SUTTON, J., delivered the opinion of the court, in which MERRITT and McKEAGUE, JJ„ joined. MERRITT, J. (p. 253), delivered a separate concurring opinion.
OPINION
SUTTON, Circuit Judge.An Ohio jury convicted Jesse Cowans of the murder of Clara Swart, and the court (consistent with the jury’s recommendation) sentenced him to death. The Ohio courts upheld his conviction and sentence on direct and collateral review. Cowans filed a federal habeas petition, which the *245district court denied. Because federal courts in habeas proceedings must defer to the state courts’ reasonable adjudications of federal constitutional claims and because the state courts’ resolution of Cowans’ claims meets this standard, we affirm.
I.
On August 29, 1996, a bus arrived at the home of Clara Swart to take her to the Senior Citizen Center. The driver honked, knocked on the door and directed someone to call the Swart residence, but Swart never answered. That evening, when Swart’s son went to her house for dinner, he found her dead with a cord tied around her neck and her hands bound.
Several pieces of evidence implicated Jesse Cowans. The day before the murder, Swart’s neighbor, Mildred Kilgore, saw a man talking to Swart. After the man left, Swart told Kilgore that she was scared of the man, whom she knew from a few weeks before, when he had picked up a chair from her trash. Several people identified the man as Cowans. A crime scene technician matched Cowans’ palm print to one found in Swart’s home. The officers scented a bloodhound with Cowans’ scent starting at the back of the Swart residence, and the bloodhound took the officers to Cowans’ home a few blocks / away.
Cowans’ parole officer, Sandra Higgins, searched Cowans’ residence and found a small clown figurine that matched one missing from the Swart residence. The police obtained written consent from Cowans’ wife to search the house and found a wooden car that came from the top of a jewelry box matching one of Swart’s missing items. Police also searched the area outside the property and found a jewelry box, jewelry, pillow cases and an adding machine, all items missing from Swart’s home, near the edge of Cowans’ property.
The police arrested Cowans. While Cowans was in jail awaiting trial, he admitted to a cell-mate that he had committed the murder. The jail-house confession included several non-public details- — that Cowans found Swart on the toilet, that he tied her with a phone cord, that he left earrings and a wedding band on Swart, that an “old people’s bus” arrived at the house and that the bus driver knocked on the door while he was there. Appx. 758.
Before trial, Cowans openly struggled with his appointed counsel. He complained that his counsel wanted him to plead guilty, and he asked for new counsel. The court granted his request. At a later pre-trial hearing, Cowans requested a change of counsel again, complaining that his new counsel also wanted him to plead guilty. The court denied his request. Cowans eventually became so angry over this and other developments that he told the court he no longer wanted to appear at the hearing. The court granted his request and removed him from the courtroom. At Cowans’ direction, his defense counsel filed a motion to withdraw. The court held a hearing, and his counsel testified that Cowans had refused to talk with them since the last hearing. The court did not grant the request.
After a trial, the jury convicted Cowans of murdering Swart. As the jury read its verdict, Cowans started swearing and challenged the jury to look him in the eye. The judge removed him from the courtroom before the foreman read the rest of the verdict.
Sentencing also had its bumps. Cowans initially asked not to be present during the mitigation hearing. When the judge removed him to watch the proceedings via closed circuit TV, Cowans disabled the TV. He also directed his counsel not to present *246any mitigating evidence. The court spoke with Cowans about this decision, and Cowans explained that he felt the jurors already had made up their minds. The jury recommended a death sentence, and the trial judge independently agreed to impose the sentence.
Cowans appealed his conviction and sentence, and the Ohio Supreme Court affirmed. State v. Cowans, 87 Ohio St.3d 68, 717 N.E.2d 298 (1999). The state courts denied his requests for post-conviction relief. State v. Cowans, No. CA98-10-090, 1999 WL 699870 (Ohio Ct.App. Sept. 7, 1999). Cowans asked the Ohio Supreme Court to reopen his proceedings, see Ohio App. R. 26(B), but the Court denied his request, State v. Cowans, 103 Ohio St.3d 1403, 812 N.E.2d 1286 (2004) (unpublished table order).
Cowans filed a federal habeas petition. The district court denied the petition, Cowans v. Bagley, 624 F.Supp.2d 709 (S.D.Ohio 2008), but granted him a certificate of appealability with respect to several claims, and we added one claim more.
II.
Cowans filed his petition for habeas corpus after the effective date of the Antiterrorism and Effective Death Penalty Act (AEDPA). We thus may grant a writ with respect to claims “adjudicated on the merits in State court proceedings” only if the state court adjudication “(1) 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; or (2) resulted in a decision that 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.
Mitigating evidence at sentencing. Cowans’ first argument — that the Constitution prevents a defendant from waiving his right to present mitigating evidence at a capital trial — fails because AEDPA allows federal courts to grant the writ only when state courts misapply “clearly established” federal law, id. § 2254(d)(1), and no such law exists. The Supreme Court has never held that the Eighth Amendment or any other constitutional provision requires a defendant to present mitigating evidence at the sentencing phase of a capital trial. The Court, in point of fact, has suggested otherwise. Schriro v. Landrigan, 550 U.S. 465, 127 S.Ct. 1933, 167 L.Ed.2d 836 (2007), reversed the Ninth Circuit’s decision to grant an evidentiary hearing on a defendant’s claim that he did not knowingly and voluntarily waive his right to present mitigating evidence at his capital sentencing hearing. The Court held that the defendant’s behavior and statements indicated he did not want to present mitigating evidence, id. at 479-80, 127 S.Ct. 1933, a holding that necessarily suggests a defendant has the right not to introduce mitigating evidence.
Cowans’ related argument — -that he did not knowingly and intelligently waive his right to present mitigating evidence— fails for similar reasons. Schriro reversed the Ninth Circuit for granting an evidentiary hearing on a similar claim, noting that the Court has “never imposed an ‘informed and knowing’ requirement upon a defendant’s decision not to introduce [mitigating] evidence.” Id. at 479, 127 S.Ct. 1933. Attempting to overcome Schriro, Cowans invokes the Ohio Supreme Court’s decision in State v. Ashworth, 85 Ohio St.3d 56, 706 N.E.2d 1231 (1999), which created a list of questions for trial courts to ask capital defendants who wish to waive the presentation of mitigating evi*247dence. A claim for relief based on state law, however, generally cannot provide grounds for federal habeas relief. 28 U.S.C. § 2254(a); Wilson v. Corcoran, - U.S. -, 131 S.Ct. 13, 16-17, 178 L.Ed.2d 276 (2010) (per curiam). Even if Ashworth meant to establish a federal constitutional rule (it is not clear), that does not help Cowans because we may grant relief based only on decisions of the Supreme Court of the United States, not, the Supreme Court of Ohio. 28 U.S.C. § 2254(d)(1).
AEDPA’s requirement that we defer to state courts’ factual determinations also undermines this claim. See id. §§ 2254(d)(2), (e)(1). The Ohio Supreme Court held that “there is nothing to indicate that Cowans did not knowingly and voluntarily relinquish his right to present mitigating evidence,” Cowans, 717 N.E.2d at 314, and there is nothing unreasonable about that determination. Cowans told his attorneys that he did not want to present any mitigating evidence and instructed potential witnesses not to testify. In open court, the sentencing judge verified that Cowans did not want to present any mitigating evidence and probed Cowans’ understanding of the consequences of that decision. The record supports this finding.
B.
Competency examination. Also unavailing is Cowans’ challenge to the district court’s decision not to order him to undergo a competency examination. If before or during trial “sufficient doubt” arises about a defendant’s competence— “the capacity to understand the nature and object of the proceedings against him, to consult with counsel, and to assist in preparing his defense” — the trial court should order a competency hearing. Drope v. Missouri, 420 U.S. 162, 171, 180, 95 S.Ct. 896, 43 L.Ed.2d 103 (1975). “There are, of course, no fixed or immutable signs” of incompetence, the standard is a high one, and the relevant factors — “evidence of a defendant’s irrational behavior, his demeanor at trial, and any prior medical opinion on competence” — “are difficult to evaluate.” Id. at 180, 95 S.Ct. 896. These open-ended standards and the high threshold for establishing incompetence give state courts wide latitude in a habeas case. When virtually everything is potentially relevant and nothing is dispositive, reasonable minds occasionally may come to different conclusions about whether to hold a competency hearing. See Yarborough v. Alvarado, 541 U.S. 652, 664, 124 S.Ct. 2140, 158 L.Ed.2d 938 (2004).
That at most is what happened here. Although Cowans’ demeanor at trial and his decision not to present mitigating evidence raised concerns about his mental capacity, the state appellate courts determined that the trial court did not have to order a competency exam, a reasonable determination in view of the universe of relevant circumstances. None of Cowans’ outbursts suggested he was “incompetent,” meaning incapable of understanding the nature of the charges against him or assisting in his defense. See Drope, 420 U.S. at 171, 95 S.Ct. 896. Cowans has no significant mental history, whether before the trial or since. At the guilt phase of the trial, he showed himself capable of self control and did not have any outbursts. His outbursts before trial and at the penalty phase also were not irrational, as they coincided with negative developments in the proceedings. His behavior — requesting new counsel and angry outbursts at the jury, judge and counsel — could be read in one of two ways: as evidence of mental incompetence or of an angry, hostile personality. The trial court, which had the benefit of interacting with Cowans, concluded that he acted out of pique, not out *248of mental incompetence. Cowans, 717 N.E.2d at 312. That was a reasonable determination on this record.
Nor does the evidence obtained since trial undermine the trial court’s decision. His psychiatrists’ affidavits include diagnoses ranging from substance abuse problems to personality disorders but not mental incompetence. The affidavits say only that some of the evidence “suggest[s]” the “possibility” of mental illness, not that he was incompetent during trial. Appx. 414. That does not suffice to displace the state court’s competency determination. See 28 U.S.C. § 2254(d)(2); Thompson v. Keohane, 516 U.S. 99, 111, 116 S.Ct. 457, 133 L.Ed.2d 383 (1995).
Cowans persists that the presumption of correctness for state court findings does not apply to the state court’s determination because the state courts never held a competency hearing. Nothing in § 2254(d)(2), however, suggests we defer to a state court’s factual findings only if the state court held a hearing on the issue. Cf Harrington v. Richter, - U.S. -, 131 S.Ct. 770, 783-84, 178 L.Ed.2d 624 (2011). “By its terms, § 2254(d) bars relitigation of any claim ‘adjudicated on the merits’ in state court, subject only to the exceptions in §§ 2254(d)(1) and (d)(2). There is no text in the statute requiring” a hearing. Id. at 784. The Supreme Court has deferred to a state court’s competency determination even when the state court did not hold a hearing, see Maggio v. Fulford, 462 U.S. 111, 117, 103 S.Ct. 2261, 76 L.Ed.2d 794 (1983) (per curiam), and we have never suggested that § 2254(d)(2) does not apply to competency determinations issued without a hearing. See Mackey v. Dutton, 217 F.3d 399, 413 n. 14 (6th Cir.2000).
C.
Dog-tracking videotape. The officers videotaped a re-enactment of the dog-tracking (absent the bloodhound or any other dog) that showed the path the officers took from the victim’s house to Cowans’ house, and they played the videotape for the jury. Cowans says that the presentation of the videotape violated his due process rights. A state evidentiary ruling, however, rises to the level of a due process violation only if admitting the evidence “so infused the trial with unfairness as to deny [the defendant] due process of law.” Estelle v. McGuire, 502 U.S. 62, 75, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991).
Cowans has not shown that this evidence rendered the proceedings “so egregious that it resulted in a denial of fundamental fairness.” Giles v. Schotten, 449 F.3d 698, 704 (6th Cir.2006). When the trial court admitted the re-enactment video, it gave a limiting instruction and directed the jury to consider the evidence with caution, stating that the video had only “slight probative value” and should be viewed with “the utmost caution.” Appx. 2846. In closing argument, the prosecution admitted that the evidence was of marginal value and conceded that the evidence by itself did not suffice to convict. During cross-examination, defense counsel pointed out the deficiencies in the videotape: how the tape differed from the actual tracking and how the bloodhound lost the scent twice in the actual tracking. It was not unreasonable for the state courts to conclude that this evidence did not deprive Cowans of a fair trial.
D.
Ineffective assistance of trial counsel. Cowans raises several claims related to the performance of his trial counsel. To prevail, he must show that his attorney’s performance was objectively unreasonable and that his attorney’s failings *249so infected the proceedings as to make the trial unfair and the verdict unreliable. See Strickland v. Washington, 466 U.S. 668, 688, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). Because the state courts adjudicated these claims on the merits, we defer to the state court’s reasonable interpretations of Strickland. Under this “doubly deferential” standard of review, Yarborough v. Gentry, 540 U.S. 1, 6, 124 S.Ct. 1, 157 L.Ed.2d 1 (2003), “the question is not whether counsel’s actions were reasonable. The question is whether there is any reasonable argument that counsel satisfied Strickland’s deferential standard,” Richter, 131 S.Ct. at 788.
Mitigating evidence. Cowans makes two arguments on this score: (1) his counsel should have ensured that Cowans knowingly and voluntarily opted not to introduce mitigating evidence at the penalty phase of the trial; and (2) his counsel should have presented mitigating evidence anyway or at least requested that independent counsel do so. Both claims fail for lack of prejudice.
Even assuming counsel should have ensured that Cowans made his decision not to present mitigating evidence knowingly and voluntarily, Cowans was not prejudiced given the Ohio Supreme Court’s determination that “Cowans’s waiver was knowing and voluntary.” Cowans, 717 N.E.2d at 315; Cowans, 1999 WL 699870, at *6. That finding stands unless the state courts unreasonably applied Supreme Court precedent or unreasonably determined the facts, and the state courts did neither. Cowans does not allege any government overreaching, which is fatal to his claim of involuntariness. See Colorado v. Connelly, 479 U.S. 157, 169-70, 107 S.Ct. 515, 93 L.Ed.2d 473 (1986). The facts also support the state court’s conclusion. Cowans first voiced his desire not to participate in the sentencing proceedings after the verdict was read. Two weeks later, at the mitigation hearing, he continued to express his wish not to contribute any defense at sentencing. His firm resolve over a period of time suggests he knew what he was doing, that his waiver was knowing and voluntary. The trial court also asked Cowans to explain his decision and verified that Cowans did not want to present mitigating evidence. The court explained the probable consequences of that decision, including that the jury likely would sentence him to death. The next day, before the jury heard any evidence, the court confirmed that Cowans had not changed his mind. At both hearings Cowans’ counsel stated that they had discussed this decision with him several times.
Cowans also challenges his attorneys’ acquiescence in his decision not to present mitigating evidence. Cowans now believes that his counsel should have proffered mitigating evidence, should have presented mitigating evidence or should have hired independent counsel to present mitigating evidence. Counsel’s failure to present mitigating evidence at sentencing, it is no doubt true, may in some circumstances constitute ineffective assistance. Martin v. Mitchell, 280 F.3d 594, 612 (6th Cir.2002). But Cowans’ attorneys did not decide for themselves on a whim not to present mitigating evidence; they reached this decision after several conversations over a period of time with their client. That was not unreasonable, as several other courts have held on similar records. See Wood v. Quarterman, 491 F.3d 196, 203 (5th Cir.2007); Shelton v. Carroll, 464 F.3d 423, 439-40 (3d Cir.2006); Jeffries v. Blodgett, 5 F.3d 1180, 1197-98 (9th Cir.1993).
Schriro also supports the state court’s decision. It held that a district court did not have to grant an evidentiary hearing on a similar ineffective-assistance claim *250predicated on counsel’s failure to pursue and present mitigating evidence at a capital sentencing hearing when the defendant had not allowed his counsel to present any-mitigating evidence. “[T]he District Court could conclude,” the Court stated, that because the defendant “would have interrupted and refused to allow his counsel” to present mitigating evidence, the defendant “could not demonstrate prejudice” from counsel’s failure to present any such evidence. 550 U.S. at 477, 127 S.Ct. 1933. The Ohio state courts reasonably could say the same — that “because of [Cowans’] established recalcitrance” in refusing to allow his counsel to present mitigating evidence (indeed Cowans contacted potential witnesses himself and directed them not to testify on his behalf), he “could not demonstrate prejudice” from his counsel’s failure to present the evidence. Id.
Competency hearing. Cowans claims that his attorneys unreasonably failed to request a competency hearing. Yet Cowans cannot establish prejudice here either, in view of the state court’s presumptively correct finding that Cowans was competent. See 28 U.S.C. § 2254(d)(2); Thompson, 516 U.S. at 111, 116 S.Ct. 457. Had the attorneys requested a competency hearing, in other words, the results of the trial would not have changed.
Search of his home. Cowans claims that his counsel should have challenged the police officers’ search of his home. Although Cowans’ attorneys argued before the state courts that the parole officer’s search was invalid, Cowans now believes the motion to suppress should have focused on the validity of his wife’s consent to search their home. This argument faces two problems.
The first is that trial counsel’s failure to make an additional (or alternative) Fourth Amendment objection does not fall below an objective standard of reasonableness. Often an attorney will have several possible arguments available to her and will choose the one she thinks is the most likely to succeed or offers the greatest possible return for her client. Choosing the ground on which to contest a search is classically the kind of strategic decision that attorneys are hired to make. See Strickland, 466 U.S. at 690-91, 104 S.Ct. 2052. Counsel ultimately decided to challenge the search of the parole officer, Higgins, rather than the validity of Judith Cowans’ consent. That is understandable because Higgins’ search uncovered the first piece of incriminating evidence linking Cowans to Swart’s murder, the clown figurine that matched one taken from Swart’s house.
The second problem is that Cowans has not established prejudice. The officers obtained consent to search the home from Judith Cowans, who was his wife and shared the home with him. Although Judith and Jesse were separated at the time and did not occupy the same rooms, that is not relevant to the validity of her consent, which turns on what the officers knew (or should have known under the circumstances). Under Illinois v. Rodriguez, 497 U.S. 177, 110 S.Ct. 2793, 111 L.Ed.2d 148 (1990), “[a] search consented to by a third party without actual authority over the premises is nonetheless valid if the officers reasonably could conclude from the facts available that the third party had authority to consent to the search.” United States v. Gillis, 358 F.3d 386, 390-91 (6th Cir.2004). A reasonable officer could conclude from the facts available to her at the time — that Judith was Jesse’s wife and was at home when the officers called — that Judith had authority to consent to a search of the home. The state courts thus reasonably concluded that Cowans would not have prevailed if *251his counsel had made a different Fourth Amendment objection to the search of his home.
Dog-tracking video. Cowans faults his counsel for failing to keep the dog-tracking video out of the trial record. Yet his counsel requested (and the court issued) a special instruction cautioning the jury about the credibility of the video, objected during testimony about the dog’s error rate, objected to the reliability of the reenactment and renewed a continuing objection to the video before the tape was played. None of this falls short of prevailing professional norms.
Pre-trial investigation. Cowans raises three ineffective-assistance claims predicated on his counsel’s failure to pursue alternative pre-trial investigations, namely: not testing biological evidence at the crime scene, not challenging the palm print identification and not requesting expert funds to assist with these forensic matters. While the parties skirmish over whether Cowans procedurally defaulted these claims by failing to raise them on direct appeal, Cowans, 1999 WL 699870, at *7-8, the point makes no difference here as they each fail on the merits.
Biological Evidence. A crime scene technician discovered blood on the floor near Swart’s body and on her coat and took swabs of the samples. Later DNA testing (in the federal habeas proceeding) revealed the blood was not from Cowans and that Swart could “not be eliminated as the source” of the blood. Cowans argues his trial counsel should have ordered these tests. Yet, at the time of counsel’s investigation, counsel reasonably could have decided not to focus on this evidence, which was not part of the State’s case against his client. The prosecution never introduced any evidence (or any theory of the crime) that Swart bled during the attack. Nor did the State contend that Swart’s assailant bled or left any biological evidence at the scene other than a palm print in the kitchen. Swart was an older woman when she died by strangulation, and there was never any indication of a struggle or a link between the blood on her coat and the perpetrator. “An attorney can avoid activities that appear ‘distractive from more important duties,’ ” Richter, 131 S.Ct. at 789, and Cowans’ counsel may have done just that. As the Court recently explained:
It is only because forensic evidence has emerged concerning the source of the blood pool that the issue could with any plausibility be said to stand apart. Reliance on “the harsh light of hindsight” to cast doubt on a trial that took place now more than 15 years ago is precisely what Strickland and AEDPA seek to prevent.
Id.
Of equal significance, Cowans has not established that he was prejudiced by his counsel’s purported failure because the significance of the biological evidence is far from clear. The State initially collected blood stains from the kitchen floor, Swart’s housecoat and Swart’s nightgown. Testing revealed that the blood from the kitchen floor and nightgown came from a female and that Swart could not be eliminated as the source. The sample from Swart’s housecoat, however, had a mixture of female and male DNA, and the lab results eliminated Cowans as the source of the male DNA. Nothing in the lab results (or anything else) indicates how much blood was on the coat or, most importantly, suggests the blood stain originated at the time of the murder. A blood sample unconnected to the defendant does little in the context of a strangulation, in the context of a murder containing no evidence that anyone bled and in the context of a sample’s having no temporal proximity to the murder.
*252No reasonable probability exists that, if the jury had heard this ambiguous evidence, the result of Cowans’ trial would have been different. Consider the evidence against him: he confessed to his cell-mate that he murdered Swart and included non-public details in his confession. The police found items from Swart’s home in and around Cowans’ house and found Cowans’ palm print in Swart’s home.
Palm Print. Cowans claims that trial counsel should have challenged the method the police used to create the palm print and should have challenged whether the evidence remained in the police’s chain of custody. As to the method, counsel did object, though unsuccessfully, and as to the chain of custody, the Constitution does not require defense counsel to pursue every imaginable trial strategy, whether likely to bear fruit or not. See Engle v. Isaac, 456 U.S. 107, 134, 102 S.Ct. 1558, 71 L.Ed.2d 783 (1982). “[Experienced trial counsel learn that objections to each potentially objectionable event could actually act to their party’s detriment” and thus often “use objections in a tactical manner.” Lundgren v. Mitchell, 440 F.3d 754, 774 (6th Cir.2006). Cowans’ attorney made numerous objections during trial, primarily to the evidence that he thought was the weakest — the dog-tracking video. On this record, another objection to another piece of the State’s evidence, the palm print, may have drawn the jury’s attention to the other, more reliable piece of evidence linking Cowans to the crime. No precedent establishes that defense counsel must challenge the chain of custody of a palm print identification or risk falling below the minimum requirements of the Sixth Amendment. Cf. Richter, 131 S.Ct. at 788. This claim also falters on the prejudice prong of Strickland. Cowans has not provided any evidence that undermines the validity of palm print identifications or that raises a question about whether the palm print in fact ever left the State’s custody or was in fact Cowans’.
Expert Funds. Cowans argues that trial counsel should have requested funds to pay for experts to challenge this biological evidence. Cowans rests his claim on Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985), which held that courts must provide a defendant access to psychiatrists if the defendant’s sanity will be a significant factor at trial. For the reasons noted, however, Cowans was not prejudiced by counsel’s decision not to request these funds. The prosecution’s theory of the crime never related to the blood evidence at the scene, so the expert’s findings at most would have been ancillary to the prosecution’s case. And Cowans has not provided evidence questioning the validity of palm print identifications or raising a reasonable probability that an expert’s assistance on that front would have changed the outcome.
E.
Ineffective assistance of appellate counsel. The standard for ineffective assistance of appellate counsel mirrors the one governing the performance of trial counsel. In order to prevail, Cowans must demonstrate that counsel’s performance fell below an objective standard of reasonableness and that, but for counsel’s deficient performance, there is a reasonable probability that the outcome of his appeal would have been different. Goff v. Bagley, 601 F.3d 445, 462-63 (6th Cir.2010). Because the state court denied Cowans’ claims, Cowans, 812 N.E.2d 1286, he can prevail only if “there was no reasonable basis for the state court to deny relief,” Richter, 131 S.Ct. at 784.
Unfortunately for Cowans, there was. In the context of claims premised on counsel’s failure to raise certain issues on ap*253peal, the question is whether the state courts had any “reasonable basis” for concluding Cowans would not have prevailed if his counsel had raised these issues on appeal. Id.; Goff, 601 F.3d at 462. Cowans faults his appellate counsel for failing to raise five claims on direct appeal, namely trial counsel’s failure (1) to ensure Cowans knowingly and voluntarily waived the presentation of mitigating evidence; (2) to test blood evidence at the crime scene; (3) to challenge the validity of a palm print identification and the State’s compliance with the chain-of-custody requirement; (4) to request expert funds to assist in (2) and (3); and (5) to argue that any death sentence would be arbitrary and capricious because the jury did not hear mitigating evidence. We rejected claims (1), (2), (3) and (4) on the merits, and the state courts could reasonably do the same. Appellate counsel’s failure to raise the fifth issue— the challenge to his death sentence — did not prejudice Cowans because the Ohio Supreme Court independently addressed and rejected this claim on direct appeal. Cowans, 717 N.E.2d at 310.
III.
For these reasons, we affirm.