
653 F.3d 790 (2011)
Richard Harley GREENWAY, Petitioner-Appellant,
v.
Dora B. SCHRIRO, Respondent-Appellee.
No. 07-99021.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted January 13, 2010.
Filed July 28, 2011.
*792 Therese M. Day, Assistant Federal Public Defender, Phoenix, AZ, for petitioner/appellant Richard Harley Greenway.
*793 Jeffrey Alan Zick, Assistant Attorney General, Phoenix, AZ, for respondent-appellee Dora B. Schriro.
Before: MARY M. SCHROEDER, JOHNNIE B. RAWLINSON, and CARLOS T. BEA, Circuit Judges.

OPINION
SCHROEDER, Circuit Judge:
Petitioner, Richard Harley Greenway, was convicted and sentenced to death in 1989 for the 1988 murders of Lili Champagne and her daughter, Mindy Peters. After the Arizona state courts denied Greenway's post-conviction petition for relief, he filed a petition for federal habeas relief under 28 U.S.C. § 2254, which the district court denied. On appeal, Greenway is seeking relief on a number of different claims, but we affirm the denial of all except those relating to ineffective assistance of counsel at trial and on direct appeal.
Greenway's most colorful claim is that the trial judge should have been disqualified from hearing the case because the trial judge himself once briefly worked with the man who had been the husband of victims Lili Champagne and the father of Mindy Peters. The evidence Greenway presented shows, at best, however, that the judge may have had a brief working relationship eighteen years before the trial, with the man who had, by the time of trial, been dead more than eleven years. We agree with the district court that there was no showing of any impropriety or appearance of impropriety.
We affirm the denial of the claims of ineffective assistance of counsel at sentencing because we conclude they lack merit. We agree with the district court that the state courts adequately considered all mitigating evidence in sentencing Greenway to death, and therefore affirm denial of that claim as lacking merit as well.
The record with respect to the claims of ineffective assistance at trial and on appeal is procedurally complex, but we conclude those claims are not procedurally barred and remand for the district court to consider their merits. After the state trial court denied Greenway's initial post-conviction petition, the Supreme Court of Arizona declined to accept jurisdiction of Greenway's Petition for Special Action to consider those claims, but it did so without prejudice to Greenway's filing a motion with the trial court for reconsideration. Greenway then went back to the trial court to file the motion and to amend his initial post-conviction petition to include additional claims of ineffective assistance of counsel at trial and on direct appeal. The trial court, however, denied the motion and declined to consider these additional claims on the ground that they had been offered too late and were barred by waiver. The district court held this was an adequate and independent state ground justifying dismissal of the claims. The relevant state rule, Rule 32.2(a)(3) of the Arizona Rules of Criminal Procedure, however, provides for waiver of claims not raised in "previous collateral proceedings." Since Greenway was still pursuing his first post-conviction petition when, in accordance with the suggestion of the state supreme court, he sought to amend his first petition, there was no "previous collateral proceeding." Hence, there was no adequate and independent state ground supporting the trial court's refusal to hear the claims of ineffective assistance at trial and on direct appeal. We therefore remand only those claims for consideration by the district court.


*794 I. FACTS AND PROCEDURAL BACKGROUND

A. The Crimes
The facts surrounding the cold-blooded murders of Lili Champagne and Mindy Peters are contained in the Arizona Supreme Court's opinion. State v. Greenway, 170 Ariz. 155, 823 P.2d 22 (1991). We summarize them here.
On March 28, 1988, Pima County Sheriffs found a burned 1983 Porsche, which officials determined belonged to Frank and Lili Champagne. A deputy went to inform the Champagnes at their home and discovered the bodies of Lili Champagne and her daughter, Mindy Peters. Lili had been shot once behind the knee and once between the eyes. Mindy had been shot twice, once in the jaw and once behind the ear. Id. at 25.
Following a news bulletin asking for information regarding the victims or the Porsche, Greenway's sister notified homicide detectives that Greenway knew something about the incident. After detectives picked up Greenway at his sister's house, Greenway told detectives that he had met a man named "Red" at a 7-Eleven convenience store, and that Red had given both Greenway and his co-defendant, Chris Lincoln, a ride in a white Porsche. Id. at 25-26.
The detectives then took Greenway and Lincoln to the police station for questioning. Greenway and Lincoln were questioned separately. Lincoln confessed to stealing and burning the Porsche, and he implicated Greenway. During further questioning, Lincoln confessed to participating in the killings and again implicated Greenway. Greenway and Lincoln were then both arrested and charged with several counts, including the murders of Lili and Mindy.
Greenway was placed in a cell with Anthony Schmanski. Schmanski, according to his trial testimony, asked Greenway why Greenway was in jail, and Greenway answered, "Well, I just blew two people away" because "they had seen [my] face." Id. at 26. Further investigation revealed that Greenway had attempted to sell the victims' car stereo to Brian Mize, Greenway's co-worker. According to Mize's trial testimony, Greenway told Mize that Greenway went to the victims' house and after taking "some stuff" from the house, Greenway sent his co-defendant out and then shot the victims. Greenway told Mize that, after he shot the older lady, "her body rolled over and blood gushed out of her head." Id.
There was also evidence that Greenway knew the victims. He met Mindy late in 1987 at a local Jack-in-the-Box fast food restaurant, and met Lili soon after, when Greenway went to Lili's house to return Mindy's wallet. Id.

B. Trial and Sentencing Proceedings
Greenway was charged with two counts of first degree murder, one count of first degree burglary, one count of armed robbery, one count of theft by control, and one count of arson. Prior to trial, the trial court ordered a mental examination of Greenway. Dr. Ronald David, a psychiatrist, interviewed Greenway about his past history, his family background, drug use, the circumstances surrounding the crimes, and asked Greenway questions in order to ascertain his mental status. Dr. David also asked Dr. Harry Saslow, a psychologist, to conduct a psychological evaluation of Greenway.
Greenway's trial began on March 14, 1989, and Judge William Scholl presided. The guilt phase lasted only three days, and the jury returned a guilty verdict on all counts on March 17, 1989. In accordance with Arizona law at the time, the trial judge made the life or death sentencing *795 decision after an aggravation-mitigation hearing. In this case, that hearing took place on May 24, 1989, and extended over a two-day period.
The defense originally wanted to call Dr. David to testify at the sentencing hearing, because he was familiar with Greenway's mental deficiencies, social problems, and miserable family background. Dr. David, however, was also familiar with Greenway's admissions about how he committed the crimes, so the trial court ruled that if Dr. David were called, he could be cross-examined on Greenway's incriminating statements. The defense therefore chose not to call Dr. David, and instead made a proffer that Dr. David would have testified that Greenway's I.Q. was low, that he had an immature personality, that he was not a psychopath or sociopath, and that he could be rehabilitated. The defense actually called the other medical expert who had examined Greenway, Dr. Saslow, to testify along with the defense investigator and lay witnesses, including Greenway's mother, half-sister, brother-in-law, former co-worker, and childhood friend.
On June 15, 1989, Judge Scholl found one mitigating factor, Greenway's age, which was nineteen at the time of the crimes, and three statutory aggravating factors: (1) the murders were committed for pecuniary gain; (2) the murders were committed in a cruel, heinous, or depraved manner; and (3) the defendant had been convicted of another homicide, which was committed during the commission of each homicide offense. Greenway, 823 P.2d at 30-34.
The judge sentenced Greenway to death on the two first degree murder counts. On direct appeal to the Arizona Supreme Court, Greenway challenged his convictions, the constitutionality of Arizona's death penalty statute, and his capital sentence. Greenway could not bring any claims of ineffective assistance of counsel on direct appeal, because in Arizona, "ineffective assistance of counsel claims should be raised in post-conviction relief proceedings pursuant to rule 32, Arizona Rules of Criminal Procedure." Lambright v. Stewart, 241 F.3d 1201, 1203-04 (9th Cir.2001).
On December 3, 1991, the Arizona Supreme Court affirmed Greenway's convictions and sentence. Greenway, 823 P.2d at 40. With respect to the death penalty, it concluded that the Arizona death penalty statute was constitutional and the death sentence was imposed in a fair and impartial manner. After an independent review, it found that a death sentence was an appropriate punishment. Id. at 35-38.

C. Post-conviction Proceedings
Greenway filed his pro se preliminary petition for post-conviction relief under Rule 32 of the Arizona Rules of Criminal Procedure ("Rule 32 petition") in state court in August 1992. Judge Scholl appointed counsel and ordered counsel to file an amended petition by February 1, 1993. Counsel then filed a short, untimely petition raising only one issue of ineffective assistance of counsel at sentencing, and Greenway asked for a change of counsel that his attorney did not oppose. No further pleadings or proof were entered by counsel pending the change of counsel ruling. The trial judge, however, in January 1994, summarily denied the post-conviction petition in a minute order, without ruling on the request for change of counsel. The trial court subsequently granted Greenway's motion to proceed in propria persona and allowed him to file a motion for reconsideration.
In April 1994, Greenway, with new counsel, moved to vacate the denial of the inadequate post-conviction petition, but the trial court denied that motion as well. Greenway then filed a petition for special action with the Arizona Supreme Court. *796 Although the Arizona Supreme Court declined to accept jurisdiction of Greenway's petition, it stated that it did so without prejudice to Greenway's filing a motion with the trial court for reconsideration of the denial of post-conviction relief.
Before Greenway filed a motion for reconsideration, his counsel learned through a juror that Judge Scholl, during the trial, had told a juror that when the judge was working for law enforcement, he had a colleague who had earlier been married to Lili Champagne and had fathered Mindy Peters. In December 1994, Greenway filed a motion to disqualify Judge Scholl, but in January 1996, the motion was denied as moot because Judge Scholl was no longer on the bench.
The case was reassigned to a different judge in January 1996. Greenway then filed the motion with the trial court seeking reconsideration of its denial of his post-conviction petition. The motion also sought leave to amend the initial petition to add additional facts to support his claims of ineffective assistance of counsel at sentencing, additional claims of ineffective assistance of counsel at other stages of the litigation, including at trial and on direct appeal, and a claim of judicial bias. The new state court judge found Greenway's claims of ineffective assistance of counsel at sentencing precluded by Arizona Rule of Criminal Procedure 32.2(a)(2) because they had already been raised and denied on the merits. The judge also concluded that Greenway's additional claims of ineffective assistance of counsel at other stages of the litigation were waived under Rule 32.2(a)(3) because they had not been raised when the initial post-conviction petition was filed. The court denied the judicial bias claim as moot in light of the state supreme court's independent review of the sentence.
Greenway again petitioned the Arizona Supreme Court to order the trial court to consider the amended petition. On October 22, 1997, the supreme court entered an order purporting to decline review of the state trial court's denial of the motion for reconsideration, but also granting the request for leave to amend the post-conviction petition. After sparring between the parties, however, in which each interpreted the order differently, the Arizona Supreme Court, on January 6, 1998, vacated the portion of that order granting the request for leave to amend the petition. The court then amended its order to deny the requested relief in its entirety.
This habeas petition in federal district court followed in 1998. In September 2007, after a number of interim rulings, the district court eventually denied the petition. During much of the intervening period, proceedings were stayed while the district court awaited exhaustion of claims relating to the constitutionality of Greenway's death sentence. See Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002) (holding unconstitutional the Arizona statute allowing a trial judge, sitting without a jury, to impose the death penalty). In addition, during the interim period, the Court decided Atkins v. Virginia, 536 U.S. 304, 122 S.Ct. 2242, 153 L.Ed.2d 335 (2002), which held that executions of mentally retarded criminals violate the Eighth Amendment. Greenway therefore filed a successive post-conviction petition in state court alleging that he was entitled to a new sentencing under Ring and that he was mentally retarded.
The United States Supreme Court in 2004 ruled that Ring did not apply retroactively. Schriro v. Summerlin, 542 U.S. 348, 124 S.Ct. 2519, 159 L.Ed.2d 442 (2004). With respect to the Atkins claim, Greenway's expert eventually concluded in the state proceedings that Greenway did not meet the criteria for mental retardation, *797 thus paving the way for the district court to consider the remaining claims.
In its denial of Greenway's habeas petition, the district court dismissed as procedurally barred the claims that he received ineffective assistance of counsel during trial and on direct appeal. It held that the state court's ruling that the claims were waived was an adequate and independent state ground supporting denial. It also dismissed, as barred, the claim that counsel failed to investigate and present mitigating evidence during the sentencing hearings. The district court dismissed on the merits Greenway's ineffective assistance of counsel claims relating to psychological evidence, and, also on the merits, dismissed Greenway's judicial bias claim. Finally, the district court found that the Arizona state courts properly considered all the mitigating evidence that was presented during the sentencing phase.
Greenway timely appealed the district court's denial of his habeas relief petition. On appeal, Greenway asserts that the district court erred by not reaching the merits of his claims of ineffective assistance of counsel at trial and on direct appeal because he contends the procedural rule that the state court relied upon is not an independent or adequate bar to federal review. Greenway also challenges the district court's ruling that his claim of ineffective assistance of counsel relating to mitigating evidence was barred. As for his claim of ineffective assistance of counsel relating to psychological evidence, Greenway contends the district court erred on the merits and that his counsel's performance was deficient. Lastly, Greenway posits that the district court erred by denying Greenway an evidentiary hearing on his judicial bias claim and by finding that the state courts properly considered and gave effect to mitigating evidence in sentencing Greenway to death.

II. DISCUSSION

A. AEDPA Applicability
Because Greenway filed his petition for writ of habeas corpus after April 24, 1996, the Antiterrorism and Effective Death Penalty Act ("AEDPA") applies. Lindh v. Murphy, 521 U.S. 320, 327, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997). Under AEDPA, we may disturb the state court's rulings only if they were "contrary to" or "involved an unreasonable application of" clearly established federal law as determined by the United States Supreme Court. 28 U.S.C. § 2254(d)(1). On appeal, however, we review de novo the district court's denial of a petition for habeas corpus relief. See Scott v. Schriro, 567 F.3d 573, 580 (9th Cir.2009).

B. Ineffective Assistance of Counsel During Trial and on Direct Appeal
The district court concluded that all of Greenway's claims of ineffective assistance of counsel, both at trial and on direct appeal, were procedurally barred by Arizona Criminal Procedure Rule 32.2(a)(3), which the district court found was consistently and regularly followed in Arizona and therefore constituted an independent and adequate ground upon which a procedural default may be found.
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." See Coleman v. Thompson, 501 U.S. 722, 729, 111 S.Ct. 2546, 115 L.Ed.2d 640 (1991). To constitute an independent and adequate state procedural ground creating a procedural bar to consideration of claims in the federal court, a state rule must be clear, consistently applied, and well-established at the *798 time of a petitioner's purported default. See Scott, 567 F.3d at 580.
The general Arizona rule governing all procedural bars is Rule 32.2, which provides:
a. Preclusion. A petitioner will not be given relief under this rule based upon any ground:
(1) Still raisable on direct appeal under Rule 31 or on post-trial motion under Rule 24;
(2) Finally adjudicated on the merits on appeal or in any previous collateral proceeding;
(3) Knowingly, voluntarily and intelligently not raised at trial, on appeal, or in any previous collateral proceeding.

Ariz. R.Crim. P. 32.2 (pre-1992) (emphasis added).[1]
The state trial court and the district court relied upon Rule 32.2(a)(3), which bars claims not raised in previous post-conviction proceedings. The state trial court denied Greenway's attempts to reopen and amend the initial Rule 32 petition to include these ineffective assistance claims on the ground that the claims should have been brought in that petition when it was originally filed. Yet, Rule 32.2(a)(3) does not provide that petitions as originally filed cannot be amended. Indeed, Arizona has a procedural rule, Rule 32.6(d), which permits amendment of a Rule 32 Petition even if the petition has already been dismissed. See Scott, 567 F.3d at 577. Rule 32.2(a)(3) expressly bars only claims not brought in a "previous collateral proceeding." In this case, Greenway was trying to amend his first petition, and there had been no earlier petition or collateral proceeding. We therefore conclude there was no "previous collateral proceeding" in which these claims should have been brought, because Greenway's first petition for post-conviction relief remained in state court proceedings while he sought to include additional claims of ineffective assistance of counsel.
We trace the procedural history of this case to illustrate that Petitioner did what he could, and, indeed, what the state supreme court effectively told him to do, in order to litigate the claims in the first petition. Greenway, with new counsel, first moved to vacate the trial court's denial of his original Rule 32 petition, and to obtain leave from the trial court to amend that petition. When that motion was denied, Greenway filed a Petition for Special Action with the Arizona Supreme Court, asking that court to order the trial court to allow the filing of an amended petition. The Arizona Supreme Court declined jurisdiction of the Special Action, but did so without prejudice to Greenway's seeking reconsideration of the denial of the post-conviction petition before the state trial court, presumably in order to amend it. The state supreme court thus appeared to authorize Greenway to seek relief in the trial court by amending his first and only Rule 32 petition.
Greenway did go back to the trial court to seek reconsideration and leave to amend his first petition to include, among other claims, claims of ineffective assistance of counsel at trial and on direct appeal. Greenway argued that the counsel who filed his initial post-conviction petition was ineffective because she missed one deadline after another, conducted no investigation to see if other meritorious claims *799 could be raised, never met with Greenway to discuss his case, and even directed a non-attorney investigator to write the entire post-conviction petition, to which counsel then made no additions or modifications.
As we recently recognized in Scott, Arizona Rules specifically allow the filing of an amended petition upon a showing of good cause, even after the trial court has already dismissed that petition. 567 F.3d at 577 (citing Arizona Rule of Criminal Procedure 32.6(d)). In this case, however, instead of determining whether Greenway had good cause to amend his petition, the state trial court, citing Rule 32.2(a)(3), denied those claims as procedurally barred because they had not been raised earlier. The state trial court thus failed to recognize the availability of the state procedural rule allowing the filing of an amended petition upon a showing of good cause. Since Arizona has a procedure for amending post-conviction relief petitions, the dismissal of claims as barred under a different rule, Rule 32.2(a)(3), cannot constitute an independent and adequate state ground barring the district court's consideration of these claims.
Our opinion in Scott is instructive and controlling in key respects. In Scott, the original post-conviction petition for relief from Scott's conviction and capital sentence raised a single issue of ineffective assistance at sentencing. Scott, 567 F.3d at 578. While this petition was pending, Scott, like Greenway, sought to replace his post-conviction counsel. The trial court summarily denied the petition for post-conviction relief in a minute order, without a hearing with respect to the request for new counsel, just as the trial court did in this case. See id.
Scott then filed a motion to represent himself and the court appointed new counsel. With new counsel, Scott, like Greenway, then filed motions to vacate the denial of the post-conviction petition and for leave to file an amended petition, arguing that his previous counsel had been ineffective. See id. at 578-79. The state court denied the motions. In an order remarkably similar to the trial court's ruling on the ineffectiveness claims sought to be added in this case, the court said it had "no authority" under Arizona Rule of Criminal Procedure 32.6(d) to allow the filing of an amended petition because the motion to amend was filed after the original petition had been denied. Id. at 579. Scott then filed a petition for review with the Arizona Supreme Court, which was summarily denied. See id.
The federal district court then dismissed Scott's subsequent federal habeas petition, just as the district court dismissed Greenway's claims, because it found that the state court's denial of post-conviction relief was based on an adequate and independent rule of state procedure. See id.
On appeal to this court, however, we reversed and remanded for a determination on the merits, holding that Rule 32.6(d) was not an adequate bar to federal review because the rule was not clear, well-established, nor consistently applied in Arizona. Id. at 581-82. We reviewed its history and concluded it had never been consistently applied to bar post-dismissal amendments to Rule 32 petitions. At least one Arizona appellate court had interpreted Rule 32.6(d) to allow the filing of an amended petition upon a showing of good cause, even if the trial court had already dismissed the original petition. Id. at 581 (citing State v. Rodriguez, 183 Ariz. 331, 903 P.2d 639, 641 (Ariz.Ct.App.1995)). Indeed, we found that the Arizona Supreme Court had subsequently followed Rodriguez and issued orders allowing defendants upon a showing of good cause to file amended or supplemental petitions even after their first petitions had been denied. *800 Scott, 567 F.3d at 581 n. 7. We therefore concluded that reliance on Rule 32.6(d) was not an independent and adequate state ground that barred Scott's claims.
In this case, as in Scott, the state court held that the new claims were brought too late without considering whether there was good cause to amend the petition. Here, the state court relied on Rule 32.2(a)(3) to bar Greenway's claims, a provision that, on its face, applies only where there has been a prior post-conviction proceeding. There was no such prior post-conviction proceeding in Greenway's case, for Greenway, like Scott, was trying to amend his first petition after it had been dismissed. The state supreme court itself effectively told Greenway to return to the trial court to seek amendment of his first petition when it declined to accept jurisdiction of his special action. Therefore, Rule 32.2(a)(3)'s bar of claims not raised in an earlier petition cannot constitute an adequate and independent ground sufficient to support a finding of procedural default, and particularly in light of Rule 32.6(d)'s provision allowing for amendments to Rule 32 petitions. See also Lambright v. Stewart, 241 F.3d 1201, 1203-06 (9th Cir.2001) (holding Rule 32.2(a)(3) does not bar federal habeas review of claims not raised in direct appeal in light of another Arizona rule prohibiting claims from being raised on direct appeal when they rely on evidence outside the record).
The State cites a number of cases in which we recognized reliance on Rule 32.2(a)(3) to have been an independent and adequate state ground for the state courts' dismissal of claims. Yet none of those cases involved an attempt to amend a first Rule 32 petition. In those cases, the petitioner had filed an earlier Rule 32 post-conviction petition that had been conclusively ruled upon and become final. Thus those petitioners were trying to bring new claims before the state court in a successive petition. In Ortiz v. Stewart, 149 F.3d 923, 930 (9th Cir.1998), for example, we held that additional claims raised for the first time in petitioner's third post-conviction petition were procedurally defaulted. In Martinez-Villareal v. Lewis, 80 F.3d 1301, 1304-06 (9th Cir.1996), we determined that claims were barred because they were raised in second and third post-conviction petitions.
The State cites no case in which we concluded Rule 32.2(a)(3) to be an independent and adequate state ground barring claims sought to be raised in state court through amendment of a first petition. Arizona has not consistently recognized any such bar, and its rules permit amendment. The district court erred in holding that Rule 32.2(a)(3) was an independent and adequate state ground that bars the consideration of Greenway's claims of ineffective assistance of counsel at the guilt phase of trial and on direct appeal.
Greenway's claims of ineffective assistance of counsel during trial and on direct appeal of the state court proceedings are therefore remanded to the district court for consideration on the merits. On remand, the district court should consider those claims de novo because there is no state court determination on the merits to which the district court can defer. Scott, 567 F.3d at 584-85 (stating that when "a state court has not reached the merits of a properly raised issue, we must review it de novo" (quotation marks and citation omitted)).

C. Ineffective Assistance at Sentencing
Greenway's claims with respect to ineffective assistance at sentencing raise two principal issues: whether counsel adequately investigated and presented mitigating evidence, and whether counsel was ineffective in declining to call Dr. David to *801 testify, and relying instead upon the testimony of Dr. Saslow. Because we conclude these claims lack merit, we affirm the district court's dismissal of them.

1. Failure to investigate and present mitigating evidence
Greenway argues that his trial counsel was ineffective at sentencing because he failed to investigate and present mitigating evidence. His federal habeas petition alleged that his counsel rendered ineffective assistance by failing to investigate Greenway and his family background, including abuse, medical history, drug usage, chaotic upbringing, and learning disabilities.
The district court dismissed this claim for failure to exhaust, holding that it was never fairly presented to the state court. Under AEDPA, a federal habeas petitioner must exhaust his claims in state court before coming to federal court. 28 U.S.C. § 2254(b)(1). A petitioner satisfies the exhaustion requirement by "fully and fairly presenting each claim to the highest state court." Scott, 567 F.3d at 582. Full and fair presentation requires the petitioner to provide the factual and legal basis for the claim to the state court. Id.
The district court concluded that this claim was never fairly presented to the state court because Greenway did not include the operative facts alleged in the habeas petition in his original state post-conviction relief petition. What the district court did not adequately take into account, however, was that Greenway's motion to amend his first post-conviction petition included these facts. That motion, filed after the state supreme court denied his petition for Special Action without prejudice to filing such a motion, sought to add allegations that included the following mitigating circumstances:
emotional abuse[,] physical abuse[,] possibility of sexual abuse[,] effects of drug usage on Petitioner[,] effects of strict religious upbringing (Jehovah's witness)[,] chaotic childhood[,] why Petitioner was on his own as a teenager[,] why Petitioner lived with his sister rather than his parents[,] learning disabilities[,] sibling rivalries[,] why Petitioner ran away at 14[,] non-violent history[,] effects of living in a draining ditch as a teenager[,] lack of paternal affection[,] psychological abuse by family members and friends[,] potential character disorders not diagnosed and therefore not treated[,] parental history....
The state trial court declined to consider these additional facts on the ground that it had already considered and dismissed, on the merits, Greenway's claim of ineffective assistance as to mitigation. In his petition for review to the Arizona Supreme Court, Greenway included in the Appendix a copy of the amended post-conviction relief petition he sought to file in the state trial court and requested the supreme court to allow the claims raised in the amended petition to proceed in the lower court. The supreme court denied his request.
We have held that this is enough to satisfy the fair presentation requirement. In Scott, petitioner asked the Arizona Supreme Court to allow the claims in his amended post-conviction relief petition to proceed in the lower court and attached the amended petition, which included the operative facts and law, in the Appendix. 567 F.3d at 582. We held that petitioner exhausted those claims because the claims were fairly presented to the Arizona Supreme Court. Id. at 583. Here, Greenway's claim of ineffective assistance of counsel relating to mitigation evidence was fairly presented to the Arizona Supreme Court because Greenway provided the factual and legal basis for the claim in his amended post-conviction relief petition. The Arizona Supreme Court knew exactly which claim Greenway sought to present *802 and chose to decline review of it. As we recognized in Scott, "[a]ll exhaustion requires is that the state courts have the opportunity to remedy an error, not that they actually took advantage of the opportunity." Id. Accordingly, we hold that Greenway fairly presented his ineffective assistance of counsel claim relating to mitigating evidence and the district court therefore erred in holding the claim unexhausted. See also Cone v. Bell, ___ U.S. ____, 129 S.Ct. 1769, 173 L.Ed.2d 701 (2009) ("When a state court refuses to readjudicate a claim on the ground that it has been previously determined, the court's decision does not indicate that the claim has been procedurally defaulted. To the contrary, it provides strong evidence that the claim has already been given full consideration by the state courts and thus is ripe for federal adjudication.").
We may nevertheless affirm the district court on any ground supported by the record. Holley v. Yarborough, 568 F.3d 1091, 1098 (9th Cir.2009). We therefore look at the merits of the claim, and we determine it should have been denied on the merits.
Under Supreme Court precedent, to prevail on a claim of ineffective assistance of counsel, Greenway must show that counsel's performance was deficient and that the deficiency prejudiced the defense. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984). The inquiry under Strickland is highly deferential, and "every effort [must] be made to eliminate the distorting effects of hindsight, to reconstruct the circumstances of counsel's challenged conduct, and to evaluate the conduct from counsel's perspective at the time." Id. at 689, 104 S.Ct. 2052.
Greenway claims that his trial counsel failed to investigate for mitigating evidence, including: emotional, physical, and possibly sexual abuse; drug use; living in a drainage ditch; strict religious upbringing; chaotic childhood; sibling rivalries; lack of paternal affection; learning disabilities; and potential psychological disorders. All of the matters that Greenway now claims were not investigated were, in fact, brought out at the aggravation-mitigation hearings. There, his trial counsel presented a total of eight witnesses, including his mother, half-sister, childhood friend, and Dr. Saslow. Greenway contends that the sentencing court did not hear testimony that Greenway was raised in a very strict environment by his father who was "an ardent Jehovah's witness" and who beat Greenway with a belt and later with his fists. Greenway's mother, however, testified that she and her husband were Jehovah's witnesses and that they made Greenway go to church. Additionally, his mother and his half-sister testified that Greenway's father beat him with a belt and later with his fists.
Greenway's mother also testified that Greenway did not graduate from the seventh grade, he had problems in school, and he had learning disabilities. She acknowledged that she criticized Greenway, and that Greenway's older brother ridiculed Greenway. She recalled an occasion when Greenway's father and brother bought him baby food when he was 12. She also testified that Greenway ran away from home and was living in a drainage ditch, and that Greenway's older brother was his father's favorite. Greenway's half-sister testified that her parents abused her and Greenway, but treated his older brother "[l]ike he could do no wrong." She also testified that Greenway did poorly in school and that he could not read. Greenway's childhood friend testified that Greenway and his brother did not get along well, and that Greenway told him that he received corporal punishment from his father. We therefore conclude that Greenway's counsel adequately investigated *803 and presented mitigating evidence relating to his family background.
Greenway also claims that his counsel was ineffective for failing to investigate and develop on information obtained by the psychiatrist, Dr. David, which Greenway alleges revealed "tantalizing indications" of mental health issues, physical and mental abuse, and past drug abuse. Greenway, however, has never explained how such indications would have led to specific and material evidence. Indeed, Dr. David himself noted in his interview worksheet that with regard to Greenway's "Mental Status Examination," Greenway "related well to the interviewer and spoke quietly with relatively good verbal skills throughout the interview.... Although he was obviously anxious, it did not seem overwhelming or to interfere with his behavior or thought processes." Furthermore, Greenway was "oriented," "had a good recent and remote memory," and "[t]here was no evidence of a gross psychotic thought disorder, but he did have difficulties [explaining] both on proverbs and similarities."
To satisfy any remaining doubts, Dr. David asked a psychologist, Dr. Saslow, to conduct a psychological evaluation of Greenway, because Dr. David "felt that there may be some question with respect to [Greenway's] intellectual functioning and for the possibility of the presence of a learning disability." Dr. Saslow subsequently interviewed Greenway on two separate occasions, and conducted four psychological and intelligence tests on him.
At the aggravation-mitigation hearing, Dr. Saslow testified that Greenway's I.Q. was a 72, which he characterized as borderline functioning. Dr. Saslow stated that although the tests he performed did not indicate any sign of sociopathology, he described Greenway's mental functioning as akin to that of an 11- or 12-year-old, which made him more prone to impulsiveness than someone who was mentally older. On cross-examination, Dr. Saslow acknowledged that he was not suggesting that Greenway suffered from any organic brain damage or that he was incapable of making judgments. Dr. Saslow's testimony thus developed the nature of Greenway's limitations.
In addition to presenting witnesses, defense counsel also prepared two sentencing memoranda arguing that Greenway's age and immaturity constituted statutory mitigating factors. His counsel further argued that Greenway's mental retardation, learning disability, remorse, prior good deeds, good behavior while in custody, lack of significant criminal history, lack of violent propensity, and potential for rehabilitation constituted additional mitigating factors. Counsel pointed out that Greenway was not raised in a supportive environment, noting that his mother mistook his learning disability for laziness and that his father and brother "constantly belittled and criticized" him.
The record shows that Greenway's counsel investigated and presented mitigating evidence at the state sentencing proceedings. His performance was not deficient. Accordingly, we conclude that the state court's denial of this claim was not an objectively unreasonable application of Strickland. We therefore affirm the district court's denial of this claim.

2. Failure to Call Dr. David to Testify
The district court denied on the merits Greenway's claim that his counsel was ineffective for failing to call Dr. David to testify. We agree that counsel's performance was not ineffective. Greenway's counsel initially intended to call Dr. David to testify at the sentencing hearing, and counsel asked the trial court to exclude incriminating statements Greenway made to Dr. David about the murders. When *804 the trial court declined to limit the cross-examination of Dr. David, defense counsel decided not to call him.
This was a reasonable strategic decision. In his interview with Dr. David, Greenway told Dr. David that he and his co-defendant were discussing committing a burglary in the weeks leading up to the murders because they were out of work and needed money. Greenway admitted that he shot the victims in the head, execution-style. He also described the murders as "a big adventure," and that he "felt like he was the master." Had Dr. David testified, the state would have cross-examined him about these inculpatory statements, and such testimony would have been highly prejudicial to the defense. Our precedent has repeatedly recognized similar decisions as being a reasonable strategy. See Wong v. Belmontes, ___ U.S. ____, 130 S.Ct. 383, 386, 175 L.Ed.2d 328 (2009) ("[I]t is necessary to consider all the relevant evidence that the jury would have had before it if [defendant] had pursued the different path  not just the mitigation evidence [defendant] could have presented, but also the... murder evidence that almost certainly would have come in with it.") (emphasis in original); Bonin v. Calderon, 59 F.3d 815, 834 (9th Cir.1995) (stating that it was reasonable for defense counsel to forego expert testimony because "it would have opened the door to precisely the type of cross-examination that [defendant] sought to avoid by refusing to call psychiatric experts").
Moreover, Dr. David's testimony would not have added much to Greenway's case. Defense counsel proffered that, "[Dr. David] would testify that in his opinion ... [Greenway had] a low I.Q., that [Greenway] had developed an immature personality, [but that] Mr. Greenway[did] not fit within any kind of characterlogical [sic] disorder ... such as a psychopath or sociopath." He went on to say that Dr. David would agree with Dr. Saslow that Greenway was functioning at an 11-or 12-year-old level, and would testify that Greenway could be rehabilitated. Thus, much of Dr. David's potential testimony would have been cumulative of the testimony provided by Dr. Saslow, while the drawbacks of calling Dr. David were substantial. Defense counsel was therefore not ineffective by his strategic decision not to call Dr. David. See also Raley v. Ylst, 470 F.3d 792, 801 (9th Cir.2006) (holding that a strategic choice not to call an expert will not constitute ineffective assistance of counsel if that choice was reasonable under the circumstances).

3. Failure to prepare Dr. Saslow
Greenway contends that his trial counsel was ineffective by failing adequately to prepare Dr. Saslow because counsel had not done enough background investigation. Greenway claims "counsel did not have sufficient background information to provide Dr. Saslow before he testified."
Yet Greenway does not allege what specific facts or information counsel should have provided to Dr. Saslow. Dr. Saslow's testimony related principally to his own testing and interviews of Greenway. Dr. Saslow testified that he was given the information garnered by the defense investigation concerning Greenway's background, but he testified that his conclusions concerning Greenway's mental status and mental functioning were predicated primarily on the psychological tests he performed. Greenway has never alleged, much less demonstrated, what more counsel should have known or discovered. Greenway's cursory and vague claim cannot support habeas relief. See James v. Borg, 24 F.3d 20, 26 (9th Cir.1994) ("Conclusory allegations which are not supported by a statement of specific facts do not warrant habeas relief.").
*805 For the reasons stated, we conclude that the state court was not objectively unreasonable in denying Greenway's claims that his counsel was ineffective for failing to investigate and present mitigating evidence, for failing to call Dr. David to testify at the sentencing hearing, and for failing properly to prepare Dr. Saslow. We therefore affirm the district court's denial of those claims.

D. Judicial Bias
The claim of judicial bias came to light in December 1994 when counsel for Greenway learned from an alternate juror that the trial judge, Judge Scholl, had mentioned his prior working relationship with Vince Peters, Lili's late husband and Mindy's father. As a result of this new information, Greenway filed a motion for a change of judge and requested discovery in order to further investigate Judge Scholl's ties to the victims. The new state court judge granted Greenway's discovery motion and ordered the Tucson Police Department ("TPD") to provide Greenway with records about Judge Scholl and Vince Peters.
The TPD record demonstrates that Scholl was employed by Tucson Police Department from July 1970 until September 1971. He was on military leave from October 1970 until March 1971. Vince Peters was employed by TPD from April 1968 until July 1978. The TPD record does not indicate whether or not Judge Scholl and Vince Peters worked together. However, the TPD discovery response states that the time period that they "could have worked together would be limited to the period from March 22, 1971 when Judge Scholl return[ed] from military leave, to May 24, 1971, when Vince Peters transferred to Narcotics."
At a status conference in August 1996, Greenway's attorney stated that she spoke with Judge Scholl and Judge Scholl admitted that he knew Vince Peters but he did not have any recollection of Lili. Greenway's attorney also claimed that she was in the process of contacting Kurt Jackson, a colleague of both Judge Scholl and Peters. Although the attorney was unable to reach Jackson, her investigator spoke with Jackson's mother, who told the investigator that Judge Scholl and Peters were close. The attorney, however, did not present an affidavit from Jackson's mother.
In September 1996, the state court dismissed the judicial bias claim, stating that although there was some indication that "Judge Scholl may have had some type of relationship with Vince Peters," the issue was moot because the Arizona Supreme Court conducted an independent review of the sentencing and approved the capital sentence.
The state court thus applied a harmless error analysis to dismiss the claim. This was incorrect because when a defendant's right to have his case tried by an impartial judge is compromised, there is structural error that requires automatic reversal. See Tumey v. Ohio, 273 U.S. 510, 535, 47 S.Ct. 437, 71 L.Ed. 749 (1927) (rejecting the argument that the judge's failure to recuse himself was harmless in light of defendant's clear guilt because "[n]o matter what the evidence was against him, he had the right to have an impartial judge"); see also Chapman v. California, 386 U.S. 18, 23, 87 S.Ct. 824, 17 L.Ed.2d 705 (1967) (recognizing the right to an impartial judge as among those "constitutional rights so basic to a fair trial that their infraction can never be treated as harmless error").
Because the state court's harmless error analysis was contrary to clearly established Supreme Court precedent, this Court must review Greenway's judicial bias claim de novo. See Panetti v. Quarterman, 551 U.S. 930, 953, 127 S.Ct. 2842, *806 168 L.Ed.2d 662 (2007) (holding that when the state court's decision is contrary to, or involved an unreasonable application of clearly established federal law, a "federal court must then resolve the claim without the deference AEDPA otherwise requires"); see also Frantz v. Hazey, 533 F.3d 724, 735 (9th Cir.2008) (en banc) (stating that if there is 2254(d)(1) error, "we must decide the habeas petition by considering de novo the constitutional issues raised").
Greenway raised the judicial bias claim in his federal habeas petition in 1998, four years after the underlying facts came to light. During the intervening years, no additional facts have been unearthed to illustrate the nature of the relationship or the possible effect it may have had upon the trial. In support of this claim, Greenway relies only on the TPD record and the affidavit from the alternate juror. In the affidavit, the juror declared that the judge had called him to his office and told him about having known the husband of one of the victims. The juror stated: "After being selected as the alternate juror, the trial judge called me into his office. During our conversation, the judge told me that he used to be a police officer. He also told me that when he was a police officer, his partner was the ex-husband of one of the victims in the Richard Greenway case."
The district court denied this claim on the merits, and without an evidentiary hearing, because the facts described could not establish bias. The court accurately stated that the evidence presented by Greenway shows, at best, "that for a brief period of time (two to three months at most), eighteen years prior to trial, Judge Scholl and Vince Peters may have worked or even partnered together as police officers. In addition, by the time of trial, Vince Peters had been deceased for eleven years. Petitioner can point to no evidence indicating that Judge Scholl had a personal relationship or even acquaintance with either Lili Champagne or Mindy Peters." The district court concluded that this evidence was insufficient to raise a colorable claim of judicial bias, and we agree.
A showing of judicial bias requires facts sufficient to create actual impropriety or an appearance of impropriety. Crater v. Galaza, 491 F.3d 1119, 1131 (9th Cir. 2007). Although Greenway argues that the district court should have held an evidentiary hearing before ruling on the merits of his judicial bias claim, he was not entitled to an evidentiary hearing unless he alleged facts which, if proven, would entitle him to relief. Gonzalez v. Pliler, 341 F.3d 897, 903 (9th Cir.2003). He has not done so.
Greenway does not contend there was any actual bias on the part of the trial judge, but only an appearance of bias on the basis of having known Peters. The Supreme Court has recognized only a few circumstances in which an appearance of bias necessitates recusal to ensure due process of law. The landmark case is Tumey v. Ohio, 273 U.S. 510, 523, 47 S.Ct. 437, 71 L.Ed. 749 (1927). There, the Supreme Court held that the judge should have recused himself because the judge had a direct, substantial pecuniary interest in the outcome of the case, because the judge received money from each conviction. The court in In re Murchison, 349 U.S. 133, 137, 75 S.Ct. 623, 99 L.Ed. 942 (1955), recognized an appearance of impropriety when the judge acted as both the grand jury and the trier of the accused. The Court stressed the improper appearance of the trial judge being "part of the accusatory process." Id. In Mayberry v. Pennsylvania, 400 U.S. 455, 465-66, 91 S.Ct. 499, 27 L.Ed.2d 532 (1971), the Court held that where the defendant had rudely insulted the trial judge, a different judge should preside over the contempt proceeding. *807 The trial judge had become embroiled in "a running, bitter controversy" with the defendant, creating an appearance of impropriety when the same judge ruled on whether the defendant had been guilty of contempt.
More recently, in a case where one party was a large donor to the judge's election campaign, the Court ruled there had been a denial of due process. The Court held recusal was required when "the probability of actual bias on the part of the judge or decisionmaker is too high to be constitutionally tolerable." Caperton v. A.T. Massey Coal Co., Inc., ___ U.S. ____, 129 S.Ct. 2252, 2257, 173 L.Ed.2d 1208 (2009) (quoting Withrow v. Larkin, 421 U.S. 35, 47, 95 S.Ct. 1456, 43 L.Ed.2d 712 (1975) (internal quotation marks omitted)).
All these cases involved some direct, personal relationship of the judge to the case, or with one of the parties, before the judge. That was not the situation here. Greenway's claim does not suggest any possible connection of the trial judge to his case that approaches the prior involvement of the judges in Tumey, Murchison, Mayberry, or Caperton. Here, Greenway has never presented any additional evidence, other than the TPD record and the alternate juror's affidavit, to support his bias claim. It continues to rest only upon a relationship that existed eighteen years before trial, lasted, at most, a few months, and was with a person who died more than eleven years before the trial. We agree with the district court that the record lacks support for a claim of judicial bias. The judge had no interest in, or relationship to, Greenway or the victims; at most, there was but a brief tangential employment relationship with a member of the victims' family. We therefore conclude that the district court did not abuse its discretion in denying Greenway's request for an evidentiary hearing, and we affirm the dismissal of this claim.

E. State Courts' Consideration of Mitigating Factors
Greenway's final claim is that the state trial court and Arizona Supreme Court failed to consider mitigating factors because they were following the then commonly applied test in Arizona requiring a nexus between mitigating factors and the crime. See Schad v. Ryan, 606 F.3d 1022, 1045-46 (9th Cir.2010), vacated on other grounds, ___ U.S. ____, 131 S.Ct. 2092, 179 L.Ed.2d 886 (2011). In Schad we cited State v. Djerf, 191 Ariz. 583, 959 P.2d 1274 (1998), as illustrating the Arizona nexus test, and concluded that such a test was found to be inconsistent with later constitutional analysis by the Supreme Court in Tennard v. Dretke, 542 U.S. 274, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004), and Smith v. Texas, 543 U.S. 37, 125 S.Ct. 400, 160 L.Ed.2d 303 (2004), which required consideration of all mitigating factors. Schad, 606 F.3d at 1045-47.
The record in this case, however, does not indicate that either the state trial court or the Arizona Supreme Court applied such a nexus test. In sentencing Greenway to death, the trial court stated that it had "considered all other mitigating factors, those presented at the aggravating-mitigating hearing, and also those which have been submitted to the Court in the sentencing memorandum and any other matters of record," and concluded that "evidence of brutality ... far outweighs his chronological, emotional and mental age," and that "there are no other mitigating factors sufficiently substantial to call for leniency." The Arizona Supreme Court's opinion indicates that it also considered *808 all of the mitigating factors and did not find them sufficient to outweigh the aggravating circumstances. Greenway, 823 P.2d at 35-38 (reviewing all the mitigating factors, including Greenway's age and low I.Q., and finding that they were "not sufficient to outweigh the three aggravating factors").
We have recently rejected a similar argument under similar circumstances. See Schad, 606 F.3d at 1046 ("[T]here is no indication that the state courts applied a nexus test...."). Accordingly, we must conclude that under the standards applicable to our habeas review, the Arizona state court decision is neither contrary to clearly established Supreme Court precedent, nor an unreasonable application of the law. See 28 U.S.C. § 2254(d)(1).

III. CONCLUSION
The dismissal of Greenway's claims of ineffectiveness with respect to the trial and on direct appeal is VACATED and the claims are REMANDED to the district court for consideration on the merits because we hold they are not procedurally barred. The district court's judgment dismissing the petition is AFFIRMED in all other respects.
AFFIRMED in part, VACATED and REMANDED in part.
NOTES
[1]  Arizona clarified that "the 1992 amendments to Rule 32 apply to `all post-conviction relief petitions filed on and after September 30, 1992.'" State v. Rodriguez, 183 Ariz. 331, 903 P.2d 639, 640 (Ariz.Ct.App.1995) (quoting Supreme Court Order, 171 Ariz. XLIV (Sept. 24, 1992)). Because Greenway's initial post-conviction petition was filed on August 28, 1992, the amendment to Rule 32.2 does not affect his petition.
