that, for about two years, his “responsibility was maintaining the machine guns that the aircraft was armed with and to provide fire power if necessary to protect the aircraft against hostile attacks.” He testified that he was injured in a helicopter crash and then went on “ground duty for a while.” In total, he stated that he was in Vietnam for almost three years. He extended his tour longer than necessary because, “the policy was that there didn’t have to be [two males in the same family] in the country,” so he stayed in Vietnam to allow his brother, Robert, to be in the United States. Jordan’s brother Robert also testified that Jordan extended his tour so that Robert could be home. Defense counsel asked Robert whether he noticed any change in Jordan after Vietnam. Robert responded, “I noticed some difference. It is hard to pinpoint. He would be nervous. I don’t *401know; just unsettled is the best way I could put it. But there was a change. There would have to be after three years in Viet Nam [sic].”
Jordan was again sentenced to death. Thereafter, the United States Supreme Court granted certiorari, vacated the death sentence, and remanded Jordan’s case to the Supreme Court of Mississippi for further consideration in light of a new Supreme Court case holding that evidence that the defendant would not pose a danger if spared (but incarcerated) must be considered potentially mitigating, and may not be excluded from the sentencer’s consideration. See Jordan v. Mississippi 476 U.S. 1101, 106 S.Ct. 1942, 90 L.Ed.2d 352 (1986) (relying on Skipper v. South Carolina, 476 U.S. 1, 106 S.Ct. 1669, 90 L.Ed.2d 1 (1986)). The Mississippi Supreme Court ordered the case remanded to the trial court for a new sentencing trial. See Jordan v. State, 518 So.2d 1186 (Miss.1987).
D.
In 1989, in preparation for the fourth sentencing trial, Jordan’s counsel obtained an affidavit from Dr. MacDonnell, the forensics expert who taught the blood stain evidence seminar that investigator Melton had attended. In this appeal, Jordan argues that the attorneys that represented him at the 1998 trial should have obtained, reviewed, and used this 1989 affidavit of Dr. MacDonnell, obtained by the earlier counsel, in preparing his defense and specifically in rebutting Melton’s testimony. In the affidavit, Dr. MacDonell averred as follows regarding Melton’s 1983 blood stain testimony:
I have reviewed the testimony of Mr. David Melton[ ].... I am the ‘Herbert McDonald’ to whom Mr. Melton refers ... and it is my course he describes as having attended, and based on which he purports to have obtained his expertise in the analysis of blood spatters.... Based on Mr. Melton’s testimony and description of the scene of the crime, I have substantial doubts about the conclusions reached by Mr. Melton.... If Mr. Melton’s description of the scene is accurate, given my years of experience and knowledge in the field of blood-stain pattern analysis, I would conclude that the victim probably was moving at the time she was shot.... I am willing to conduct further investigation for the defense attorneys, and testify if necessary, if compensation is available for my work.
In 1989, Jordan’s attorney also obtained supporting affidavits from psychologist Dr. John P. Wilson and psychiatrist Dr. Sheldon Zigelbaum. In his affidavit, Dr. Wilson averred that there is a “high incidence of PTSD” among Vietnam veterans. He stated that he had not met with Jordan, but “certain basic information concerning Mr. Jordan” had been relayed to him and, based on that information and the doctor’s experience and research, he believed that it was “extremely likely” that, if evaluated, Jordan would be diagnosed with PTSD. Dr. Wilson stated that he was available and willing to evaluate Jordan and present testimony in mitigation if paid his “standard rates.” Dr. Zigelbaum similarly averred that he had “been informed that Mr. Jordan served almost three tours of duty in Vietnam” and concluded, based on experience and research, that “it is entirely possible that Mr. Jordan may have had at the time of the crime at least some manifestations of PTSD.”
E.
Instead of undergoing a new sentencing trial, Jordan reached an agreement in 1991 under which he would be sentenced to life imprisonment without parole in exchange for his promise not to challenge that sen*402tence. During the plea agreement process Jordan was represented by his attorneys at the time, Robert McDuff and Joseph Hudson, and the state was represented by Owen as special prosecutor. The court accepted the plea and Jordan was sentenced to life imprisonment without parole pursuant to the agreement in December 1991.
Several years later, the Mississippi Supreme Court held that a sentencing agreement to life without parole for a crime committed before that sentence was available under then-existing statutory law was against public policy and “void ab initio.” Lanier v. State, 635 So.2d 813, 816-17 (Miss.1994). The Mississippi Supreme Court held that such an agreement was invalid, and that both parties were therefore “placed back in the positions which they occupied prior to entering into the agreement.” Id.
Following the Mississippi Supreme Court’s decision in Lanier, Jordan filed a motion in the state trial court contending that his own sentence to life without parole was invalid. Before the trial court ruled on Jordan’s motion, the Mississippi legislature amended the statute so that death, life with parole, or life without parole were all available sentences for the offense. See 1994 Miss. Laws Ch. 566 (amending Miss. Code Ann. § 97-3-21).3 The Mississippi trial court then denied Jordan’s motion in full, and Jordan appealed to the Mississippi Supreme Court.
The Mississippi Supreme Court held that Jordan’s life without parole sentence was invalid:
[T]his case must be reversed and remanded because the contract in the case sub judice is void, even though ... Jordan entered into the agreement knowingly, voluntarily and intelligently. The agreement providing for life without the possibility of parole was not a permissible sentencing option under [state law] in 1987, thus the circuit court had no authority to issue such a sentence. Additionally, the agreement is void as against public policy.
Jordan v. State, 786 So.2d 987, 1000 (Miss.2001) (citing Jordan v. State, No. 95-KP-00113-SCT (Miss. August 7, 1997)). The Mississippi Supreme Court vacated Jordan’s sentence and remanded to the trial court for re-sentencing, stating that “the State has the right to seek the death penalty” on remand. Id.
On remand Jordan asked Owen to reinstate the earlier agreement for a sentence of life imprisonment without parole, which was permissible pursuant to the state’s post-Lamer legislation. Owen declined. Jordan filed a motion in the trial court requesting a sentence of life imprisonment without parole. Owen contested the motion and refused to waive imposition of the death penalty. The court denied the motion.
F.
Jordan’s fourth sentencing trial took place in 1998. Owen again acted as special prosecutor. Attorneys Tom Sumrall and Waide Baine represented Jordan. In this appeal, Jordan contends that these attorneys failed to provide him constitutionally required effective assistance of counsel.
Prior to trial, Jordan moved for a mental health examination to determine whether he suffered from PTSD due to his military service. The prosecution did not object to *403an examination but argued that it was entitled to a copy of the examiner’s report. Jordan was examined by Dr. Henry A. Maggio, and the doctor’s report was furnished to both sides.
Dr. Maggio’s report recited Jordan’s personal history. Jordan’s counsel did not provide Dr. Maggio with Jordan’s military records or honorable discharge form, or the affidavits of Dr. Wilson and Dr. Zigelb-aum, and those alleged errors are at issue here. In creating his report, Dr. Maggio reviewed the 1976 reports prepared by Dr. Davis for the earlier trial. Apparently in reliance on Dr. Davis’s reports, Dr. Mag-gio stated erroneously that Jordan was dishonorably discharged from the military. Dr. Maggio’s report stated:
Review of the previous intake interview and psychiatric evaluation reveals a consistency of some of the history; however, there are moments of inconsistency in which Mr. Jordan previously acknowledged that he had always been a good con man. He has done a number of illegal activities but had not been caught except on one or two occasions; that he had been fired or asked to resign because of embezzlement of $43,000.00; that while he was under financial pressures he wrote bad checks and then was searching for a way for quick money at which time he considered bank robbery with kidnapping and extortion and had worked out the plan himself. He then readily blames the F.B.I. more or less for the woman’s death shrugging it off by saying “better luck next time.” He apparently displayed little remorse, held the F.B.I. responsible, no overt sadness. The review also shows that he joined the Army in 1964 and had been charged with check forgery and agreed to join the Army so the charges would be dropped. He was also court martialed in 1970 for falsification of official documents and sentenced to 9 months in Leavenworth. He received a Dishonorable Discharge from the Army in 1971. All of this is in contrast and contradiction to what he told me when he denied having any difficulty with authority figures, having an Honorable Discharge from the military and being a good guy prior to this murder and has been a good guy since then while he’s in prison.
Dr. Maggio concluded, like Dr. Davis did before, that Jordan had antisocial personality disorder and was competent to stand trial.
At the trial, Dr. Maggio did not testify and his report was not introduced into evidence. However, the prosecution used Dr. Davis’s and Dr. Maggio’s reports in cross-examining a boyhood friend of Jordan’s, Richard Luther King. Jordan’s attorney stated he was not going to call two additional character witnesses because of the possibility of their being cross-examined on the basis of Dr. Maggio’s report. Then, several prison employees testified as to Jordan’s good work and disciplinary record in prison.
Once again, the prosecution argued that Jordan shot Marter in the back of the head, “execution-style,” while she was on her knees. This theory was part of the prosecution’s case for the application of the “especially heinous, atrocious or cruel” statutory aggravating circumstance under Mississippi Code § 99 — 19—101 (5)(i).4 Melton testified that, based on his examination of the crime scene, he was of the opinion that Marter “was in a stationary position” rather than running when Jordan shot her. *404On cross-examination, defense counsel brought out the fact that, even though Melton believed that Marter was shot from above in the back of the head while she was on her knees, investigators found no evidence of where the bullet hit the ground despite a “[v]ery thorough visual inspection” of an area in which the bullet should have landed if the execution-style shooting theory were correct.
Defense counsel also attempted to demonstrate that Jordan must have been more than six feet away from Marter when he fired the shot because he was not bloodstained. On redirect, Melton reiterated that there was no doubt in his mind that Marter was stationary. On re-cross, Melton testified that “the position of the [victim’s] body would also play a great role in whether or not the [shooter] would get blood on [him]. If, for example, [the victim] w[as] on [her] knees [the shooter] would get no blood on [him]”; but also that it would be “reasonable to assume” that if the shooter was “standing right behind the wound,” he would get blood on him. On further redirect, Melton reiterated that he “believed” that Marter was on her knees when shot.
Dr. Atchison again testified in support of the execution-style shooting theory. Referring to illustrations of bullet wounds in Marter’s head, Dr. Atchison described his findings and concluded that Marter was killed by a shot fired from between a few inches and thirty inches away while “in a stationary position.” He further testified that it “had been [his] feeling all along” that Marter was on her knees when shot, and that it was his opinion “[t]hat she was executed.” Dr. Atchison later described Marter as “possibly in a praying position” when she was shot. On cross-examination, defense counsel pointed out that, in his 1983 testimony, Dr. Atchison had testified that it was possible either that Marter was running and falling or that she was kneeling. However, Dr. Atchison concluded his testimony by reiterating, “[i]f my theory is correct then she was shot in the kneeling position in a near close wound.”
The defense called its own expert, Dr. Leroy Riddick, a forensic pathologist and Alabama state medical examiner. In contrast to Dr. Atchinson, Dr. Riddick testified that, based on his examination of the evidence, he had concluded that Marter’s gunshot wound was a “distant wound or an intermediate range one” from somewhere between three and ninety feet rather than a contact wound or a near wound. Dr. Riddick also testified that he “couldn’t tell” and “didn’t know how anybody could tell” whether Marter was stationary or moving when she was shot. On cross-examination, Owen asked Dr. Riddick to reiterate that he did not dispute that Jordan could have shot Marter from as close as three feet away and that he did not have any opinion as to whether Marter was on her knees when Jordan shot her in the back of the head. On redirect, Dr. Riddick clarified his opinion that there was insufficient evidence for any pathologist to determine that Marter was kneeling rather than standing and running when she was shot.
Defense counsel asserted Jordan’s military service in Vietnam as a mitigating factor, and it was included as a possible mitigating circumstance in a jury sentencing instruction. Owen argued, “[t]here is no evidence about what [Jordan] did [in Vietnam] or particularly what he did after he got out.”
The jury sentenced Jordan to death. The Mississippi Supreme Court affirmed the conviction on direct appeal in April 2001. Jordan, 786 So.2d at 987. Jordan filed a state post-conviction petition in January 2003. In March 2005, the Mississippi Supreme Court, holding that all of Jordan’s claims were without merit, denied *405Jordan’s application for leave to proceed on his claims for post-conviction relief. See Jordan v. State, 912 So.2d 800 (Miss.2005); see also Miss.Code Ann. § 99-39-7 (requiring leave of the Mississippi Supreme Court in certain circumstances before a defendant may pursue post-conviction relief in state trial court).
Having exhausted his remedies in Mississippi courts, Jordan sought federal ha-beas relief. On August 30, 2010, the district court denied relief on all of Jordan’s claims. See Jordan v. Epps, 740 F.Supp.2d 802 (S.D.Miss.2010). The district court also denied Jordan’s request for a COA, required for his appeal to this court. See 28 U.S.C. § 2253(c)(1)(A). Jordan requests a COA allowing him to appeal one claim of prosecutorial vindictiveness and several claims of ineffective assistance of counsel.
II.
“[A] prisoner seeking a COA need only demonstrate ‘a substantial showing of the denial of a constitutional right.’ ” Miller-El v. Cockrell, 537 U.S. 322, 327, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (quoting 28 U.S.C. § 2253(c)(2)). “A petitioner satisfies this standard by demonstrating that jurists of reason could disagree with the district court’s resolution of his constitutional claims or that jurists could conclude the issues presented are adequate to deserve encouragement to proceed further.” Id. (citing Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)). “[A] petitioner need not show that an appeal will succeed in order to be entitled to a COA. The question is the debatability of the underlying constitutional claim, not the resolution of that debate.” Cardenas v. Dretke, 405 F.3d 244, 248 (5th Cir.2005) (citations and internal quotation marks omitted).
In making the COA determination, “we view the petitioner’s arguments through the lens of the deferential scheme laid out in 28 U.S.C. § 2254(d).” Druery v. Thaler, 647 F.3d 535, 538 (5th Cir.2011) (alteration and internal quotation marks omitted). Under § 2254(d)(1), a state prisoner’s application for a writ of habeas corpus “shall not be granted with respect to any claim that was adjudicated on the merits in State court proceedings unless the adjudication of the claim ... resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.” 28 U.S.C. § 2254(d).
“A federal court’s collateral review of a state-court decision must be consistent with the respect due state courts in our federal system. Where 28 U.S.C. § 2254 applies, our habeas jurisprudence embodies this deference.” Miller-El, 537 U.S. at 340, 123 S.Ct. 1029. “Factual determinations by state courts are presumed correct absent clear and convincing evidence to the contrary, § 2254(e)(1), and a decision adjudicated on the merits in a state court and based on a factual determination will not be overturned on factual grounds unless objectively unreasonable in light of the evidence presented in the state-court proceeding.” /¿.(citing 28 U.S.C. § 2254(d)(2)).
III.
We begin with Jordan’s prosecutorial vindictiveness claim. In Blackledge v. Perry, 417 U.S. 21, 94 S.Ct. 2098, 40 L.Ed.2d 628 (1974), the Supreme Court explained that the Due Process Clause is offended by the possibilities of increased punishment upon retrial after appeal that pose a realistic likelihood of vindictiveness on the part of a prosecutor. Id. at 28, 94 *406S.Ct. 2098. “[I]t [is] not constitutionally permissible for the State to respond to [a criminal defendant’s] invocation of his statutory right to appeal by bringing a more serious charge against him prior to the trial de novo.” Id. at 28-29, 94 S.Ct. 2098. To prove prosecutorial vindictiveness, a defendant may (1) show actual vindictiveness or (2) show sufficient facts to create a presumption of vindictiveness. United States v. Saltzman, 537 F.3d 353, 359 (5th Cir.2008).
A.
Jordan argues that Owen acted with actual vindictiveness by refusing to re-enter into a sentencing agreement for life without parole following Jordan’s successful challenge to the validity of the 1991 agreement. Jordan contends that, because the sentencing agreement he challenged had been held void ab initio by the Mississippi Supreme Court, he “was punished for doing nothing more than ‘what the law plainly allows him to do.’ ” A defendant pursuing a actual vindictiveness claim has the burden of proving his claim, by a preponderance of the evidence, “by presenting objective evidence that the prosecutor’s actions were designed to punish a defendant for asserting his legal rights.” Id. A defendant’s “failure to offer any tangible evidence in support of his [actual] vindictiveness claim dooms it to failure.” United States v. Cooks, 52 F.3d 101, 106 (5th Cir.1995); see also United States v. Goodwin, 457 U.S. 368, 373, 102 S.Ct. 2485, 73 L.Ed.2d 74 (1982); Blackledge, 417 U.S. at 28, 94 S.Ct. 2098. Here, Jordan has not presented any evidence of actual prosecutorial vindictiveness.
Jordan appears to contend that he need not point to such evidence of Owen’s actual retaliatory intent because, as the Mississippi Supreme Court expressly found, “Owen declined Jordan’s offer and indicated that he would not make a plea agreement with Jordan since Jordan had previously violated his agreement with the State that he would not appeal his plea and sentence of life imprisonment without the possibility of parole.” Jordan, 786 So.2d at 1000. In effect, Jordan argues that Owen’s statement constitutes an admission of impermissible retaliatory intent.
We disagree. As the Supreme Court explained in Bordenkircher v. Hayes, it is not vindictive for a prosecutor to follow through on a threat made during plea negotiations. 434 U.S. 357, 363-64, 98 S.Ct. 663, 54 L.Ed.2d 604 (1978); cf. Hayes v. Cowan, 547 F.2d 42, 43, 45 (6th Cir.1976) (stating that where the prosecutor warned the defendant during plea negotiations “that if he did not plead guilty, he would be charged under the habitual criminal statute” carrying a much longer sentence, and the prosecutor then carried out that threat, “a vindictive motive need not be inferred” because “[t]he prosecutor has admitted it”), rev’d by Bordenkircher, 434 U.S. 357, 98 S.Ct. 663. Rather, it merely establishes a motive — enforcement of the threat implicit in the plea agreement. See Bordenkircher, 434 U.S. at 363-64, 98 S.Ct. 663.
As the Bordenkircher Court explained:
[T]he plea may have been induced by promises of a recommendation of a lenient sentence or a reduction of charges, and thus by fear of the possibility of a greater penalty upon conviction after a trial. While confronting a defendant with the risk of more severe punishment clearly may have a “discouraging effect on the defendant’s assertion of his trial rights, the imposition of these difficult choices [is] an inevitable” — and permissible — “attribute of any legitimate system which tolerates and encourages the negotiation of pleas.”
*407Id. (second alteration in original) (citations omitted). The fact that Owen carried out the threat implicit in the plea agreement does not serve as evidence of Owen’s actual vindictiveness. The state court’s statement that “Owen ... indicated that he would not make a plea agreement with Jordan since Jordan had previously violated his agreement with the State” does not amount to a finding of an admission of vindictive motive by which Jordan can “prove objectively that [Owen’s] ... decision [to refuse to again offer a sentence of life without parole] was motivated by a desire to punish him for doing something that the law plainly allowed him to do.” See Goodwin, 457 U.S. at 370-73, 102 S.Ct. 2485. Jordan presented no additional evidence, and thus fails to prove his actual vindictiveness claim.
B.
Jordan does not explicitly raise a presumptive vindictiveness claim, and we are not convinced that there is such a claim before us. Jordan’s brief addresses the prosecutor’s “vindictiveness” in general, without ever specifying which of the two forms of vindictiveness he is asserting here. For example, Jordan appears to make an actual vindictiveness claim when he states:
The District Court quoted this language but failed to consider the very different context of Jordan’s case. There was no need to consider whether circumstances justified a presumption of vindictiveness because there is no dispute that the Special Prosecutor, whose decision is at issue here, refused to agree [sic] a deal that he previously found that acceptable only because Jordan exercised a legal right.
(emphasis added). Jordan also argues:
Here, there is more than a “presumption ” of vindictiveness. The Mississippi Supreme Court has already resolved the key fact — that the prosecutor refused Jordan’s offer only because of his legal challenge — in Jordan’s favor.
(emphasis added). Jordan thus appears to argue that the prosecutor engaged in actual rather than presumptive vindictiveness. Nevertheless, because the dissenting opinion addresses a presumption of vindictiveness claim, we address why — even assuming arguendo that Jordan had raised a presumption of vindictiveness claim — any such argument is foreclosed by our court’s binding precedent in Deloney v. Estelle, 713 F.2d 1080, 1085 (5th Cir.1983).
Our presumption of vindictiveness analysis begins with the Supreme Court’s decision in Blackledge, 417 U.S. 21, 94 S.Ct. 2098. In Blackledge, the defendant was charged with a misdemeanor of assault with a deadly weapon based on an altercation with another inmate. Id. at 22, 94 S.Ct. 2098. The defendant was found guilty and received a six-month sentence. Id. The procedural rules in North Carolina gave the defendant the right to appeal and receive a de novo trial. Id. After the defendant filed his notice of appeal, the prosecutor obtained an indictment from a grand jury, charging the defendant with the felony of assault with a deadly weapon with intent to kill and inflict serious bodily injury for the same conduct for which the defendant had been previously tried and convicted of a misdemeanor. Id. at 23, 94 S.Ct. 2098. The defendant pleaded guilty and received a sentence of five to seven years. Id. The Supreme Court held that charging the defendant with a more serious crime for the same act created a presumption of prosecutorial vindictiveness, explaining:
A person convicted of an offense is entitled to pursue his statutory right to a trial de novo, without apprehension that the State will retaliate by substituting a *408more serious charge for the original one, thus subjecting him to a significantly increased potential period of incarceration.
Id. at 28, 94 S.Ct. 2098.
In contrast to the prosecutor in Blackledge, Owen never attempted to charge Jordan with any crime other than the one that Owen had repeatedly charged him with over the proceeding three decades. In Deloney, we found this distinction critical and thus held that there is no claim for prosecutorial vindictiveness absent an increase in charges beyond those raised in the original indictment. 713 F.2d at 1085. As we stated in Deloney:
We stress that in this case the asserted increased seriousness of the charges stems from the reduction of the charges pursuant to the plea bargain. The charges were not enhanced beyond the original indictments. Thus actually De-loney’s claim reduces itself to a bootstrap device in three steps: First, plea bargain to get the charges cut down. Second, get the plea bargain set aside for lack of understanding and coercion of his agreement by his attorney. Third, insist that it would be prosecuto-rial vindictiveness now to be prosecuted at the same level of jeopardy to punishment that the original indictments called for. The law does not find this to be prosecutorial vindictiveness. This Court has held that a prosecutor may, without explanation, refile charges against the defendant whose bargained-for guilty plea to a lesser charge has been withdrawn or overturned on appeal, provided that an increase in the charges is within the limits set by the original indictment. The charges facing Deloney under the second indictment were not only within the limits of those in the first indictment, but were the same.
Id. (internal quotation marks and citations omitted).
Jordan attempts to use an identical three-step bootstrapping technique here: First, he was originally indicted with capital murder — a crime that at the time carried an automatic death sentence under Mississippi law. Jordan went to trial three separate times. Each time Jordan was charged with murder, and each time Owen sought the death penalty. Jordan then entered into a plea agreement to get the sentence reduced from death to life without parole. Second, Jordan got the plea bargain set aside as void ab initio. Third, he insists “that it would be prosecu-torial vindictiveness now to be prosecuted at the same level of jeopardy to punishment that the original indictments called for.” Id. Owen never imposed a charge or sentence greater than the one that he originally — and repeatedly — charged Jordan with before the plea bargain. As a result, Owen’s actions do not give rise to a presumption of prosecutorial vindictiveness. See Miracle v. Estelle, 592 F.2d 1269, 1275 (5th Cir.1979) (noting that the “sine qua non of a prosecutorial vindictiveness claim is that the second charge is [in] fact harsher than the first” and refusing to focus on the “end result” regarding whether a conviction would result in a different punishment (citing Jackson v. Walker, 585 F.2d 139, 146 (5th Cir.1978))).
We disagree with the dissenting opinion that Deloney is distinguishable because the defendant in Deloney wanted to go to trial on the merits while Jordan did not want to go to trial, but instead wanted to reinstate his prior bargained-for life sentence without parole. We fail to see how this distinction matters under Deloney. Deloney’s reasoning does not hinge on whether Delo-ney wanted a plea agreement. Instead, Deloney instructs us to make a simple and straightforward comparison between the *409original indictment and the later indictment that follows the exercise of a legal right. If there is no change in the charges filed or punishment sought, then there is no presumption of vindictiveness. As we explained in Deloney, there is no prosecu-torial vindictiveness when “the asserted increased seriousness of the charges stems from the reduction of the charges pursuant to the plea bargain. The charges were not enhanced beyond the original indictments.” 713 F.2d at 1085. In Jordan’s case, the original charges and the later charges were likewise the same.
Moreover, it is not clear from the decision in Deloney that there is actually any distinction between that case and this one. Certainly, Deloney filed a motion for new trial in his case, which was granted. Id. at 1081. He also wanted the court to enter a judgment of acquittal. Id. at 1086 (“Delo-ney next claims that he was denied due process and equal protection when the trial court granted his motion for a new trial ... but failed to enter a judgment of acquittal.”). Beyond this, the opinion tells us nothing about Deloney’s state of mind or whether he wanted or attempted to secure another plea bargain before his trial. De-loney’s desire for a plea agreement is not discussed in the court’s analysis, and thus cannot serve as our basis for distinguishing this precedent.
The dissenting opinion identifies two elements under Blackledge for establishing circumstances that present a realistic likelihood of prosecutorial vindictiveness. According to the dissenting opinion, the first element is that the prosecutor has a “considerable stake” in maintaining the status quo and discouraging action that could upset such status quo. The second element is that the prosecutor responds by “upping the ante” by imposing, or subjecting the defendant to, the risk of harsher punishment.
Our court has not yet adopted such a test for claims of presumptive prosecutorial vindictiveness. Even if this were the test, the prosecutor here does not meet either element. First, when our case law discusses the prosecutor having a “considerable stake” in maintaining the status quo, it discusses the desire on the part of prosecutors to avoid having to again go to trial. See, e.g., Bordenkircher, 434 U.S. 357, 98 S.Ct. 663; Blackledge, 417 U.S. at 27-28, 94 S.Ct. 2098. In Blackledge, the Supreme Court explained:
A prosecutor clearly has a considerable stake in discouraging convicted misde-meanants from appealing and thus obtaining a trial de novo in the Superior Court, since such an appeal will clearly require increased expenditures of prose-cutorial resources before the defendant’s conviction becomes final, and may even result in a formerly convicted defendant’s going free. And, if the prosecutor has the means readily at hand to discourage such appeals — by “upping the ante” through a felony indictment whenever a convicted misdemeant pursues his statutory appellate remedy— the State can insure that only the most hardy defendants will brave the hazards of a de novo trial.
417 U.S. at 27-28, 94 S.Ct. 2098. These circumstances are not present here: Owen made the choice to go to trial rather than enter into another plea agreement. Because Jordan requested a plea agreement, it was Owen, rather than Jordan who decided to expend additional prosecutorial resources. See Goodwin, 457 U.S. at 376-77, 102 S.Ct. 2485 (“[Blackledge ] reflects] a recognition by the Court of the institutional bias inherent in the judicial system against the retrial of issues that have already been decided,” which “might” “subconsciously motivate a vindictive prosecu-torial or judicial response to a defendant’s *410exercise of his right to obtain a retrial of a decided question.”); United States v. LaDeau, 734 F.3d 561, 569-70 (6th Cir.2013) (“When the prosecution is forced to do over what it thought it had already done correctly, ... the prosecution’s stake in discouraging the defendant’s exercise of a right may be considerable.” (internal quotation marks and citations omitted)).
Bordenkircher further highlights a necessary ingredient for the presumption of vindictiveness that was absent there, but present in Blackledge — circumstances suggesting a high possibility of retaliation against the defendant for challenging results the prosecutor previously sought and obtained. See Bordenkircher, 434 U.S. at 363, 98 S.Ct. 663; see also Goodwin, 457 U.S. at 381-82, 102 S.Ct. 2485 (discussing Bordenkircher). Namely, there was no presumption of vindictiveness in Bordenkircher because the prosecutor did not have to re-litigate a matter that had already resulted in judgment, and by contrast, there was a presumption of vindictiveness in Blackledge because the prosecutor there did. Like the prosecutor in Bordenkircher, Owen was not required to re-litigate Jordan’s ease in order to obtain a conviction for murder because Jordan was willing to plead guilty. Second, as we have already noted, Owen in no way “upped the ante.” He merely sought the same punishment that he had sought before entering into the invalidated plea agreement.
Furthermore, as Jordan himself contends, the plea agreement was “null from the beginning” and never had any legal “force or effect.” See Hood ex rel. State Tobacco Litig., 958 So.2d 790, 815 (Miss.2007); Richardson v. Canton Farm Equip., Inc., 608 So.2d 1240, 1254 (Miss.1992); see also Lanier, 635 So.2d at 817 (explaining that, because the agreement is void ab initio, “both parties are placed back in the positions which they occupied prior to entering into the agreement”). If the parties are placed back in the exact same situation that they were in before the plea agreement, it is hard to understand how Jordan is in any different situation now than he was at the end of his previous trial, where Owen similarly sought, and Jordan received, the death penalty. Declaring the plea agreement void ab initio is akin to saying that the plea agreement never occurred at all. If the plea agreement never occurred, then Owen’s actions in pursuing the exact same penalty that he had pursued in the three previous trials cannot be the pursuit of a “more severe punishment than initially sought and obtained.”
We have declined to find a presumption of prosecutorial vindictiveness where, first, the criminal defendant and the prosecutor reached a plea agreement that was accepted by the court; second, the defendant succeeded in having the plea agreement set aside, proceeded to trial, and was found guilty; and third, at sentencing, contended that it would be vindictive for the prosecution to ask for a sentence greater than the one to which it had initially agreed. In such cases, we have concluded that the defendant should not be able to use vindictiveness doctrines to abuse the ordinary plea negotiation process by demanding the benefits, but not the burdens, of the bargain. See, e.g., Ehl v. Estelle, 656 F.2d 166, 171 (5th Cir. Unit A 1981) (“We have not found a case from any jurisdiction that holds that a defendant can accept a plea bargain, take back his part of the bargain, insist upon a trial on the merits, and yet bind the prosecutor, and thus the Court, on the original promised recommendation of punishment after the prosecutor has lost all benefits of the bargain. To permit this situation would undercut the entire purpose and aim of the *411plea bargaining process.”); accord United States v. Moulder, 141 F.3d 568 (5th Cir.1998); Deloney, 713 F.2d 1080. The dissenting opinion cites the stipulations supporting the prosecutor’s initial decision to enter into a plea agreement with Jordan. There were no doubt many reasons, including those in the stipulations, why the prosecution may have decided to pursue a plea agreement rather than another trial. But when we evaluate a presumption of vindictiveness claim, we focus instead on a different and narrower question: Is there an increase in the charge between the initial indictment and the indictment following the exercise of a right? Because the answer here is no, our inquiry is at an end.5
IV.
We now turn to Jordan’s ineffective assistance of counsel claims, on which he also requests a COA.
“In all criminal prosecutions, the accused shall enjoy the right ... to have the Assistance of Counsel for his defence.” U.S. Const, amend. VI. Under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), to prevail on a claim that a criminal defendant’s attorneys failed to provide constitutionally required effective assistance of counsel, the defendant must show “(1) that his counsel’s performance was deficient, and (2) that the deficient performance prejudiced his defense.” Woodward v. Epps, 580 F.3d 318, 325 (5th Cir.2009).
A.
Jordan contends that his attorneys performed deficiently for five related reasons involving Melton’s “execution-style shooting” testimony: (1) they were unprepared to cross-examine Melton; (2) they were not prepared to show that Melton had no record of his alleged blood spatter observations; (3) they did not request funds for an expert who could have helped prepare for cross-examination and who could have testified in rebuttal to Melton; (4) they failed to rebut the prosecution’s execution-style killing theory with available expert testimony, through cross-examining Melton with his teacher, Dr. Herbert MacDonell’s affidavit or treatise, or with transcripts of prior proceedings; and (5) they were unable to use the previous trial transcript to show the jury that the prosecution had previously accepted Jordan’s version that the killing was unintended. Jordan contends that he was prejudiced by these failings because, had his attorneys rebutted Melton’s testimony as he argues they should have, the jury may not have sentenced him to death.
The Mississippi Supreme Court found that Jordan’s attorneys performed defi-ciently, and the state does not challenge that conclusion. See Jordan, 912 So.2d at 812. Accordingly, we assume arguendo that the attorneys performed deficiently *412and proceed to assess whether the deficient performance prejudiced Jordan’s defense, which the Mississippi Supreme Court decided against Jordan. See Woodward, 580 F.3d at 330.
“Under Strickland, a defendant is prejudiced by his counsel’s deficient performance if ‘there is a reasonable probability that, but for counsel’s unprofessional errors, the result of the proceeding would have been different.’ ” Porter v. McCollum, 558 U.S. 30, 40, 130 S.Ct. 447, 175 L.Ed.2d 398 (2009) (quoting Strickland, 466 U.S. at 694, 104 S.Ct. 2052). “A reasonable probability is a probability sufficient to undermine confidence in the outcome.” Wiggins v. Smith, 539 U.S. 510, 534, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003) (quoting Strickland, 466 U.S. at 694, 104 S.Ct. 2052). In the capital sentencing context, like here, to assess prejudice, we must “reweigh the evidence in aggravation against the totality of available mitigating evidence.” Id.
Jordan fails to make the requisite substantial showing of prejudice for several reasons. First, the sentencing jury’s finding that the shooting was “execution-style” was only one of two reasons the jury determined that Jordan’s crime satisfied Mississippi’s “especially heinous, atrocious, or cruel” statutory aggravating circumstance. See Miss.Code Ann. § 99-19-101(5)(i). The jury also found that the murder was “especially heinous, atrocious, or cruel” because Marter “was subjected to extreme mental torture caused by her abduction from the home wherein she was forced to abandon her unattended three-year-old child and removed to a wooded area.” Jordan fails to demonstrate a reasonable probability that a stronger rebuttal of Melton’s testimony would have altered the jury’s “extreme mental torture” finding.
Furthermore, in addition to the “especially heinous, atrocious, or cruel” factor, the jury also found that two other statutory aggravating circumstances were present: first, that the crime was committed while Jordan was engaged in the commission of a kidnapping, Miss.Code Ann. § 99-19-101(5)(d), and second, that the crime was committed for pecuniary gain, id. § 99—19—101(5)(f). Those findings of the jury were clearly supported by the evidence, and Jordan has shown no reason to think that better rebuttal of Melton would have had any effect on those findings. Moreover, even if Jordan’s counsel had better rebutted Melton’s testimony, the prosecution could have still pointed to Dr. Atchinson’s independent testimony as a basis for the execution-style shooting theory.
In sum, there is little reason to think that a better rebuttal of Melton’s testimony would have significantly affected the jury’s findings regarding aggravating factors. Accordingly, we are not persuaded that reasonable jurists could find the district court’s resolution of this claim to be debatable. We decline Jordan’s request for a COA on this ineffective assistance of counsel claim.
B.
Jordan’s next ineffective assistance of counsel claim involves Dr. Mag-gio’s report that stated erroneously that Jordan was dishonorably discharged. The report was not introduced into evidence but was used to cross-examine a few of Jordan’s witnesses. We understand Jordan to have the following grievances with his attorneys: (1) they failed to provide Dr. Maggio with correct information of Jordan’s honorable discharge; (2) they failed to warn Jordan of the consequences of participating in Dr. Maggio’s examination; and (3) they failed to pursue a men*413tal health evaluation on PTSD from a doctor other than Maggio.
Assuming arguendo that Jordan’s counsel acted deficiently in these respects, we are not persuaded that there is a debatable question of prejudice. Given the minimal role Dr. Maggio’s report played in the sentencing trial — again, it was used only in cross-examination of a few witnesses and was not introduced into evidence — and the fact that most of the damaging material in the report, including Jordan’s statement to Dr. Davis blaming the FBI and blithely saying “better luck next time,” is not contended to be inaccurate, we do not think there is a reasonable case to be made that Jordan’s counsel’s performance regarding Dr. Maggio prejudiced Jordan’s defense. We are not persuaded that the district court’s resolution is debatable.
As for the claim that his attorneys’ failure to pursue a mental health evaluation on PTSD from a doctor other than Dr. Maggio, we agree with the district court that Jordan has not shown a reasonable probability that a different doctor would have provided a more favorable evaluation and we are not persuaded that the district court’s conclusion is debatable.
Because we do not think the question of prejudice as to Jordan’s claims relating to Dr. Maggio is debatable, we decline the request for a COA on these ineffective assistance of counsel claims.
V.
Jordan’s request for a COA is DENIED.
. See Jordan v. Mississippi, 912 So.2d 800, 815-16 (Miss.2005) ("Dr. Davis' report [states] that Jordan was dishonorably discharged from the Army. Jordan includes evidence that he was honorably discharged. From the record, we find little explanation for this error in the report.'').
. Melton incorrectly referred to Dr. MacDon-nell as "Herbert McDonald.”
. Jordan contends in this appeal that, after the July 1994 amendment was enacted, Mississippi law would have allowed Owen in a subsequent sentencing to agree again — lawfully this time — to a life without parole sentence. The state does not contest Jordan's argument.
. At the time of the trial, the "especially heinous, atrocious or cruel” statutory aggravating circumstance was codified at § 99-19-101(5)(h). It was moved to § 99 — 19—101(5)(i) on April 25, 2013. See 2013 Miss. Laws Ch. 556.
. The dissenting opinion also notes that the Ninth Circuit addressed similar circumstances and granted the defendant relief in Adamson v. Ricketts, 865 F.2d 1011 (9th Cir.1988). While the Ninth Circuit may have taken a different approach to this question, we are bound by our own prior precedent on this issue. United States v. Short, 181 F.3d 620, 624 (5th Cir.1999) ("[T]his panel is bound by the precedent of previous panels absent an intervening Supreme Court case explicitly or implicitly overruling that prior precedent.”). As a result, even assuming ar-guendo that Jordan raises a presumption of vindictiveness claim, it would fail under our precedent. Cf. White v. Woodall, - U.S. -, 134 S.Ct. 1697, 1706, 188 L.Ed.2d 698 (2014) ("Section 2254(d)(1) provides a remedy for instances in which a state court unreasonably applies this Court’s precedent; it does not require state courts to extend that precedent or license federal courts to treat the failure to do so as error.”).