
622 F.3d 1237 (2010)
Robert Charles TOWERY, Petitioner-Appellant,
v.
Dora B. SCHRIRO, Respondent-Appellee.
No. 08-99022.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted February 4, 2010.
Filed September 22, 2010.
*1239 Daniel D. Maynard, Maynard, Cronin, Erickson, Curran & Sparks, PLC, Phoenix, AZ, for the petitioner-appellant.
Terry Goddard, Attorney General, Kent E. Cattani, Chief Counsel, and Jon G. Anderson (argued), Assistant Attorney General, Phoenix, AZ, for the respondent-appellee.
Before: MARY M. SCHROEDER, RAYMOND C. FISHER and N. RANDY SMITH, Circuit Judges.

OPINION
FISHER, Circuit Judge:
Robert Towery was convicted of first-degree murder, armed robbery, first-degree burglary, kidnapping, theft and attempted theft. He was sentenced to death. Towery's habeas petition raises *1240 numerous issues, but the district court certified only one for appeal. We have jurisdiction under 28 U.S.C. § 2253(a) and affirm the district court's denial of habeas corpus on the certified claim. As discussed in Part II below, we grant a certificate of appealability (COA) as to two other claims, but hold that they also do not entitle Towery to habeas relief.

I. Certified Issue: Prosecutorial Misconduct
The issue that the district court certified concerns whether the prosecutor's use of witness testimony for inconsistent purposes constitutes misconduct that warrants reversal. In the murder trial, the witness testified he overheard Towery refer to a struggle with a victim who was an "old man." In a previous trial in a different case, however, the same prosecutor had elicited this testimony to prove that Towery committed an unrelated robbery, not the murder at issue here. The Arizona Supreme Court concluded that, even assuming the prosecutor changed his mind in good faith as to which crime the overheard statement referred to, he committed misconduct by failing at least to alert the court that the first conviction was based on problematic evidence. Without specifically addressing whether this misconduct constituted a due process violation, the Arizona Supreme Court held that any error was harmless beyond a reasonable doubt. We first hold that this harmless error determination was objectively reasonable, and we further conclude that any prosecutorial misconduct did not rise to the level of a due process violation under the various frameworks recognized by the Supreme Court.

A. Factual Background
Robert Towery lived with Randy Barker and John Meacham in Scottsdale, Arizona, and shared his bedroom with his girlfriend and her young daughter. As the Arizona Supreme Court recognized, the case against Towery relied largely on the testimony of Barker, who testified in exchange for a reduced charge of second-degree murder. See State v. Towery, 186 Ariz. 168, 920 P.2d 290, 296-97 (1996). Unless otherwise indicated, the following facts are based on Barker's account.
On September 4, 1991, Barker and Towery agreed to rob Mark Jones, whom Towery had previously met, at Jones' house. That evening, the two of them drove in Barker's car to a Denny's Restaurant and from there took a taxi to be dropped off in Jones' neighborhood. They knocked on Jones' door, and Towery asked if they could use his telephone because their vehicle had broken down. Towery said, "Do you remember me? I'm from R and D Automotive."
After the two were let in, Barker pretended to make a telephone call, while Towery pulled a gun out of his briefcase. Towery told Jones that they were robbing him, both men put gloves on and Barker handcuffed Jones. Over the course of about two hours, Barker kept watch on Jones while Towery collected about $1,200 in cash and loaded Jones' car with jewelry, electronics and other items.
Towery and Barker then led Jones to the master bedroom at gunpoint, asking him whether he expected anyone soon. Towery asked Jones whether he preferred to be tied up or to be injected with a drug that would put him to sleep. Jones chose the latter option and was laid face down on the bed. Towery then tried several times to inject Jones with a large veterinary syringe that Barker believed contained battery acid.
Believing Jones was pretending to have fallen asleep, Towery created a noose using a set of tie wraps from his briefcase and began to strangle him. Jones did not struggle, but made choking and gagging *1241 sounds. After removing the noose, Towery determined that Jones was not yet dead, made another noose and repeated his previous action. Towery and Barker then drove Jones' car to the Denny's to get Barker's car, unloaded the goods at their house and abandoned Jones' car in the parking lot of an apartment complex. A security guard at the complex saw the men and later identified Towery in a photo lineup. Jones' body was discovered the next morning.
Towery testified and offered an alibi. He said he dropped Barker off at the Denny's and saw him get picked up by someone else. Towery then drove Barker's car to meet Tina Collins at an adult book shop. Towery drove with Collins to another parking lot, where they talked for about two hours. Afterward, not finding Barker at their planned meeting spot, Towery drove home. Barker arrived at the house with Jones' car and property, and Towery helped him unload the goods and dispose of the car. Towery also claimed that he bought the stolen items that the police found in his possession from Barker.
Collins' videotaped deposition was admitted to corroborate Towery's story. She said they had first met a couple of weeks earlier and arranged to meet on September 4. She did not talk with Towery again until February 9, when she visited the prison at the suggestion of a friend of hers who happened to be visiting Towery's cellmate. In his closing argument, the prosecutor suggested that Collins had never met Towery prior to the prison visit and fabricated her testimony to bolster his alibi.

B. Procedural History
Towery and Barker were charged with first-degree murder, armed robbery, first-degree burglary, kidnapping, theft and attempted theft. After their trials were severed, the jury convicted Towery on all counts, and he was sentenced to death.
During the trial, Towery's roommate John Meacham testified that on the morning after a large amount of property had appeared in their house, he heard Towery say he was "having a hard time with an old man so he hadhe had a hard time tying him up, so he had to knock him down." Earlier, in March 1992, six months after the murder and five months before the murder trial, Towery was tried and convicted of an unrelated armed robbery in a separate case, but prosecuted by the same county attorney, John Ditsworth. In the robbery trial, Ditsworth had elicited Meacham's testimony that he heard Towery say, "I tried to get this old man to do what I wanted him to do, but he wouldn't do it." The parties agree that Meacham's testimony in both trials referred to the same overheard statement. The same judge presided over both trials, but Towery had different defense lawyers.
On automatic appeal, the Arizona Supreme Court affirmed the murder conviction and death sentence. See Towery, 920 P.2d at 312. On the issue of Meacham's testimony, the court first ruled that judicial estoppel did not apply to bar the state from taking inconsistent positions, because Meacham's testimony was a minor part of the robbery case. See id. at 306. The court then considered whether the prosecutor had committed misconduct, noting Ditsworth's explanation that he came to the conclusion after the first trial that the overheard statement was more likely made in reference to the murder. See id. at 306 & n. 15. The court reasoned that even assuming the prosecutor had changed his mind in good faith, he committed misconduct by failing to give the court in the first case any notice that testimony had wrongly been admitted. See id. at 306.
*1242 The court decided, however, that under state law any error would be harmless if it could "conclude beyond a reasonable doubt that [the error] did not contribute to or affect the verdict." Id. at 307 (citing State v. Bible, 175 Ariz. 549, 858 P.2d 1152, 1191, 1203 (1993)). The court noted that Towery's lawyer on cross-examination had elicited Meacham's testimony that he thought the overheard statement referred to a prior incident and not the murder of Jones. The court concluded that "[a]ny impeachment defense counsel would have obtained from having known of the testimony in the prior trial was effectively achieved," and thus "the prosecutor's misconduct did not affect the verdict." Id.
Towery filed a petition for post-conviction relief and a motion to disqualify Judge Hendrix, who had presided over both of his trials. Another judge denied the disqualification motion, rejecting Towery's claims of bias. Judge Hendrix denied the petition, which raised due process, false evidence, Confrontation Clause, ineffective assistance of counsel and other claims. A different judge, Judge Keppel, denied Towery's motion for rehearing of the petition. The Arizona Supreme Court denied review except with regard to one issue that has now been resolved and is not relevant to this appeal. See State v. Towery, 204 Ariz. 386, 64 P.3d 828, 830 (2003) (holding that the federal constitutional right to have a jury decide whether aggravating circumstances exist in capital cases does not apply retroactively).
In 2003, Towery filed a petition for a writ of habeas corpus in the federal district court for the district of Arizona, raising eight claims. On the prosecutorial misconduct issue, the court concluded that Towery had not shown that the prosecutor knowingly presented false testimony or failed to disclose exculpatory information. It also agreed with the Arizona Supreme Court that Towery suffered no prejudice. After denying all other grounds for relief, the court granted a COA on the prosecutorial misconduct issue only. See 28 U.S.C. § 2253(c).

C. Standard of Review
A district court's decision to deny a petition for a writ of habeas corpus is reviewed de novo. Moses v. Payne, 555 F.3d 742, 750 (9th Cir.2009). Because Towery filed his habeas petition after April 24, 1996, our review is governed by the Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA). Id. at 750-51. Under AEDPA, a federal court may grant relief only if the underlying state court decision "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States," or "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)(1)-(2).

D. Discussion
On habeas review of a prosecutorial misconduct claim, we may grant relief only if the misconduct rises to the level of a due process violationnot merely because we might disapprove of the prosecutor's behavior. See Sechrest v. Ignacio, 549 F.3d 789, 807 (9th Cir.2008). Although formally presented as a single question, the prosecutorial misconduct issue actually encompasses several different due process claims drawing on distinct lines of precedent. First, Towery argues that the prosecutor put on false evidence in violation of Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959). Second, he argues that the prosecutor failed to disclose exculpatory evidence in violation of Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Finally, Towery relies on more general cases discussing when *1243 prosecutorial misconduct violates due process.
The Arizona Supreme Court concluded that there was prosecutorial misconduct, but did not specifically find a due process violation or otherwise analyze the issue within any of the above frameworks. It instead resolved the case on the basis of harmless error. See Towery, 920 P.2d at 307. We begin our analysis there to give proper deference to the Arizona Supreme Court and hold that Towery's claim can be rejected on the harmless error ground alone. Nevertheless, we shall also consider whether Towery has established a due process violation under any of the prosecutorial misconduct frameworks recognized by the Supreme Court, and we conclude that he has not.

1. Harmless Error
A constitutional violation arising from prosecutorial misconduct does not warrant habeas relief if the error is harmless. See Sandoval v. Calderon, 241 F.3d 765, 778 (9th Cir.2000). When a state court has found a constitutional error to be harmless beyond a reasonable doubt, a federal court may not grant habeas relief unless the state court's determination is objectively unreasonable. See Mitchell v. Esparza, 540 U.S. 12, 17-18, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003) (per curiam); Cooper v. Brown, 510 F.3d 870, 921 (9th Cir. 2007). Here, the Arizona Supreme Court did not specifically address whether Towery's federal due process rights were violated, but found beyond a reasonable doubt that the prosecutor's misconduct did not contribute to the verdict. It thereby performed the same harmless error analysis it was required to do for a constitutional violation under Chapman v. California, 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967), and its conclusion warrants our deference. See Early v. Packer, 537 U.S. 3, 8, 123 S.Ct. 362, 154 L.Ed.2d 263 (2002) (per curiam) (explaining that deference is proper "so long as neither the reasoning nor the result of the state-court decision contradicts" Supreme Court precedent).
The Arizona Supreme Court reasoned that if Towery's lawyer had been aware of Meacham's prior testimony in the robbery trial, the trial court would nevertheless have permitted the evidence to be introducedsubject to impeachment based on its prior inconsistent use. See Towery, 920 P.2d at 307. The court then noted the cross-examination that actually did take place:
Q. Do you know for sure that [Towery was] talking about Mr. Jones [the victim]?
A. I thought [Towery was] talking about when [he] got busted before.
Q. So, in fact, you didn't think [Towery was] talking about Mr. Jones?
A. No, sir, I didn't.
Id. On redirect, the prosecutor attempted to rehabilitate the witness, but his attempt was limited to showing that Meacham was uncertain either way about what Towery was referring to:
Q. Okay. The conversation that you overheard, was it before or after all of this property came into the house?
A. I believe it was after.
Q. And you don't really know what the conversation that you heard pertains to, do you?
A. No, sir.
Id. Because these exchanges undercut the value Meacham's testimony had to the prosecution's case, the Arizona Supreme Court concluded that "[a]ny impeachment defense counsel would have obtained from having known of the testimony in the prior trial was effectively achieved." Id.
This conclusion was objectively reasonable. We agree that the cross-examination of Meacham created significant doubt *1244 about whether the overheard statements had anything to do with the murder of Jones. If Towery's lawyer had known about Meacham's testimony in the robbery trial, any further impeachment based on this prior inconsistent use would have been largely cumulative. See Williams v. Woodford, 384 F.3d 567, 599 (9th Cir.2004) (holding the defendant suffered no prejudice from the suppression of cumulative impeachment evidence because the witness at issue would not have been cast in a significantly worse light).
We are also unpersuaded by Towery's argument that Meacham's testimony was crucial to the prosecution's case. Towery notes the relative lack of physical evidence and the state's heavy reliance on Barker's testimony, and he suggests Meacham's testimony provided the primary source of corroboration. It is true that the prosecutor relied on Meacham's testimony in his closing argument. Towery's counsel rebutted this argument in his closing, however, highlighting both Meacham's hearing disability and his expressed uncertainty about what the statement referred to.
Moreover, even granting that Meacham's testimony was important enough for the prosecutor to mention, we still must view that evidence in the context of the case as a whole. The prosecutor asserted from the outset of his closing that his case rested on Barker's testimony. After extensively summarizing Barker's testimony, the prosecutor offered several sources of corroboration. Some of these, such as the stolen items found in Towery's room and the security guard's identification of Towery as one of the people he saw dropping off Jones' car, were technically consistent with Towery's alibi, as he admitted to purchasing items from Barker and being involved in the disposal of Jones' car. However, the prosecutor's strongest source of corroboration was the testimony of Monique Rousseau, who was Barker's girlfriend at the time of the incident. She testified that she heard Towery remark upon seeing gay pornographic photographs found among the stolen items, "[Jones] deserved it. The guy's a pervert."[1] She also testified that Towery took the lead in evenly dividing the stolen money between himself and Barker, and that Barker was in a state of shock, corroborating his testimony that he was unprepared for and horrified by Towery's murder of Jones.
Even though Rousseau was not an ideal witness, given her arguable bias as Barker's girlfriend at the time and her acknowledged drug use, her detailed testimony of the evening's events had substantially more corroborative value than Meacham's equivocal testimony. In sum, the Arizona Supreme Court's harmless error determination was objectively reasonable.
Because we must deny habeas relief if the error is harmless, we would affirm the district court on this ground alone. However, given the stakes involved, we think it is important to analyze the issues thoroughly. We shall therefore explain why Towery's constitutional rights were not violated under any of the clearly established due process frameworks governing prosecutorial misconduct.

2. Napue Violation
The knowing use of false evidence by the state, or the failure to correct false evidence, may violate due process. See Napue, 360 U.S. at 269, 79 S.Ct. 1173. To establish a Napue claim, a petitioner must show that "(1) the testimony (or evidence) was actually false, (2) the prosecution knew or should have known that the *1245 testimony was actually false, and (3) ... the false testimony was material." United States v. Zuno-Arce, 339 F.3d 886, 889 (9th Cir.2003) (citing Napue, 360 U.S. at 269-71, 79 S.Ct. 1173).
We hold that Towery's argument fails at the second Napue prong and thus do not decide whether it would also fail at the first. The state argues there was no false evidence, because Meacham testified accurately about what he had heard and then acknowledged on cross-examination that he thought the statement referred to a different incident. In response, Towery argues that Meacham's testimony "as used in the murder trial" was false. In other words, the testimony, even if technically accurate about what Towery had said, was elicited in a manner that would mislead the jury about what Towery actually meant. There is some support for Towery's view that accurate testimony could be delivered in a sufficiently misleading context to make the evidence false for Napue purposes. Compare United States v. Vozzella, 124 F.3d 389, 390 (2d Cir.1997) (recognizing that Napue applied to "the use of evidence that was in part false and otherwise so misleading as to amount to falsity"), and United States v. Barham, 595 F.2d 231, 240-41 (5th Cir.1979) (holding evidence was false when witnesses testified they had not been offered leniency by "any of the attorneys" or "anybody in the Northern District of Alabama," but had in fact received promises from other authorities), with Byrd v. Collins, 209 F.3d 486, 517 (6th Cir.2000) (noting that "in order to establish a claim of prosecutorial misconduct or denial of due process, ... the defendant must show that the statement in question was `indisputably false,' rather than merely misleading." (quoting United States v. Lochmondy, 890 F.2d 817, 823 (6th Cir.1989))).
We do not decide whether the use of Meacham's testimony was sufficiently misleading to satisfy the first Napue prong, because to satisfy its second prong Towery would in any event still have to show that the state knowingly created a false impression. In Barham, 595 F.2d at 239, for example, the prosecution knew its witnesses had received leniency promises and were answering questions in a very specific manner to create the misleading impression that they had not. Here, by contrast, the prosecutor did not have knowledge of any such underlying facts. Towery argues that Ditsworth knew Meacham believed the statement referred to the robbery incident. But because Towery's statement was actually ambiguous, Meacham's subjective belief about what Towery was referring to is irrelevant. Ditsworth could not have knowingly created a false impression unless he knew what Towery himself meant, and Towery does not argue that Ditsworth had any such knowledge. We therefore hold that Towery's Napue claim fails at the second prong.

3. Brady Violation
Under Brady, "suppression by the prosecution of evidence favorable to an accused upon request violates due process where the evidence is material either to guilt or to punishment, irrespective of the good faith or bad faith of the prosecution." 373 U.S. at 87, 83 S.Ct. 1194. For a Brady claim to succeed, "[t]he evidence at issue must be favorable to the accused, either because it is exculpatory, or because it is impeaching; that evidence must have been suppressed by the State, either willfully or inadvertently; and prejudice must have ensued." Banks v. Dretke, 540 U.S. 668, 691, 124 S.Ct. 1256, 157 L.Ed.2d 1166 (2004) (quoting Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999)) (internal quotation marks omitted).
*1246 Towery argues that the state failed to disclose it had already relied on Meacham's testimony for a different purpose in the previous unrelated robbery case. The state argues that the prosecutor fulfilled his disclosure obligation by informing defense counsel that Meacham had testified in the prior trial. As the Supreme Court made clear in Banks, the prosecution's obligation under Brady includes the disclosure of potential impeachment evidence, and the use of Meacham's testimony for a different purpose would certainly have been a helpful impeachment device. Therefore, the question is whether the prosecutor was obligated to do more than he did to make the defense aware of Meacham's prior testimony and the manner in which it was used.
We agree with the reasoning of United States v. Albanese, 195 F.3d 389, 393 (8th Cir.1999), which held that the government's failure to notify the defense that a witness was testifying inconsistently did not violate Brady. In Albanese, the court reasoned that, because the witness "gave his prior testimony at a public proceeding" and "defense counsel had ample opportunity to learn about [the] prior testimony," there was no Brady violation. Id. Here, as in Albanese, Towery could have obtained Meacham's prior testimony to review for possible inconsistencies and to ascertain how the prosecutor had used it. It is true that the trial court denied Towery a transcript of the robbery trial, but the denial was without prejudice. The court required defense counsel to set forth "some facts which demonstrate an actual need other than the bare conclusion that he needs the transcripts `to prepare a defense.'" There is no evidence that Towery attempted to make such a showing regarding Meacham's testimony or its use at trial. Given these circumstances, we hold that the state's failure to provide more precise information about Meacham's prior testimony did not violate Brady.

4. General Prosecutorial Misconduct
Finally, we note the more general line of authority regarding prosecutorial misconduct and due process. These cases do not address particular forms of misconduct, but instead establish the test for whether some generic misconduct rises to the level of a due process violation. "The relevant question is whether the prosecutors' [misconduct] `so infected the trial with unfairness as to make the resulting conviction a denial of due process.'" Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (quoting Donnelly v. DeChristoforo, 416 U.S. 637, 643, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974)). The Arizona Supreme Court found that there was misconduct even if it was unintentional. Towery, 920 P.2d at 306. Assuming that is so, we need only decide whether the prosecutor's misconduct so tainted the trial as to violate due process.
In section I.D.1, supra, we have held that the Arizona Supreme Court's harmless error determination was objectively reasonable. For the same reasons, we also hold that the court's analysis was correct and that it applies here. Because we agree that "beyond a reasonable doubt... the prosecutor's misconduct did not affect the verdict," Towery, 920 P.2d at 307, we conclude the trial was not significantly "infected" with unfairness. Any misconduct by Ditsworth therefore did not violate due process under the Darden/Donnelly standard.
* * *
Because the Arizona Supreme Court's harmless error determination was objectively reasonable, we hold that Towery is not entitled to habeas relief based on Ditsworth's prosecutorial misconduct. We further hold that any prosecutorial misconduct that did take place did not constitute a violation of due process cognizable in a *1247 federal habeas petition governed by AEDPA.

II. Uncertified Issues
Towery raises several additional claims that were not certified for appeal either by the district court or this court. Under Ninth Circuit Rule 22-1(e), uncertified issues raised on appeal "will be construed as a motion to expand the COA and will be addressed by the merits panel to such extent as it deems appropriate." We grant Towery's motion to expand the COA as to the two claims discussed below, and deny it as to all other claims.

A. Standard of Review for a Certificate of Appealability
A COA should issue if a habeas prisoner can show "that reasonable jurists could debate whether (or, for that matter, agree that) the petition should have been resolved in a different manner or that the issues presented were adequate to deserve encouragement to proceed further." Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000) (internal quotation marks and citation omitted); accord Lambright v. Stewart, 220 F.3d 1022, 1025 (9th Cir.2000). A claim "can be debatable even though every jurist of reason might agree, after the COA has been granted and the case has received full consideration, that petitioner will not prevail." Miller-El v. Cockrell, 537 U.S. 322, 338, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).

B. Judicial Bias at the Murder Trial
We grant Towery's motion to expand the COA on this claim because we conclude that jurists of reason might debate whether it has been procedurally defaulted. See Slack, 529 U.S. at 484, 120 S.Ct. 1595. Nonetheless, we hold that an independent and adequate state default rule applies and federal habeas review is barred.

1. Background
The presiding judge at Towery's murder trial, Judge Hendrix, had previously presided over Towery's trial and conviction for armed robbery. Towery argues that because of this, Judge Hendrix was biased against him at his murder trial and his resulting conviction violates the Due Process Clause. He points to several adverse rulings and statements Judge Hendrix made during the murder trial that he contends show she based some of her rulings on facts she learned outside of that proceeding.
Two different Arizona state courts addressed the judicial bias claim in reasoned decisions. First, Judge Hendrix rejected the claim on the merits in denying Towery's petition for post-conviction relief.[2] Second, Judge Keppel addressed it in Towery's motion for rehearing of the petition for post-conviction relief. Judge Keppel both rejected the claim on the merits and found that it was "precluded under [Arizona Rule of Criminal Procedure] 32.2(a)(3) because it was not raised on direct appeal." The Arizona Supreme Court summarily denied Towery's single petition for further review of both decisions on this claim.
The district court rejected the judicial bias claim in Towery's federal habeas petition, *1248 concluding that Judge Keppel's was the last reasoned state court judgment addressing the claim, see Ylst v. Nunnemaker, 501 U.S. 797, 803, 111 S.Ct. 2590, 115 L.Ed.2d 706 (1991), and that federal habeas review of the claim was barred because Judge Keppel explicitly found a procedural default under state law. See 28 U.S.C. § 2254(d).

2. Analysis
Towery makes a colorable argument that he has successfully exhausted his judicial bias claim before the state courts because (1) Judge Hendrix addressed it on the merits, without applying a state default rule; (2) that decision was never vacated or set aside; and (3) Towery also sought further review before the Arizona Supreme Court. According to Towery, we should ignore Judge Keppel's decision for purposes of federal habeas review because he denied rehearing and left Judge Hendrix's decision in place, even though he did so in a reasoned decision addressing the underlying claims, and Judge Hendrix's decision did not rely on procedural default. Of course, when state courts overlook a procedural default and decide the merits of a federal claim, federal review is not precluded. See Panther v. Hames, 991 F.2d 576, 580 (9th Cir.1993) (per curiam).
Towery's position is ultimately unpersuasive. We cannot ignore Judge Keppel's decision explaining his denial of Towery's motion for rehearing. When it is evident from a state court's decision that the court has actually considered a claim, we will not ignore the decision just because it is technically framed as a denial of rehearing or further review. Cf. Bonner v. Carey, 425 F.3d 1145, 1147, 1148 n. 13 (9th Cir.2005) (according AEDPA deference to a California state court's reasoned denial of a "request for rehearing" of a state habeas petition).
Because Judge Keppel found that relief for the judicial bias claim was barred under an independent and adequate state procedural default rule, it follows that federal habeas relief is also barred. See 28 U.S.C. § 2254(d).[3] Therefore, although we grant Towery's motion to expand the COA because jurists of reason might debate whether his claim was procedurally defaulted, see Slack, 529 U.S. at 484, 120 S.Ct. 1595, we conclude that it was defaulted and deny Towery's habeas petition as to this claim.

C. Ineffective Assistance of Counsel: Failure to Challenge Syringe Testimony
We grant Towery's motion to expand the COA on this claim because we conclude that it is adequate to deserve encouragement to proceed further. Id. Nonetheless, we ultimately reject the claim because, even according Towery's arguments the weight they are due, he has failed to establish that the state court's rejection of this claim was "contrary to, or involved an unreasonable application of, clearly established Federal law ... or was based on an unreasonable determination of the facts in light of the evidence presented." 28 U.S.C. § 2254(d).

1. Background
Barker testified at trial that Towery was the murderer and that, before strangling Jones, Towery had repeatedly and unsuccessfully attempted to inject him with battery acid, using an abnormally large syringe. The County Medical Examiner's testimony also suggested that someone *1249 had made multiple, "not too skillful" attempts to inject the murder victim with an unknown substance. Towery contends his counsel rendered ineffective assistance by failing to introduce evidence that Towery was a skilled intravenous drug user who would not have been so clumsy and would have had access to regular-sized syringes. In Towery's view, this would have impeached the credibility of Barker's testimony and bolstered Towery's alibi, suggesting that Towery was not the murderer.
Towery raised this ineffective assistance claim before the state court in his petition for post-conviction relief. The state court denied the claim, finding that "[a]sking the defendant about his proficiency with a syringe would have been more prejudicial than probative" because "[it] would have unequivocally established defendant as an I.V. drug user" and "telling the jury about defendant's I.V. drug use is more prejudicial than probative." Therefore, according to the state court, Towery could not establish prejudice under Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), because there was "no demonstrable reality that if trial counsel had [challenged the syringe testimony] the outcome of the trial would have been different." The court also noted that "[n]o affidavit ha[d] been provided to substantiate the element that the prevailing professional norms were not met." Towery raised the same claims in his petition for review by the Arizona Supreme Court, which summarily denied review. The district court upheld the state court's decision under AEDPA as a reasonable application of federal law, reaching similar conclusions.

2. Analysis
Both the state post-conviction relief court and the habeas district court understated the impeachment value of evidence showing Towery's skill in intravenous drug use and overstated the likely prejudice from admitting intravenous drug use to the jury.
Regarding impeachment value, the state court opined that Towery "would not have been able to state that `if I had been the one trying to stab the victim with a syringe, I could have done it with greater proficiency.'" The supposed import of this finding is not entirely clear, but the court apparently believed that he could not have benefitted from attacking the plausibility of Barker's testimony ascribing to Towery the clumsy, brutal way the murder was carried out.[4] This reasoning is flawed. To the contrary, casting Barker's testimony as implausible would certainly have bolstered Towery's claim that Barker was lying about who committed the murder, and that the murderer likely was Barker himself, not Towery.[5]
Similarly, the habeas district court concluded that evidence establishing Towery's *1250 skill with needles would have been of limited value because "the jury could readily have concluded that there is a difference in the care and skilled[sic] applied when injecting oneself for the purpose of getting high as opposed to injecting another person with the purpose of killing him." This is true, but a jury could reasonably have reached a contrary conclusion. Considering how important Barker's testimony was to Towery's conviction, the mere fact that an opportunity to impeach might have failed does not necessarily establish that it was reasonable for Towery's counsel not to attempt it.
With regard to likely prejudice, Towery's drug use was already before the jury, a fact neither the state court nor the district court recognized. Among several references to his client's drug use, Towery's counsel explained in his opening statement that it was "not in dispute" that Towery "was using crystal, or speed, or whatever you want to call it" during the time of the murder. He also specifically elicited testimony from Barker that Towery was using methamphetamine, and that Barker and Towery had jointly purchased approximately $400 of methamphetamine immediately after the crime. Although we have not found in the record specific testimony about intravenous drug use, one might reasonably doubt whether the additional prejudicial impact of admitting intravenous drug use would clearly outweigh the evidence's value to Towery's defense.
In light of these considerations, we conclude that this issue is adequate to deserve encouragement to proceed further and therefore grant in part Towery's motion to expand the COA. See Slack, 529 U.S. at 484, 120 S.Ct. 1595. But that does not end the matter. We must still determine if relief is warranted. We conclude that it is not.
Strickland v. Washington and its progeny set a high bar for a criminal defendant to establish that counsel's performance was deficient. See Strickland, 466 U.S. at 689, 104 S.Ct. 2052 ("[A] court must indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance; that is, the defendant must overcome the presumption that, under the circumstances, the challenged action might be considered sound trial strategy." (internal quotation marks and citation omitted)); accord Matylinsky v. Budge, 577 F.3d 1083, 1090-91 (9th Cir.2009). Although both the state post-conviction relief court and the district court understated the potential net value of the syringe evidence Towery claims his trial counsel should have introduced, it is true that additional evidence about Towery's intravenous drug use might have had some prejudicial impact. Indeed, Towery's trial attorney might have deliberately avoided any reference to Towery's intravenous drug use for fear of leading the jury to consider it more likely that Towery was the murderer given his use of and access to hypodermic needles, notwithstanding the evidence that the murder involved an abnormally large needle and multiple, unskilled punctures. Under these circumstances, declining to introduce evidence of Towery's skill with and access to syringes probably did not fall outside "the wide range of reasonable professional assistance." Strickland, 466 U.S. at 689, 104 S.Ct. 2052.
More to the point, even if Towery could establish deficient performance, the state court's explicit holding that there was no prejudice under Strickland's second prong was not "objectively unreasonable." See Lockyer v. Andrade, 538 U.S. 63, 75, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). To establish prejudice, "[t]he defendant must show that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland, 466 U.S. at 694, 104 S.Ct. *1251 2052. Although the evidence about the syringe use was horrific and likely had a strong impact on the jury as well as the sentencing judge, the prejudice analysis must take into account that it was undisputed that the murder was actually accomplished in this clumsy, horrific manner. Towery's alibi defense disputed the identity of the murderer, not the nature of the crime. In this context, establishing Strickland prejudice would require Towery to show that if he had argued to the jurors that he was a skilled intravenous drug injector, there is a reasonable probability that they would have disbelieved Barker's testimony that Towery was the murderer.
Although the state court's analysis was brief, we cannot say that its conclusion that Towery failed to make this showing was objectively unreasonable. Even if evidence of Towery's skill with syringes would not have added to the opprobrium flowing from evidence of his drug use already before the jury, it nonetheless might have led the jury to consider it more likely that Towery was the murderer given his use of and access to hypodermic needles, instead of less likely on the theory that a skilled drug user probably would not have used a big needle and miss veins. More importantly, considerable other evidence linked Towery to the murder, including Jones' gold dental crown and car keys found in Towery's briefcase, other stolen items found in Towery's bedroom, Towery's fingerprint found on the housing of the compact disc player that had been removed from Jones' car and Barker's girlfriend's testimony that Barker and Towery split the stolen money evenly and that Towery showed her photographs taken from the victim's home and said "the guy deserved it."[6] On this record, it was not objectively unreasonable for the state court to conclude that "there is no demonstrable reality that if trial counsel had [introduced this kind of evidence] the outcome of the trial would have been different."
In sum, we hold that this claim was adequate to deserve encouragement to proceed further, see Slack, 529 U.S. at 484, 120 S.Ct. 1595, and therefore grant the motion to expand the COA to include it, but we conclude that federal habeas relief is barred under AEDPA. Although the post-conviction relief court's discussion was brief and not entirely persuasive, it applied the correct standard and reached a result that was not "objectively unreasonable." Lockyer, 538 U.S. at 75, 123 S.Ct. 1166.

III. Conclusion
The district court's denial of habeas corpus is AFFIRMED.
NOTES
[1]  Towery admitted to having made this statement, but indicated that he was referring to what Barker had done to Jones.
[2]  On the same day that he filed his motion for post-conviction relief, Towery moved to disqualify Judge Hendrix from presiding over his post-conviction relief proceedings, alleging bias. Although his motion to disqualify was factually related to the claim that his underlying conviction was unconstitutional because of Judge Hendrix's bias, it was legally distinct. Therefore, that the motion to disqualify was addressed and rejected on the merits has no bearing on whether the due process claim we consider here was exhausted or procedurally defaulted.
[3]  This result is unaffected by the fact that Judge Keppel also addressed the merits of the claim. See Harris v. Reed, 489 U.S. 255, 264 n. 10, 109 S.Ct. 1038, 103 L.Ed.2d 308 (1989); Comer v. Schriro, 480 F.3d 960, 964 n. 6 (9th Cir.2007).
[4]  The relevant discussion in the state court's opinion reads in its entirety:

Asking the defendant about his proficiency with a syringe would have been more prejudicial than probative. It would have unequivocally established defendant as an I.V. drug user. The defendant would not have been able to state that "if I had been the one trying to stab the victim with a syringe, I could have done it with greater proficiency."
The Court has been unable to find the testimony in the transcript that identifies the syringe used on the defendant as an "animal" syringe as opposed to a large syringe. Again, telling the jury about defendant's I.V. drug use is more prejudicial than probative.
[5]  For the same reason, the state's contention that this evidence would have been "inconsistent with, or at least irrelevant to" Towery's alibi defense is wholly unpersuasive. It certainly supports Towery's alibi to argue that the actions of whoever was present that night were not consistent with how Towery himself would have acted had he been there.
[6]  As noted previously, some of this evidence was also technically consistent with Towery's alibi. See section I.D.1, supra.
