ORDER
The opinion filed February 20, 2008, is amended by the opinion filed concurrently with this order. With the filing of the amended opinion, the panel has voted to deny the petition for panel rehearing and the petition for rehearing en banc. The full court has been advised of the petition for rehearing en banc and no judge of the court has called for a vote on en banc rehearing. See Fed. R.App. P. 35(f). The petition for panel rehearing and petition for rehearing en banc are DENIED. No further petitions for rehearing or petitions for rehearing en banc may be filed.
OPINION
Petitioner Daniel Wayne Cook appeals the denial of his 28 U.S.C. § 2254 petition. Cook waived counsel and represented himself at trial through sentencing. A jury convicted him of two counts of first-degree murder and the court sentenced him to death under Arizona Revised Statutes §§ 13-503 and 13-703. Cook now claims that his decision to waive counsel was involuntary because his original appointed trial counsel was ineffective; that his co-defendant, John Eugene Matzke’s plea agreement violated Cook’s right to a fair trial; and that the prosecutor improperly commented on Cook’s failure to testify and his post-Miranda silence. In addition, Cook claims that the trial court erred by failing to instruct the jury on second-degree murder. Cook also argues that the ineffectiveness of his appellate counsel excuses his procedural default of some of his remaining claims. Finally, Cook argues that the sentencing court failed to consider evidence of intoxication and his prior mental health history as mitigating factors before imposing the death penalty. We affirm the district court’s denial of Cook’s petition for a writ of habeas corpus.
On July 19,1987, Cook and Matzke were living together in a two bedroom apartment in Lake Havasu City, Arizona. Carlos Cruz-Ramos, a co-worker at a local restaurant, who recently had moved in with Cook and Matzke, slept on the floor. After Matzke returned from work that afternoon, Cook told Matzke that he knew Ramos had a lot of money and that he wanted to take it. At approximately 6:00 p.m., Cook suggested that Matzke take Ramos upstairs to show him the view from Matzke’s bedroom balcony. After Matzke and Ramos returned downstairs, Ramos discovered his money pouch was missing, and Cook suggested that Ramos look for the pouch upstairs. When Ramos went upstairs, Cook grabbed him, Matzke ripped up some bedsheets, and they tied Ramos to a chair in Cook’s bedroom. Cook punched and taunted Ramos before putting Ramos in Cook’s closet so that Cook and Matzke could look through Ramos’s other possessions. Ramos escaped from the closet, but Cook chased him down, took him back upstairs, and re-tied him to the chair.
Cook and Matzke began beating Ramos with a metal pipe and a stick. Cook and Matzke also burned Ramos’s chest, stomach, and genitals with cigarettes. Cook cut Ramos’s chest with a knife, and Matz-ke put a bandage on the cut to stop the bleeding. At around 9:45 p.m., Matzke went to the Acoma Stop and Shop to buy beer. When Matzke returned to the apartment, he saw Cook sodomize Ramos. Cook also used a mini-stapler on Ramos’s foreskin. Matzke asked Cook why he was torturing Ramos, and Cook replied, “I’m having fun.”
At around 11:00 p.m., Matzke told Cook that they could not let Ramos go, and Cook responded, “Well, you can kill him at midnight; the witching hour.” Cook and Matzke continued torturing Ramos until midnight, then Matzke attempted to strangle Ramos with a sheet and the pipe. Matzke eventually placed Ramos on the floor, placed the pipe across Ramos’s neck, and stood on the pipe until Ramos’s heart stopped beating at around 12:15 a.m. After throwing Ramos’s body down the stairs, Cook and Matzke placed the body in Matz-ke’s closet.
At around 2:30 or 3:00 a.m., Kevin Swa-ney arrived at Cook’s apartment. At first, Cook told Swaney to leave but then Cook asked Swaney to come into the apartment. Cook told Swaney that they had some drugs they wanted to get rid of, and pushed a couch in front of the door so nobody would come into the apartment. Then Cook and Matzke told Swaney about the dead body. Cook took Swaney upstairs to show him the body and, when they returned downstairs, Cook told Matz-ke to get bindings and a gag. Cook forced Swaney to take off his clothes, and Matzke and Cook tied Swaney to a chair. Matzke asked Cook what Cook was planning to do, and Cook said he was going to talk to Swaney. Matzke told Cook that if he was going to torture Swaney, Matzke did not want any part of it. Matzke went to the living room and fell asleep.
At around 4:30 or 5:00 a.m., Cook woke Matzke. Swaney was still tied up and crying. Cook told Matzke that he sodomized Swaney so now they had to kill him. Cook took a sheet from around his neck and wrapped it around Swaney’s neck. Matzke and Cook each took one end of the *1009sheet and pulled, but Matzke’s end kept slipping out of Ms hand. At that point, Cook said “This one’s mine,” put Swaney on the floor, and strangled him. Matzke and Cook took Swaney’s body up to Matz-ke’s room and placed the body in the closet. Matzke and Cook went back downstairs and slept.
That afternoon, Matzke went to work for two and a half hours before quitting because he was concerned about what Cook would do if he was not there. When Matz-ke got home, he and Cook went to a bar and drank for several hours. At 10:30 p.m., they returned to the apartment and met Byron Watkins and other friends by the pool of their apartment complex. Cook and Matzke invited their friends into the apartment. The next morning, Matzke showed Watkins the bodies. Watkins convinced Matzke to go to the police. Matzke and Watkins went to the police department, and Matzke gave a videotaped confession.
Officers responded to the apartment and arrested Cook at around 4:50 a.m. After Detective David Eaton gave Cook Miranda warnings, Cook said, “we got to partying; things got out of hand; now two people are dead.” Cook then said that “my roommate killed one and I killed the other.” He admitted to choking Swaney to death. After making those admissions, Cook refused to make any further statements.
PROCEDURAL HISTORY — TRIAL
On July 21,1987, Cook and Matzke were charged with two counts of first-degree murder, including a death penalty allegation under Arizona Revised Statute § 13-703. Claude Keller was appointed to represent Cook. A grand jury returned an indictment on two counts of first-degree murder against Cook and Matzke.
Cook was given psychological evaluations on October 23, and November 17, 1987. The court held a hearing on January 4, 1988, and concluded that Cook was competent to stand trial. Cook’s counsel filed a motion for an additional mental examination on January 14, 1988, and a neurological examination was performed on or about February 13, 1988. The results of the February 13, 1988, examination were filed with the court.
On April 11, 1988, Cook filed a pro se motion to waive counsel and have his counsel appointed as advisory counsel. During the April 21, 1988, hearing on Cook’s motion to waive counsel, Cook asked for a different advisory counsel, stating, “If you’re amenable to my waiver of counsel, I would ask that you not appoint Mr. Keller as my legal advisor.” Cook explained, “Mr. Keller has worked hard for my defense; cares about the outcome of my trial. My personal beliefs is that he cannot advise me according to my defense.” Cook then asked for Mr. O’Brien to be his advisory counsel, but the court indicated that Mr. Forrester was the only other contract counsel available. Cook rejected Mr. For-rester. Judge Steven F. Conn of the Mohave County Superior Court gave Cook a lengthy explanation of the perils of self-representation. Cook still wanted to represent himself. After conducting extensive questioning pursuant to Faretta v. California, 422 U.S. 806, 835, 95 S.Ct. 2525, 45 L.Ed.2d 562 (1975), the court found that Cook voluntarily, knowingly, and intelligently gave up his right to counsel. The court granted Cook’s motion and appointed Mr. Keller as Cook’s advisory counsel.
Matzke entered into a stipulated guilty plea and executed an agreement to testify truthfully in a manner consistent with his videotaped confession on October 30, 1987. The trial judge sentenced Matzke to twenty years in prison. Cook’s investigators and his advisory counsel attended Matz-*1010ke’s sentencing hearing. Matzke testified at Cook’s trial on June 28, 1988, and again on July 5,1988.
On December 16, 1987, the State filed a motion of potential election and motion to preclude evidence of intoxication. At a hearing on June 24, 1988, Cook did not oppose the motion, stating: “What [the prosecutor] brings up in his motion basically does not even apply to my defense, your Honor.”2 At trial, Cook elected general denial and alibi theories as his affirmative defenses. Cook reiterated that he did not want to present evidence of drinking or drug use by him or Matzke during a pre-trial conference.
Cook also claimed in his opening statement that he “merely repeated the detective’s statement and I asked for an attorney and I have nothing further to say,” and denied confessing. During the trial, Cook questioned Detective Eaton extensively about his contact with Cook on July 21. Cook attempted to discredit Detective Eaton’s testimony that Cook confessed to killing Swaney by asking about the circumstances of the statement and why the statement was not videotaped. Detective Eaton eventually responded that Cook’s confession was not taped because Cook invoked his right to remain silent. Cook asked to approach the bench and later moved for a mistrial. The trial judge denied the motion for a mistrial, finding that Detective Eaton’s testimony was in response to Cook’s line of questioning and a proper explanation for why Cook’s confession was not taped.
In Cook’s closing argument, he attempted to argue that he was not at the apartment, and blamed Matzke and Watkins for the murders. He argued that he could not tell the jury about any party in his apartment, stating, “Mr. Matzke stated in his testimony there was a party that night at the apartment. I couldn’t tell you. I don’t know.” Later, Cook claimed that, “[a]t no time did any of the officers ever state that I confessed to killing someone.” Cook argued extensively about Matzke’s possible motive to lie.
In the prosecutor’s rebuttal argument, he argued that Cook failed to tell defense witness and fellow jail inmate, Terry Holt, where he had been to establish an alibi, and that Cook had something to hide because Cook had covered up his dagger tattoo with a large bandage. In addition, when arguing that Matzke’s videotaped statement was reliable, the prosecutor referred to Cook’s cross-examination of De*1011tective Eaton about why Cook’s statement was not on tape. The prosecutor argued:
John Matzke made [a videotaped statement] and we heard continuous cross-examination of the detective about why the Defendant didn’t make one. He didn’t make one because he, the Defendant, was the one that cut off the interview. If he had made one, you would have had the statements we got to partying a little bit and things got out of hand. My roommate killed one and I killed the other. I killed Kevin. You would have heard the exact same statements.
In addition, the prosecutor commented on the potential witnesses to the crime, stating: “There were only four people there at that time of the deaths; two of them are dead; one is in prison; one is the Defendant.” The prosecutor followed this comment by discrediting Cook’s alibi defense — noting that Cook’s alibi witness was in jail at the time and that a rebuttal witness testified that Cook was present in the apartment on July 19th and 20th. Cook did not object at the time these comments were made, but moved for a mistrial during jury deliberations. The court denied the motion for a mistrial on the same grounds that it denied Cook’s earlier motion after Detective Eaton’s testimony.
After the conclusion of the testimony, the court distributed its proposed jury instructions to Cook and the prosecutor. The judge specifically informed Cook that he did not include any lesser-included instructions or alternative jury verdicts. Cook did not object to a first-degree murder instruction using “knowingly” as the required mental state. Cook requested the second-degree murder instruction because Matzke had pleaded guilty to second-degree murder under the terms of his plea bargain. After hearing argument, the judge concluded that there was no evidence to show a lack of premeditation and denied Cook’s request to give a second-degree murder instruction.
The court gave its instructions, and the jury began deliberations at 2:07 p.m. on July 6, 1988. The jury returned with a guilty verdict on both counts later that afternoon at 3:23 p.m.
Cook filed a motion for further mental health evaluation on July 29,1988. At oral argument on the motion, Cook argued that a post-trial examination under Arizona Rule of Criminal Procedure 26.5 would serve a different purpose from his pretrial examinations under Arizona Rule of Criminal Procedure 11.2. The trial judge heard argument on the motion on August 4,1988, and denied the motion, concluding that, unless Cook could articulate a reason that the Rule 11 examinations were insufficient, there was no reason for further examination. The judge informed Cook that, if he wanted the judge to consider the prior mental health evaluations, the judge would consider them when deciding whether or not there were mitigating circumstances.
At sentencing, Cook declined to present any evidence to the court. Cook complained that he was not given proper access to the Mohave County law library, and then said that the “[o]nly sentence I will accept from this Court at this time is the penalty of death, your Honor. I have nothing further.” The court reviewed the pre-sentence report, the Rule 11 mental health evaluations, the State’s sentencing memorandum, a letter from Cook, the trial evidence, and matters from hearings in the case. The trial judge found the following aggravating factors: 1) that Ramos was killed for pecuniary gain under Arizona Revised Statutes § 13 — 703(F)(4); 2) that the murders of Ramos and Swaney were done in an especially heinous, cruel, or depraved manner under Arizona Revised Statutes § 13-703(F)(6); and 3) that multiple murders were committed under Ari*1012zona Revised Statutes § 13-703(F)(8). When considering Cook’s capacity to appreciate the wrongfulness of his conduct under Arizona Revised Statutes § 13-703(G), the court found that there was insufficient evidence that Cook’s intoxication affected his ability to appreciate the wrongfulness of his conduct. In addition, the judge considered Cook’s prior history of mental illness, suicide attempts, and other mental problems and found that there was no connection between Cook’s prior mental problems and the murders. The court found no mitigating factors to offset the aggravating factors, and sentenced Cook to the death penalty.
PROCEDURAL HISTORY— POST-TRIAL
On direct appeal, Cook raised the following issues: 1) error in denying his Sixth Amendment right to counsel because the trial court allowed him to waive appointed counsel and failed to permit hybrid representation; 2) error in allowing the prosecution to proceed under a “knowingly” rather than “intentionally” theory and in precluding evidence of intoxication; 3) error in refusing to grant a mistrial over the prosecutor’s comments on Cook’s invocation of his Fifth Amendment rights; 4) error in dismissing a juror during trial; 5) error in refusing to continue the trial to allow Cook to secure additional witnesses; 6) error in admitting Cook’s statements at his arraignment; 7) error in admitting of Matzke’s testimony pursuant to a coercive plea agreement; 8) error in refusing to instruct the jury on second-degree murder; 9) finding the multiple homicide aggravating circumstance; 10) finding that Ramos’s murder was especially “cruel, heinous and depraved”; 11) finding Ramos’s murder was for pecuniary gain; 12) finding Swaney’s murder “cruel, heinous and depraved”; 13) precluding of evidence of voluntary intoxication for the purposes of mitigation; 14) failing to consider Cook’s mental health history as a mitigating factor; 15) failing to consider the disparity between Matzke’s and Cook’s sentences; and 16) error in failing to conclude that the Arizona death penalty statute was unconstitutional.3 State v. Cook, 170 Ariz. 40, 821 P.2d 731, 738-39 (1991).
While his direct appeal was pending, Cook asked to have his counsel relieved for failing to communicate with him or explain the issues to him. Cook also filed a petition for post-conviction relief (“PCR”) asserting ineffective assistance of appellate counsel. Cook’s counsel on direct appeal filed an explanation of his position, and moved to withdraw or, in the alternative, to have the Arizona Supreme Court clarify his status. The Arizona Supreme Court denied the motion to withdraw on December 19, 1990. On February 25, 1991, the Arizona Supreme Court issued a minute order finding Cook’s post-conviction petition was premature, appointing a different attorney as counsel for post-conviction proceedings under Arizona Rule of Criminal Procedure 32, and granting additional time to file an amended petition for post-conviction relief if necessary. On December 5, 1991, the Arizona Supreme Court affirmed Cook’s conviction and sentence. Cook, 821 P.2d at 756. The United States Supreme Court denied Cook’s petition for a writ of *1013certiorari. Cook v. Arizona, 506 U.S. 846, 113 S.Ct. 137, 121 L.Ed.2d 90 (1992).
On September 1, 1993, Cook’s PCR counsel filed a Supplement to Petition for Post-Conviction Relief. The supplemental petition raised nine issues: 1) Cook was forced to choose between ineffective counsel and self-representation, denying him of his Sixth Amendment right to counsel; 2) Cook’s counsel was ineffective prior to Cook’s motion to represent himself, therefore the entire trial was tainted; 3) Matz-ke’s testimony was coerced by an unconstitutional plea agreement;4 4) Cook made an unrecorded objection to the testimony of Matzke; 5) Cook was denied access to a law library to prepare his case; 6) the trial court did not conduct the required hearing under State v. Tison, 160 Ariz. 501, 774 P.2d 805 (1989), to determine whether Cook had a reckless indifference to human life under a felony murder theory; 7) the trial court was required to appoint counsel for the penalty phase even if Cook wanted to waive counsel and be put to death; 8) Cook was not competent to represent himself; and 9) Cook’s appellate counsel was ineffective for failing to raise these issues.
On October 5, 1994, the court issued an order finding that issues 5, 6, and 7 were precluded under Arizona Rule of Criminal Procedure 32.2 because Cook failed to preserve them on direct appeal. The court also ruled that issue 9 failed to raise a colorable claim for relief because any failure by appellate counsel to preserve the issue was caused by Cook. The court then scheduled evidentiary hearings on the remaining claims to hear any newly discovered evidence. The court heard evidence on the PCR petition on August 23, 1994, and December 2, 1994, and denied the petition for post-conviction relief on February 3, 1995.
On April 3, 1995, Cook filed a motion for rehearing under the applicable version of Arizona Rule of Criminal Procedure 32.9, requesting rehearing on: the voluntariness of his decision to represent himself (PCR supp. issue 1); the testimony of Matzke and his plea agreement (PCR supp. issue 3); newly discovered evidence of Matzke’s intoxication (a new issue); violation of Cook’s due process rights by the trial judge’s refusal to recuse himself (a new issue); the denial of access to a law library (PCR supp. issue 5); the trial court’s finding that Cook had a reckless disregard for human life (PCR supp. issue 6); and the trial court’s failure to appoint counsel at sentencing to put on a mitigation defense (PCR supp. issue 7). The trial court denied the motion for rehearing on April 13, 1995. Cook filed a timely petition for review pursuant to Arizona Rule of Criminal Procedure 32.9 that relied on the statement of issues in his motion for rehearing. The Arizona Supreme Court denied the petition for review on July 5, 1996. The United States Supreme Court denied a petition for writ of certiorari.
Cook filed his federal habeas petition on January 24, 1997. On February 28, 1997, the district court appointed habeas counsel and granted Cook’s motion to proceed in forma pauperis. Cook advanced twenty-one claims for relief: 1) Cook’s request to represent himself was not knowing, voluntary, and informed because he was forced to choose between ineffective counsel and self-representation; 2) Cook was not competent to represent himself; 3) pre-trial counsel’s ineffectiveness, the refusal to grant a continuance, and the lack of access *1014to the law library denied Cook his Sixth Amendment rights; 4) allowing Cook to exercise his right to represent himself violated the Sixth, Eighth and Fourteenth Amendments; 5) admission of Cook’s statement at arraignment violated his Fifth Amendment right to remain silent and his right to counsel; 6) Matzke’s testimony was coerced by an unconstitutional plea agreement; 7) proceeding under a “knowingly” theory of premeditation and precluding evidence of voluntary intoxication violated Cook’s Sixth Amendment right to call witnesses on his behalf; 8) the prosecutor’s investigation into the excused juror’s activity violated Cook’s right to a trial by jury; 9) refusal to give a second-degree murder instruction violated due process under Beck v. Alabama, 447 U.S. 625, 638, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980); 10) the prosecutor’s comments on Cook’s failure to explain his whereabouts and Cook’s silence violated his Fifth Amendment right to remain silent; 11) the trial court’s determination that Cook had a reckless indifference to human life when committing the murders was unconstitutional; 12) the trial court’s refusal to grant an additional mental health evaluation at sentencing violated Ake v. Oklahoma, 470 U.S. 68, 105 S.Ct. 1087, 84 L.Ed.2d 53 (1985); 13) the failure to appoint counsel for Cook during the penalty phase violated his Eighth Amendment rights and due process; 14) the failure of the trial court to receive evidence of intoxication as mitigating evidence violated Cook’s Eighth Amendment rights; 15) Arizona’s death penalty statute was unconstitutional because it allowed judge-imposed sentences, created a presumption in favor of the death penalty, and shifted the burden of proof concerning aggravating and mitigating factors; 16) the trial court’s failure to consider Cook’s history of neurological trauma, mental dysfunction, and suicide attempts violated his Eighth Amendment rights; 17) the failure of the trial judge to recuse himself after knowingly appointing an incompetent lawyer, accepting Matzke’s coercive plea agreement, and making rulings at trial violated Cook’s right to due process; 18) the trial court erred in finding the murder of Ramos was “cruel, heinous or depraved”; 19) the trial court’s finding that Ramos’s murder was for “pecuniary gain”; 20) the trial court’s finding that Swaney’s murder was “cruel, heinous or depraved”; and 21) the trial court’s finding of multiple homicides as an aggravating factor.
On September 17, 1999, the district court issued an order ruling that claims 7, 11, 12, 13, 17, 18, 19, and 20 were procedurally barred because Cook failed to present them to the Arizona Supreme Court. The district court also ruled that claim 3, except the portion claiming that the denial of continuances deprived Cook of due process, and claim 21, except the portion claiming that the State did not give notice of its intent to seek a multiple homicide aggravating factor, were procedurally barred. The district court then considered the remaining claims on the merits, ruled that Cook was not entitled to relief, and denied Cook’s petition on March 28, 2006. The district court simultaneously issued a certificate of appealability under Federal Rule of Appellate Procedure 22(b) on claims 1, 2, 6, 10, and the procedural default rulings on claims 17 through 20.5 This appeal followed. On October 30, 2007, we issued an order granting a certificate of appealability as to claims 3, 7, 9,12, and 16.
*1015STANDARDS OF REVIEW
Under the Antiterrorism and Effective Death Penalty Act of 1996 (“AED-PA”),6 we may grant habeas relief from a state conviction only if it is contrary to, or an unreasonable application of, clearly established law as determined by the United States Supreme Court, or it was based on an unreasonable determination of the facts in light of the evidence presented in the state courts. See Mitchell v. Esparza, 540 U.S. 12, 15, 124 S.Ct. 7, 157 L.Ed.2d 263 (2003) (per curiam) (discussing AEDPA standards). We review de novo the district court’s decision to grant or deny a petition for a writ of habeas corpus. Clark v. Murphy, 331 F.3d 1062, 1067 (9th Cir.2003). We review the last reasoned state-court judgment to determine whether that decision was contrary to, or unreasonably applied federal law. Ylst v. Nunnemaker, 501 U.S. 797, 803, 111 S.Ct. 2590, 115 L.Ed.2d 706 (1991). A state court decision is “contrary to” federal law if it misstates or fails to identify the controlling Supreme Court precedent or if it reaches a different result in a case that is materially indistinguishable from a Supreme Court case. Williams v. Taylor, 529 U.S. 362, 405-07, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000). A decision is an “unreasonable application” of federal law if it is objectively unreasonable. Id. at 409, 120 S.Ct. 1495.
A state court’s factual determination may not be overturned unless we cannot “reasonably conclude that the finding is supported by the record.” Taylor v. Maddox, 366 F.3d 992, 1000 (9th Cir.2004). The burden of proof rests with the petitioner. Woodford v. Visciotti 537 U.S. 19, 25, 123 S.Ct. 357, 154 L.Ed.2d 279 (2002) (per curiam). We review de novo the failure to exhaust state court remedies. Castillo v. McFadden, 399 F.3d 993, 998 (9th Cir.2005).
DISCUSSION
I. Ineffective assistance of pre-trial counsel.
Cook argues that his pre-trial counsel’s ineffectiveness forced him to choose to represent himself; therefore, his waiver of counsel was not voluntary. Cook also argues that the trial court had a duty to inquire into his reasons for wanting to represent himself, and that the trial court should have discovered pre-trial counsel’s ineffectiveness. The state trial court for Cook’s post-conviction relief petition rejected this argument and found that counsel’s pre-waiver representation was not ineffective. The district court found that there is no Supreme Court case law that requires a trial court, faced with a defendant who wants to represent himself, to inquire why he wants to exercise his right to self-representation.
Under AEDPA, we defer to the state court’s finding that Cook’s waiver of the right to counsel was knowing, intelligent, and voluntary unless it is contrary to or an unreasonable application of Faretta, 422 U.S. 806, 95 S.Ct. 2525. See Weaver v. Palmateer, 455 F.3d 958, 963 n. 6 (9th Cir.2006) (noting standard of review for mixed questions of law and fact), cert. denied, — U.S. -, 128 S.Ct. 177, 169 L.Ed.2d 120 (2007). A state court’s decision may be an “unreasonable application” of Federal law if it “extends or fails to extend a clearly established legal principle to a new context in a way that is objectively unreasonable.” Hernandez v. Small, 282 F.3d 1132, 1142 (9th Cir.2002). In this case, the state trial court’s determination that Cook’s waiver of his right to counsel was voluntary after hearing Cook’s post-conviction relief petition, was not objectively unreasonable. The state trial court first *1016concluded that Cook failed to show prejudice from any of pre-trial counsel’s actions under Strickland v. Washington, 466 U.S. 668, 687, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984) (stating counsel’s actions must fall below an objective standard of reasonableness and be prejudicial in order to constitute ineffective assistance of counsel). The trial court, when denying Cook post-conviction relief, also found that Cook could not point to any specific action that was ineffective. The court noted that evidence of pre-trial counsel’s reputation was insufficient to establish ineffective assistance of counsel.
Those factual determinations are supported by the record. Cook’s claimed prejudice was the lost opportunity to have a stronger presentation on a reasonable doubt defense, to impeach Matzke with Matzke’s intoxication, or to challenge Matzke’s plea agreement. The record is clear, however, that Cook was aware of Matzke’s intoxication, and Cook’s own choice of cross-examination questions cannot be imputed to his former counsel.7 Cook failed to point to any evidence that his original appointed counsel should have uncovered that would create “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. 2052. Therefore, the trial court’s rulings on Cook’s ineffective assistance of counsel claims were not contrary to or unreasonable applications of Strickland.
Finally, the trial court noted that the federal case law cited by Cook involved clearly-expressed dissatisfaction with appointed counsel and that none of the case law created an obligation for trial courts to inquire into the reasons why a defendant wants to represent himself. The Supreme Court has never held that a defendant who does not inform the court that he wants to represent himself because he believes that his counsel is ineffective was coerced into representing himself; therefore, the trial court’s rejection of that argument was not contrary to, or an unreasonable application of Faretta. As noted by the district court, we rejected Cook’s argument that the trial court has a duty to inquire into a defendant’s relationship with counsel when he invokes the right of self-representation in United States v. Robinson, 913 F.2d 712, 716 (9th Cir.1990). In that case, we concluded that a district court only has a duty to inquire into the relationship between defendant and counsel “once a defendant has made a motion or request for substitute counsel.” Id. In addition, we noted that a defendant’s disagreement with counsel over the defenses to pursue does not create the need for further inquiry into the attorney-client relationship or to offer new counsel sua sponte. Id. We held that “a criminal defendant may be asked to choose between waiver and another course of action, so long as the course of action offered is not constitutionally offensive.” Id. at 717.
In this case, like in Robinson, Cook never made a motion for substitute counsel. Although Cook stated that he did not want pre-trial counsel appointed as advisory counsel, he indicated that it was because of the defenses he wanted to advance at trial. When the trial court noted that it could not appoint the attorney Cook requested as his advisory counsel, and offered a local alternative, Cook rejected that option and accepted his previously appointed counsel as advisory counsel.
The trial court then conducted a “probing and thorough” colloquy before finding Cook’s waiver of his right to counsel was *1017knowing, intelligent, and voluntary, satisfying its obligations under Faretta. See Moran v. Godinez, 57 F.3d 690, 699 (9th Cir.1994), overruled on other grounds by Lockyer v. Andrade, 538 U.S. 63, 75-76, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003). The district court and the state trial court properly distinguished the cases cited by Cook because he neither provided notice of ineffective assistance nor moved for substitute counsel. See Schell v. Witek, 218 F.3d 1017, 1024-25 (9th Cir.2000) (en banc) (motion for substitute counsel never addressed); Crandell v. Bunnell, 25 F.3d 754, 754-55 (9th Cir.1994) (per curiam) (defendant informed the court that he had not seen counsel for two months); United States v. Padilla, 819 F.2d 952, 955-56 (10th Cir.1987) (rejecting involuntariness argument where attorneys would not cooperate in presenting defendant’s preferred defense). Therefore, the trial court’s determination that Cook’s decision to represent himself was voluntary was not contrary to or an unreasonable application of Faretta, and Cook is not entitled to habeas relief.
II. Matzke’s plea agreement and the truthfulness of Matzke’s testimony.
Cook contends that his right to a fair trial under the Due Process Clause was violated because Matzke’s testimony was coerced by Matzke’s plea agreement. The agreement required that Matzke “agree to be interviewed without the presence of defense counsel” and that he “agree to testify, if requested, at any criminal proceedings brought by the State of Arizona against Daniel Wayne Cook.” The agreement also required that
Matzke will, during such interviews and during such testimony, provide truthful responses to any questions put to him and will not knowingly make any false or misleading statements. The making by John Eugene Matzke of two or more statements during such testimony or interviews which are inconsistent, so that at least one of them must be false, will be considered a violation of th[e] Agreement without the State[’s] being required to establish which statement was false.
(Emphasis added.) Matzke testified at the PCR hearing that he believed the agreement required him to testify consistently with his initial videotaped confession.
Matzke also testified at the PCR hearing that his testimony at trial was truthful. The trial court found that Matzke testified truthfully, and there was no evidence of perjured testimony as a result of the plea agreement. The district court agreed with the state trial court’s analysis of the case law and found that there is no Supreme Court case law establishing that consistency clauses in plea agreements violate due process. In addition, the district court also found that there was no evidence that Matzke’s testimony was false.
We agree that there is no Supreme Court case law establishing that consistency clauses violate due process or any other constitutional provision. Because it is an open question in the Supreme Court’s jurisprudence, we cannot say “that the state court ‘unreasonably applied clearly established Federal lav^ ” by rejecting Cook’s claim based on the consistency agreement. Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 654, 166 L.Ed.2d 482 (2006).
Although the Supreme Court has held that the knowing use of perjured testimony violates the due process clause, there is no real evidence that Matzke’s testimony was false in this case.8 Matzke *1018reaffirmed the truthfulness of his testimony at the PCR hearing. Although Matzke felt he was still bound by the terms of his agreement to testify consistently, Cook did not produce any witnesses or other evidence that the state knowingly used perjured testimony from Matzke or that Matzke’s account was false. Giving due deference to the state trial court’s factual findings, there was simply no perjured testimony or deliberate deception to support Cook’s claimed due process violation. See Allen v. Woodford, 395 F.3d 979, 995 (9th Cir.2005) (rejecting due process claim where petitioner failed to establish that testimony was false). As a result, Cook is not entitled to relief on his claim that Matzke’s testimony was false because he has not shown falsity, and therefore prejudice from the testimony. See Morris v. Ylst, 447 F.3d 735, 745-46 (9th Cir.2006) (discussing need to show false testimony was prejudicial to obtain habeas relief).
III. The prosecutor’s rebuttal argument.
Cook argues that the prosecutor violated his right to remain silent and right to not testify against himself by referring to Cook’s Miranda invocation and his failure to testify. Cook challenges four types of statements made by the prosecutor:
1. Never once was Terry Holt told by this man where he was. Never once does Dan Cook, ladies and gentlemen say I wasn’t there because I was at McDonald’s in Kingman or out of state or somewhere. Why was he never told where Dan Cook was? Was Dan Cook afraid of getting beaten again when Holt confirmed that he raped a sixteen-year old rather than just reading it out of a newspaper report?
2. And I’ll tell you, ladies and gentlemen, John Matzke doesn’t have anything to hide. This man does.
How do we know that? Remember voir dire when we were selecting everybody? His left forearm has a tattoo of a dagger on it. He has covered that tattoo from the first day of the trial until today. He has had a large Band-Aid over that dagger. He covered that up. I suppose he didn’t want you to think that he does have violent tendencies. If you saw that dagger on his forearm you could suppose that he did have such so he covered it up.
*1019We wonder what else he covered up. But we don’t have to wonder long. We don’t have to wonder hard because he’s done a poor job of covering everything else up.
3. When he says John Matzke is a liar, he is not. No man would underrated [sic] himself to the degree that he did not just with the murders but his lifestyle. He’s not a liar. He was there. He is one of the remaining people who are alive who were there. The other one sits at that table.
There were only four people there at that time of the deaths; two of them are dead; one is in prison; one is the Defendant.
4. And what about the videotape. John Matzke made one and we heard continuous cross-examination of the detective about why the Defendant didn’t make one. He didn’t make one because he, the Defendant, was the one that cut off the interview. If he had made one, you would have had the statements we got to partying a little bit and things got out of hand. My roommate killed one and I killed the other. I killed Kevin. You would have heard the exact same statements.
The Arizona Supreme Court rejected Cook’s claim of error on direct appeal, finding that the prosecutor’s comments were not directed at Cook’s decision not to testify, and that the comment about the videotape was invited by Cook’s cross-examination and argument. Cook, 821 P.2d at 741-43. The district court agreed that the comments were either comments on the state of the evidence or invited by Cook’s arguments and cross-examination. In addition, the district court found that, if there was error, it was harmless under Brecht v. Abrahamson, 507 U.S. 619, 631, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993).
Comment on the refusal to testify at trial violates a defendant’s Fifth Amendment right against self-incrimination. See Griffin v. California, 380 U.S. 609, 615, 85 S.Ct. 1229, 14 L.Ed.2d 106 (1965) (holding “that the Fifth Amendment ... forbids either comment by the prosecution on the accused’s silence or instructions by the court that such silence is evidence of guilt.”). Also, a prosecutor’s comment on a defendant’s post-Miranda silence violates the Due Process Clause. See Doyle v. Ohio, 426 U.S. 610, 619, 96 S.Ct. 2240, 49 L.Ed.2d 91 (1976) (‘We hold that the use for impeachment purposes of petitioners’ silence, at the time of arrest and after receiving Miranda warnings, violated the Due Process Clause of the Fourteenth Amendment.”). The Supreme Court, however, concluded that Griffin error did not mandate automatic reversal if it was harmless. Chapman v. California, 386 U.S. 18, 22, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967); see also United States v. Hasting, 461 U.S. 499, 509, 103 S.Ct. 1974, 76 L.Ed.2d 96 (1983) (holding that Chapman mandates harmless error analysis of Griffin error). In Brecht, the Supreme Court held that Doyle error does not entitle a petitioner to habeas corpus relief unless it ‘“had substantial and injurious effect or influence in determining the jury’s verdict.’ ” 507 U.S. at 622, 113 S.Ct. 1710 (quoting Kotteakos v. United States, 328 U.S. 750, 776, 66 S.Ct. 1239, 90 L.Ed. 1557 (1946)).
The Supreme Court concluded in United States v. Robinson, 485 U.S. 25, 32, 108 S.Ct. 864, 99 L.Ed.2d 23 (1988), that, “where ... the prosecutor’s reference to the defendant’s opportunity to testify is a fair response to a claim made by defendant or his counsel, we think there is no violation of the privilege.” In Robinson, the defendant’s trial counsel “charged that the Government had unfairly denied respondent the opportunity to explain his actions” several times, and “concluded by informing the jury that respondent was not required *1020to testify, and that although it would be natural to draw an adverse inference from respondent’s failure to take the stand, the jury could not and should not do so.” Id. at 27-28, 108 S.Ct. 864. The prosecutor then commented on the insurance fraud defendant’s prior statements to investigators before saying, “[h]e could have taken the stand and explained it to you, anything he wanted to. The United States of America has given him, throughout, the opportunity to explain.” Id. at 28, 108 S.Ct. 864. The Supreme Court held “that the prosecutor’s statement that respondent could have explained to the jury his story did not in the light of the comments by defense counsel infringe upon [the defendant’s Fifth Amendment rights.” Id. at 31, 108 S.Ct. 864.
A. The comment about Cook’s conversations with Holt.
The Arizona Supreme Court and the district court characterized the first argument about Cook’s conversations with Holt as commentary on the evidence. Cook, 821 P.2d at 742. Holt testified that he talked with Cook almost every day and acted as a jailhouse lawyer for Cook. Holt also testified that Matzke told him that Cook was not at the apartment during the murders. On cross-examination, Holt testified that Cook had an alibi defense, but that Cook never told Holt where he was.
Prosecutors may comment on the failure of the defense to produce evidence to support an affirmative defense so long as it does not directly comment on the defendant’s failure to testify. See Lockett v. Ohio, 438 U.S. 586, 595, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) (allowing comments concerning opportunity to call witnesses where defense focused on potential testimony).9 In this case, the prosecutor’s comment was aimed at attacking the credibility of Holt’s testimony concerning the believability of Cook’s alibi defense. At most, the prosecutor’s comment is a reference to Cook’s statements to Holt while in jail together, not a direct comment on Cook’s failure to testify. See Sims v. Brown, 425 F.3d 560, 589 (9th Cir.2005) (no violation from questioning about defendant’s hearsay statements to a witness). The Arizona Supreme Court’s interpretation of this comment was not objectively unreasonable; therefore, there was no Griffin error.
B. The comments concerning Cook’s tattoos.
In addition, the Arizona Supreme Court considered the prosecutor’s comment on Cook’s bandage covering a dagger tattoo to be a rhetorical device rather than a comment “calculated to draw the jury’s attention” to the fact that Cook did not testify. State v. Cook, 821 P.2d at 742. Cook implied during his closing argument that Matzke and Watkins tried to cover up the murders, arguing that Watkins quit his job, disappeared, and helped Matzke dispose of the bodies. The prosecutor’s comment was a response to Cook’s argument that Matzke had a motive to lie and a comment on readily observable facts in the courtroom that did not deprive Cook of a fair trial. See Darden v. Wainwright, 477 U.S. 168, 181, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986) (argument that did not manipulate or misstate evidence or implicate oth*1021er specific rights and was invited by or responsive to the opening summation of the defense of the defendant did not deprive defendant of a fair trial). Read objectively, the prosecutor’s comment was not “manifestly intended to call attention to the defendant’s failure to testify, or is of such a character that the jury would naturally and necessarily take it to be a comment on the failure to testify.” Lincoln v. Sunn, 807 F.2d 805, 809 (9th Cir.1987). Therefore, the state court’s factual finding that this comment was rhetorical is supported by the record and objectively reasonable.
C. The prosecutor’s comments about Cook’s presence at the crime scene.
When evaluating the third group of comments, the district court ruled that the comment arguing that Matzke’s eyewitness testimony was accurate was not intended to call attention to Cook’s failure to testify, and if there was error, it was harmless. Because neither the Arizona Supreme Court nor the state trial court addressed these comments, we review the district court’s decision de novo. See Himes v. Thompson, 336 F.3d 848, 852-53 (9th Cir.2003) (noting this court conducts an “independent review of the record” where there is no reasoned state court decision on an issue). Assuming, without deciding, that the comment was Griffin error, we agree with the district court that any error was harmless.
The Supreme Court held that Griffin error is subject to harmless error analysis in Chapman, 386 U.S. at 22, 87 S.Ct. 824. In Anderson v. Nelson, 390 U.S. 523, 524, 88 S.Ct. 1133, 20 L.Ed.2d 81 (1968) (per curiam), the Court announced that Griffin error is reversible error only “in a case where such comment is extensive, where an inference of guilt from silence is stressed to the jury as a basis of conviction, and where there is evidence that could have supported acquittal.” See also Jeffries v. Blodgett, 988 F.2d 923, 934 (9th Cir.1993) (as amended) (adopting that test). In this case, only two references to Cook being the only eyewitness other than Matzke were made in the prosecutor’s rebuttal argument. Arguably, the prosecutor was not associating guilt from Cook’s silence: rather, the prosecutor merely was emphasizing that Matzke had been an eyewitness.
In addition, the evidence of Cook’s guilt was overwhelming. Although Cook introduced Holt’s testimony that Matzke had confessed to both murders, the jury found Matzke more credible, and there was no physical or other evidence to impeach Matzke. Matzke testified, and the prosecution played Matzke’s videotaped statement before the jury. The physical and forensic evidence largely corroborated Matzke’s story, and there was no physical or forensic evidence showing that Matzke tortured or killed Swaney. In addition, Detective Eaton testified that Cook had admitted to killing Swaney. The jury deliberated for just over an hour before returning a guilty verdict on both counts. Given the strong evidence of Cook’s guilt, and the relatively minor effect of the two references in the context of the prosecutor’s rebuttal argument, it is “clear beyond a reasonable doubt that the jury would have returned a verdict of guilty” even if the prosecution had not referred to his failure to testify. Hasting, 461 U.S. at 511, 103 S.Ct. 1974. Therefore, the district court properly denied Cook’s habeas petition because the prosecutor’s comment in context did not have a “substantial and injurious effect or influence in determining the jury’s verdict.” Brecht, 507 U.S. at 623, 113 S.Ct. 1710 (internal quotation marks omitted).
D. The comment about the lack of a videotaped statement from Cook.
The Arizona Supreme Court and the district court both found that the pros*1022ecutor’s reference to the lack of a videotaped statement from Cook was a fair comment on the evidence and a proper rebuttal to Cook’s denial that he confessed to Detective Eaton. Cook, 821 P.2d at 743. In Cook’s opening statement, he acknowledged that he made inculpatory statements, but claimed that he was merely repeating what the detective told him. Cook also volunteered that he invoked his right to an attorney during his opening statement. Detective Eaton testified that Cook made the following inculpatory statements: “we got to partying; things got out of hand; now two people are dead”; “my roommate killed one and I killed the other”; when asked by Eaton which one Cook killed, he replied, “Kevin”; and when asked if he was solely responsible for Kevin’s death, Cook replied ‘Yeah, I killed Kevin.” Through cross-examination of Detective Eaton, Cook attempted to argue that he never made those statements, evidenced by the lack of a recording of his statements. Cook’s questioning resulted in the following exchange:
Cook: Sir, is it true that everybody else that was interviewed by you was recorded in some way other than myself?
Eaton: We recorded Mr. Matzke. At the conclusion of my interview with you, you requested not to be recorded because you didn’t want to make a statement. We had the tape playing so we recorded Mr. Watkins.
Cook: But you didn’t record me; is that correct?
Eaton: That’s correct. You invoked your right to remain silent and I terminated the interview.
The trial court refused to declare a mistrial based on this exchange, finding that Cook had invited error. After the court denied Cook’s motion for a mistrial, Cook continued questioning Detective Eaton about his failure to videotape Cook’s side of the story. During Cook’s closing statement, Cook returned to this evidence, arguing:
I was — I was arrested on the morning of July 21, 1987 at my apartment. I had been contacted by several police officers prior to my interview with Mr. Eaton. At no time did any of the officers ever state that I confessed to killing someone. They did, however, state Mr. Matzke confessed to them about killing two people.
The prosecutor responded in his rebuttal closing by arguing that, if there had been a videotaped statement, the jury would have seen the statements Detective Eaton testified that Cook made. After Cook objected and moved for a mistrial based on the prosecutor’s statements, the trial court denied the motion, finding that Cook had invited the error by his questioning.
We have interpreted Doyle to allow prosecutors to comment on post -Miranda silence in response to defense arguments. See Bradford v. Stone, 594 F.2d 1294, 1296 (9th Cir.1979) (per curiam), overruled on other grounds by Harris v. Reed, 489 U.S. 255, 109 S.Ct. 1038, 103 L.Ed.2d 308 (1989) (“By electing to dwell on the justifications for petitioner’s silence after arrest, defense counsel opened the door for the prosecutor to suggest contrary inferences.”); see also United States v. Kennedy, 714 F.2d 968, 977 (9th Cir.1983) (allowing invited comment that defendant was “not like every other witness in the case” in response to defense counsel’s argument).
In this case, the state trial court’s interpretation of the comment as a fair comment on the evidence was a reasonable one because Cook attempted to show that he had not made any incriminating statements when he cross-examined Detective Eaton by asking why Cook’s alleged confession was not videotaped. Furthermore, the state trial court’s decision that the prosecutor’s comments were fair rebuttal *1023was reasonable because Cook argued again in his closing that the officers never stated that Cook confessed. The district court properly denied Cook’s habeas petition on his Doyle claim.
IV. Withdrawal of a second-degree murder instruction.
Cook objected to the trial court’s withdrawal of a second-degree murder instruction, however, stating he wanted the instruction because Matzke was given a second-degree murder conviction under the terms of his plea bargain. The trial court concluded that there was no evidence that the murder was not premeditated and denied Cook’s request to give a second-degree murder instruction. On direct appeal, the Arizona Supreme Court affirmed the trial court’s finding that “there was no basis for a jury to find that the murders were committed without premeditation.” Cook, 821 P.2d at 750. The district court agreed with the Arizona Supreme Court that there was no evidence that would permit a rational trier of fact to find that the murders were not premeditated.
In Beck v. Alabama, 447 U.S. at 638, 100 S.Ct. 2382, the Supreme Court held that “if the unavailability of a lesser included offense instruction enhances the risk of an unwarranted conviction, Alabama is constitutionally prohibited from withdrawing that option from the jury in a capital case.” The Supreme Court found that an all-or-nothing approach to capital cases was unfair if the evidence supported a lesser crime; stating that:
[W]hen the evidence unquestionably establishes that the defendant is guilty of a serious, violent offense—but leaves some doubt with respect to an element that would justify conviction of a capital offense—the failure to give the jury the “third option” of convicting on a lesser included offense would seem inevitably to enhance the risk of an unwarranted conviction.
Id. at 637, 100 S.Ct. 2382.
In Hopper v. Evans, 456 U.S. 605, 611, 102 S.Ct. 2049, 72 L.Ed.2d 367 (1982), the Court stated that “due process requires that a lesser included offense instruction be given only when the evidence warrants such an instruction.” The defendant in Hopper “made it crystal clear that he had killed the victim, that he intended to kill him, and that he would do the same thing again in similar circumstances.” Id. at 612, 102 S.Ct. 2049. As a result, “[t]he evidence not only supported the claim that [he] intended to kill the victim, but affirmatively negated any claim that he did not intend to kill the victim. An instruction on the offense of unintentional killing during this robbery was therefore not warranted.” Id. at 613,102 S.Ct. 2049.
At trial, Cook denied the murders and claimed that he had an alibi. Cook affirmatively disclaimed intoxication as a defense prior to trial. Now, Cook argues that his statement “we got to partying, things got out of hand, now two people are dead” was evidence of heat of passion. There was no other evidence introduced at trial, however, that the murders were accidental or were committed in the heat of passion, nor did Cook’s defenses suggest as much. Rather, the evidence demonstrated that Cook planned to rob Ramos, tortured him, and wanted Ramos killed at midnight, and then participated in strangling Ramos. With Swaney, Cook barred Swaney’s exit, took Swaney to see Ramos’s body, tortured and sodomized Swaney, and then said, “this one’s mine” to Matzke before strangling Swaney to death.
At the time the crimes were committed, Arizona defined premeditation to mean:
that the defendant acts with either the intention or the knowledge that he will kill another human being, when such *1024intention or knowledge precedes the killing by a length of time to permit reflection. [A]n act is not done with premeditation if it is the instant effect of a sudden quarrel or heat of passion.
Ariz.Rev.Stat. § 13-1101(1) (1997). In Clabourne v. Lewis, 64 F.3d 1373, 1380 (9th Cir.1995), we affirmed the Arizona Supreme Court’s denial of a habeas petition where the petitioner presented minimal evidence of intoxication and “[t]he evidence that [he] acted with premeditation[was] overwhelming.” We concluded that “[t]o prove premeditation, the state was required to show only that Clab-ourne had had time to reflect after forming the intent to kill; any length of time would have been sufficient, even if it was ‘as instantaneous as [the time] it takes to form successive thoughts in the mind.’ ” Id. (alteration in original) (quoting State v. Neal, 143 Ariz. 93, 692 P.2d 272, 276 (1984)). Because we have similarly interpreted Beck and Hopper not to require a second-degree murder instruction where evidence of premeditation is overwhelming and the petitioner’s defenses are not directed at negating premeditation, the Arizona Supreme Court’s ruling on the issue was objectively reasonable. See Carriger v. Lewis, 971 F.2d 329, 336 (9th Cir.1992) (en banc) (“Further, the record does not support such an instruction. The killer bound Shaw, beat him over the head with a cast iron skillet and a ring sizer, and then strangled him with a necktie. These acts were premeditated and designed to cause death.”). According to Cook’s defenses at trial, either he was not present at the murders, or the murders proceeded as methodically as Matzke described. Therefore, Cook is not entitled to relief.
V. Procedurally defaulted claims.
A. Procedural background.
Cook argues that he did not procedurally default the following substantive claims: 1) that Cook’s pre-trial counsel was ineffective for failing to investigate mitigating evidence (claim 3); 2) that the trial court erred in precluding evidence of Cook’s intoxication during the guilt phase of his trial (claim 7); 3) that the trial court erred in denying Cook’s request for further mental health examination (claim 12); and 4) that the failure of the trial judge to recuse himself violated Cook’s right to a fair trial (claim 17). The state trial court found during the PCR proceedings that Cook failed to raise a colorable claim that his appellate counsel was ineffective (PCR claim 9). After the denial of Cook’s post-conviction relief petition, Cook moved for rehearing on the following issues: 1) Cook’s decision to proceed pro se was not voluntary; 2) Matzke’s plea agreement tainted the fact-finding function of the court; 3) newly discovered evidence of Matzke’s intoxication impeached his credibility; 4) the trial judge’s refusal to recuse himself was unfair; 5) Cook’s entitlement to a hearing on a felony murder theory; and 6) the court’s failure to appoint counsel for sentencing.10 Cook’s petition for review after the denial of the motion for reconsideration simply stated: “Daniel Wayne Cook, through counsel and pursuant to Rule 32.9 of the Arizona Rules of Criminal Procedure, petitions the Arizona Supreme Court for review.”
The district court ruled in its order dated September 17,1999, that most of Cook’s claims were procedurally barred. Regarding Cook’s ineffective assistance of counsel claim (claim 3),11 the district court *1025found that Cook failed to fairly present it because he failed to preserve it in his motion for rehearing. The district court found that Cook failed to present the intoxication evidence at trial (claim 7) as a federal claim on direct appeal, and therefore failed to alert the Arizona Supreme Court that he was raising a federal claim. See Cook, 821 P.2d at 740-41 (relying on Arizona state cases exclusively). The district court concluded that claim 12—con-cerning the trial court’s refusal to grant Cook’s motion for a mental health evaluation prior to sentencing—was procedurally defaulted because Cook never raised the claim on direct appeal or in his post-conviction relief petition. Finally, the district court concluded that Cook failed to present his judicial bias allegations (claim 17) as a federal claim; therefore it was procedurally barred. The district court further found that Cook failed to establish any cause and prejudice for the defaults.
B. Applicable law.
“Before a federal court may grant habeas relief to a state prisoner, the prisoner must exhaust his remedies in state court.” O’Sullivan v. Boerckel, 526 U.S. 838, 842, 119 S.Ct. 1728, 144 L.Ed.2d 1 (1999); see also Rose v. Palmateer, 395 F.3d 1108, 1110 (9th Cir.2005) (“Pursuant to 28 U.S.C. § 2254(b)(1)(A), a federal court may not consider the merits of Rose’s Fifth Amendment claim unless he has exhausted all available state court remedies.”). “[EJxhaustion of state remedies requires that petitioners ‘fairly present’ federal claims to the state courts in order to give the State the opportunity to pass upon and correct alleged violations of its prisoners’ federal rights.” Duncan v. Henry, 513 U.S. 364, 365, 115 S.Ct. 887, 130 L.Ed.2d 865 (1995) (per curiam) (internal quotation marks omitted). We may not “consider any federal-law challenge to a state-court decision unless the federal claim ‘was either addressed by or properly presented to the state court that rendered the decision we have been asked to review.’” Howell v. Mississippi, 543 U.S. 440, 443, 125 S.Ct. 856, 160 L.Ed.2d 873 (2005) (per curiam) (quoting Adams v. Robertson, 520 U.S. 83, 86, 117 S.Ct. 1028, 137 L.Ed.2d 203 (1997) (per curiam)).
Federal courts “will not review a question of federal law decided by a state court if the decision of that court rests on a state law ground that is independent of the federal question and adequate to support the judgment.” Coleman v. Thompson, 501 U.S. 722, 729, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). “This rule applies whether the state law ground is substantive or procedural.” Id.
In all cases in which a state prisoner has defaulted his federal claims in state court pursuant to an independent and adequate state procedural rule, federal habeas review of the claims is barred unless the prisoner can demonstrate cause for the default and actual prejudice as a result of the alleged violation of federal law, or demonstrate that failure to consider the claims will result in a fundamental miscarriage of justice.
Id. at 750, 111 S.Ct. 2546. Where a state prisoner’s federal claim is waived or precluded by violation of a state procedural rule, it is procedurally defaulted unless the prisoner can demonstrate cause and prejudice. See id. at 732, 111 S.Ct. 2546 (noting that “a habeas petitioner who has failed to meet the State’s procedural requirements for presenting his federal claims has deprived the state courts of an opportunity to address those claims in the first instance”); Wainwright v. Sykes, 433 U.S. 72, 87, 97 S.Ct. 2497, 53 L.Ed.2d 594 (1977) (applying cause and prejudice standard to contempo*1026raneous objection rule). Preclusion of issues for failure to present them at an earlier proceeding under Arizona Rule of Criminal Procedure 32.2(a)(3)12 “are independent of federal law because they do not depend upon a federal constitutional ruling on the merits.” Stewart v. Smith, 536 U.S. 856, 860, 122 S.Ct. 2578, 153 L.Ed.2d 762 (2002) (per curiam).
C. Cook procedurally defaulted his ineffective assistance of trial counsel claim (claim S).
Cook’s claim that the amendment of Rule 32.9(c) somehow excuses the failure of his post-conviction relief counsel to preserve general ineffective assistance of trial counsel claims lacks merit because he failed to preserve any ineffective assistance of trial counsel claim under the applicable rule. Furthermore, he cannot demonstrate cause to excuse the procedural default. Cook failed to raise ineffective assistance of counsel on direct appeal. Cook plainly failed to preserve a general ineffective assistance of trial counsel claim in his motion for rehearing. Furthermore, Cook’s petition for review failed to preserve any claims in addition to those preserved by the motion for rehearing.
Prior to 1992, the Arizona Rule of Criminal Procedure 32.9 provided, in relevant part:
a. Motion for Rehearing; Response; Reply. Any party aggrieved by a final decision of the trial court in these proceedings may, within 10 days after the ruling of the court, move the court for a rehearing setting forth in detail the grounds wherein it is believed the court erred. There shall be a response filed within 10 days.
c. Petition for Review. Upon denial of a motion for rehearing, any party aggrieved may petition the appropriate Appellate Court for review of the actions of the trial court. The petition shall be filed with the clerk of the trial court and within 10 days after the denial of the motion for rehearing.
The changes ordered by the Arizona Supreme Court eliminated the requirement of a detailed motion for rehearing — making it optional. Instead, the amended rule made the petition for review into a detailed statement of the case and the issues presented and added an explicit statement that “[fjailure to raise an issue in the petition or cross-petition for review shall constitute a waiver of appellate review of that issue.” The Arizona Supreme Court explicitly made the new rule applicable to those defendants sentenced after December 1, 1992.
Prior to the amendments to Rule 32.9, the failure of the petitioner to file a motion for rehearing setting forth in detail the grounds for rehearing waived further review. See State v. Gause, 112 Ariz. 296, 541 P.2d 396, 397 (1975) (dismissing appeal from denial of post-conviction relief under Rule 32.9(a), where petitioner failed to file a petition for rehearing or a petition for review). When amending Rule 32.9(a) in 1992, the Arizona Supreme Court explicitly stated that “[t]he attached amendments shall be applicable to defendants sentenced after December 1, 1992.” June 2, 1999, Ariz. Supreme Court Order Amending Rule 32, Ariz. R.Crim. P. Furthermore, Cook’s post-conviction relief counsel realized that the former Rule 32.9 governed the case and filed an unopposed motion for *1027rehearing to conform to the old rule. Accordingly, preclusion for failure to preserve the issue on the motion for rehearing was proper under Arizona Rule of Criminal Procedure 32.2(a)(3) and Arizona Rule of Criminal Procedure 32.9(c). As a result, Cook must demonstrate cause and prejudice in order to excuse his procedural default. Coleman, 501 U.S. at 750, 111 S.Ct. 2546.
Ordinarily, “cause” to excuse a default exists if the petitioner “can show that some objective factor external to the defense impeded counsel’s efforts to comply with the State’s procedural rule.” Murray v. Carrier, 477 U.S. 478, 488, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986). Examples of sufficient causes include “a showing that the factual or legal basis for a claim was not reasonably available to counsel,” or “that ‘some interference by officials’ made compliance impracticable.” Id. (citations omitted) (quoting Brown v. Allen, 344 U.S. 443, 486, 73 S.Ct. 397, 97 L.Ed. 469 (1953)). Ineffective assistance of counsel may be cause to excuse a default only if the procedural default was the result of an independent constitutional violation. See Edwards v. Carpenter, 529 U.S. 446, 451, 120 S.Ct. 1587, 146 L.Ed.2d 518 (2000) (“Not just any deficiency in counsel’s performance will do, however; the assistance must have been so ineffective as to violate the Federal Constitution.”). Put another way, “[s]o long as a defendant is represented by counsel whose performance is not constitutionally ineffective under the standard established in Strickland v. Washington, [the federal courts] discern no inequity in requiring him to bear the risk of attorney error that results in a procedural default.” Murray, 477 U.S. at 488, 106 S.Ct. 2639.
In this case, Cook’s post-conviction relief counsel failed to preserve his ineffective assistance of trial counsel claims in the motion for rehearing or in the subsequent petition for review. Thus, post-conviction petition counsel failed to “fairly present” the ineffective assistance of pre-trial counsel claim to the Arizona Supreme Court. Castille v. Peoples, 489 U.S. 346, 351, 109 S.Ct. 1056, 103 L.Ed.2d 380 (1989). Cook attempts to argue that ineffective assistance of appellate counsel excuses the procedural default. There is no constitutional right to counsel, however, in state collateral proceedings after exhaustion of direct review. Pennsylvania v. Finley, 481 U.S. 551, 556, 107 S.Ct. 1990, 95 L.Ed.2d 539 (1987) (“[I]t is the source of that right to a lawyer’s assistance, combined with the nature of the proceedings, that controls the constitutional question. In this case, respondent’s access to a lawyer is the result of the State’s decision, not the command of the United States Constitution.”). Under Arizona law, a defendant is only entitled to counsel through the disposition of his or her first post-conviction petition. State v. Smith, 184 Ariz. 456, 910 P.2d 1, 4 (1996) (“After counsel or the pro per defendant submits the post-conviction petition to the court and the trial court makes its required review and disposition, counsel’s obligations are at an end.”). Because Cook had no constitutional right to counsel at the motion for rehearing stage, any errors by his counsel could not constitute cause to excuse the default. See Coleman, 501 U.S. at 752-53, 111 S.Ct. 2546 (“Consequently, a petitioner cannot claim constitutionally ineffective assistance of counsel in [state post-conviction] proceedings.”); Harris v. Vasquez, 949 F.2d 1497, 1513-14 (9th Cir.1990) (“Because [the petitioner] has no constitutional right to counsel in his earlier habeas proceedings, no error by his habeas counsel could constitute a sixth amendment violation or, therefore, cause.... ” *1028(citation omitted)). Therefore, Cook cannot show cause to excuse his procedural default.13
Cook may also qualify for relief from his procedural default if he can show that the procedural default would result in a “fundamental miscarriage of justice.” Schlup v. Delo, 513 U.S. 298, 321, 115 S.Ct. 851, 130 L.Ed.2d 808 (1995). To qualify for the “fundamental miscarriage of justice” exception to the procedural default rule, however, Cook must show that a constitutional violation has “probably resulted” in the conviction when he was “actually innocent”, of the offense. Murray, 477 U.S. at 496, 106 S.Ct. 2639. “To be credible, such a claim requires petitioner to support his allegations of constitutional error with new reliable evidence— whether it be exculpatory scientific evidence, trustworthy eye-witness accounts, or critical physical evidence'—-that was not presented at trial.” Schlup, 513 U.S. at 324, 115 S.Ct. 851.
In this case, although Cook presented evidence concerning his pre-trial counsel’s reputation in the community, he did not present any evidence that there were actual independent witnesses to support an alibi defense, or that shows that he did not participate in the murders of Ramos and Swaney. As a result, Cook has not shown that pre-trial counsel’s ineffective assistance of counsel, if any, resulted in a fundamental miscarriage of justice because he is actually innocent. Therefore, Cook cannot excuse his procedural default and the district court properly found that his ineffective assistance of trial counsel claim was barred from review.
D. Cook procedurally defaulted his claim that precluding evidence of intoxication violated his constitutional rights (claim 7).
On direct appeal, Cook relied exclusively on state law in arguing his claim that voluntary intoxication negated his premeditation for the murder of Ramos. First, the Arizona Supreme Court found that Cook waived this claim by failing to object at trial. Cook, 821 P.2d at 741. Then, the Arizona Supreme Court ruled that Cook failed to establish fundamental error, relying entirely on state law. Id. at 740-41. Under Arizona law, evidence of intoxication alone cannot negate knowledge for the purposes of finding premeditation for first-degree murder. See State v. Schurz, 176 Ariz. 46, 859 P.2d 156, 164-65 (1993) (collecting cases approving of refusal to consider voluntary intoxication under a knowing or knowingly first-degree murder theory); Neal, 692 P.2d at 277 (“[E]ven assuming Neal was intoxicated and the jury believed Dr. Biegal’s testimony, the jury could still properly convict him of first degree murder if they believed he ‘knowingly’ caused the victim’s death.”).
“A litigant wishing to raise a federal issue can easily indicate the federal law basis for his claim in a state-court petition or brief ... by citing in conjunction with the claim the federal source of law on which he relies or a case deciding such a claim on federal grounds, or by simply labeling the claim ‘federal.’ ” Baldwin v. Reese, 541 U.S. 27, 32, 124 S.Ct. 1347, 158 L.Ed.2d 64 (2004). If a petitioner fails to properly present a federal claim to the state supreme court, and the state supreme court decides the issue on “adequate and independent” state law grounds, *1029federal courts are barred from reviewing the claim. Howell, 543 U.S. at 442-43 (dismissing writ of certiorari as improvidently granted because petitioner’s failure to present a federal claim to the state supreme court “prevents us from reaching petitioner’s constitutional claim.”).
Here, Cook waived this claim by failing to object at trial and then procedurally defaulted the claim by failing to fairly present it as a federal claim on direct appeal. See Coleman, 501 U.S. at 729, 111 S.Ct. 2546 (failure to present federal claim); Wainwright, 433 U.S. at 87, 97 S.Ct. 2497 (failure to object at trial). Exclusive citation to Arizona state court cases in a counseled petition for review is not sufficient to give a “fair opportunity” to the Arizona Supreme Court to decide a federal claim. Peterson v. Lampert, 319 F.3d 1153, 1159 (en banc) (9th Cir.2003). Because Cook failed to raise an ineffective assistance of appellate counsel claim on this issue, and cannot raise an ineffective assistance of counsel claim as to his own performance under Faretta, 422 U.S. at 834 n. 46, 95 S.Ct. 2525, he cannot show cause to excuse his defaults. See Murray, 477 U.S. at 488, 106 S.Ct 2639.
As noted above, evidence of voluntary intoxication alone cannot negate premeditation under Arizona law. See State v. Lavers, 168 Ariz. 376, 814 P.2d 333, 346 (1991) (approving of State’s strategy to charge “knowingly” rather than “intentionally” to preclude introduction of evidence of defendant’s intoxication). Therefore, Cook cannot establish actual innocence based on voluntary intoxication. Furthermore, there is no new evidence to support an actual innocence claim. Schlup, 513 U.S. at 324, 115 S.Ct. 851. Therefore, the district court properly found that Cook procedurally defaulted his claim that the preclusion of voluntary intoxication evidence was erroneous.
E. Cook procedurally defaulted his claim that the trial court erred by failing to order an additional mental health examination prior to sentencing (claim 12).
Cook failed to present the issue of an additional mental health examination prior to sentencing on direct appeal or in his post-conviction relief proceedings. Like his other procedurally defaulted claims, Cook cannot establish cause to excuse the default by showing a non-defaulted claim of ineffective assistance of appellate counsel. Murray, 477 U.S. at 488, 106 S.Ct. 2639. In addition, Cook did not introduce any new evidence to support a finding that there would be a fundamental miscarriage of justice because he was legally insane at the time of the murders, or that his mental state was sufficient to overcome the aggravating factors in his case. See Sawyer v. Whitley, 505 U.S. 333, 350, 112 S.Ct. 2514, 120 L.Ed.2d 269 (1992) (requiring petitioner “to show by clear and convincing evidence that but for constitutional error at his sentencing hearing, no reasonable juror would have found him eligible for the death penalty understate] law”). Therefore, the district court properly found that Cook procedurally defaulted this claim.
F. Cook’s claim that the trial judge should have recused himself is barred (claim 17).
On his claim that the trial judge was biased and should have recused himself, Cook argues that he fairly presented the claim to the Arizona Supreme Court through his petition for special action. The district court found that Cook relied exclusively on Arizona law when arguing that the trial judge should have recused himself. The district court found that the federal claim was technically exhausted, but that the state courts would find that *1030the claim was precluded under Arizona Rule of Criminal Procedure 32.2(a)(3).
In Cook’s recusal motion during the PCR proceedings, he only cited Arizona state cases and Arizona Rule of Criminal Procedure 10.114 and 32.4(e).15 After an independent judge denied the recusal motion, Cook sought special relief, citing the same rules and Rule 81, Canon 3(c) of the Arizona Rules of Judicial Conduct, which states that a judge should disqualify himself if his impartiality may be reasonably questioned or where the judge has a personal knowledge of disputed evidentiary facts concerning the proceeding. In his motion for rehearing, Cook once again relied exclusively on Arizona state law in arguing that the trial judge was biased and should be recused.
Cook failed to “indicate a federal law basis for his claim in a state-court petition or brief’ as required by Baldwin, 541 U.S. at 32, 124 S.Ct. 1347. See Peterson, 319 F.3d at 1159. Mere invocations of due process do not meet the “minimal requirement that it must be clear that a federal claim was presented.” Adams, 520 U.S. at 89 n. 3, 117 S.Ct. 1028. Even if Arizona’s standards for determining judicial bias are “somewhat similar” to the federal standard requiring a direct, personal, substantial, pecuniary interest in Tumey v. Ohio, 273 U.S. 510, 522, 47 S.Ct. 437, 71 L.Ed. 749 (1927), that is insufficient to raise a federal claim. See Duncan, 513 U.S. at 366, 115 S.Ct. 887 (“[M]ere similarity of claims is insufficient to exhaust.”). Failure to exhaust the claim bars federal review. See Fields v. Waddington, 401 F.3d 1018, 1020-21 (9th Cir.2005) (discussing standards for fairly presenting a federal claim). Furthermore, the district court was correct in concluding that the state courts would find the federal claim precluded under Arizona Rule of Criminal Procedure 32.2. See Peterson, 319 F.3d at 1161 (noting failure to fairly present federal claim coupled with time limits for filing petition for review procedurally defaults the claim, requiring a showing of cause and prejudice).
As with Cook’s other claims, he has not shown cause to excuse his procedural default. Nor has Cook established that the default results in any fundamental miscarriage of justice. Therefore, the district court properly found that Cook’s claim concerning the bias of the trial judge was procedurally defaulted.
YI. Sentencing consideration claims.
The Arizona Supreme Court examined the record and concluded that:
Moreover, after conducting our independent review of the record, we do not believe that Cook’s mental history demands or even justifies leniency, especially when balanced against the aggravating factors found to be present in this case.
Cook, 821 P.2d at 755. “AEDPA also requires federal habeas courts to presume the correctness of state courts’ factual findings unless applicants rebut this presumption with ‘clear and convincing evidence.’ ” Schriro v. Landrigan, — U.S. -, 127 S.Ct. 1933, 1939-40, 167 L.Ed.2d 836 (2007) (quoting 28 U.S.C. § 2254(e)(1)). “Under AEDPA, we must do more than *1031find the statement ambiguous — we would have to conclude that the Arizona Supreme Court was objectively unreasonable in concluding the sentencing court did, in fact review all the proffered mitigating evidence.” Lopez v. Schriro, 491 F.3d 1029, 1037-38 (9th Cir.2007), cert. denied, — U.S.-, 128 S.Ct. 1227, 170 L.Ed.2d 140 (2007).
The Arizona Supreme Court’s analysis is precisely what the Supreme Court requires — consideration of the character and record of the individual and the circumstances of the offense. See Woodson v. N. Carolina, 428 U.S. 280, 304, 96 S.Ct. 2978, 49 L.Ed.2d 944 (1976) (requiring “consideration of the character and record of the individual offender and the circumstances of the particular offense as a constitutionally indispensable part of the process of inflicting the penalty of death”). The record contains extensive testimony concerning intoxication at the post-conviction relief hearing and that supports the rejection of Cook’s argument.
The record also contains psychological reports discussing Cook’s prior history of mental illness that show that Cook was able to appreciate the wrongfulness of his actions at the time of the murders. None of the psychiatric or psychological reports state that Cook did not understand what he was doing or could not conform his activity to the confines of the law at the time of the murders. The Arizona Supreme Court’s conclusion that the mitigating factors did not outweigh the aggravating factors after considering both intoxication and Cook’s psychological history as mitigation was not objectively unreasonable on this record. See Lopez, 491 F.3d at 1037-38 (concluding that where the state court clearly considered proper mitigating factors, this court could not reverse under AEDPA). Therefore, the district court properly denied Cook’s claim based on failure to consider mitigating factors.
CONCLUSION
Cook’s decision to represent himself was knowing, intelligent, and voluntary as required by Faretta. Matzke’s plea agreement did not taint Cook’s trial with perjured or untruthful testimony; therefore it did not violate Cook’s due process right to a fair trial as clearly established by Supreme Court precedent. The prosecutor’s comments in rebuttal were not comments on Cook’s silence: they were fair comments on the evidence or fair rebuttals to Cook’s arguments and defenses, and in the context of this trial were harmless.
There was no evidence to warrant a second-degree murder instruction, so the trial court properly refused to give a lesser included offense instruction. The sentencing court properly considered Cook’s intoxication and mental history and concluded that they did not outweigh the aggravating factors in this case. Finally, the district court properly found Cook’s remaining claims to be procedurally defaulted.
AFFIRMED.