
671 F.3d 708 (2009)
Edward Harold SCHAD, Petitioner-Appellant,
v.
Charles L. RYAN,[*] Arizona Department of Corrections, Respondent-Appellee.
No. 07-99005.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted May 14, 2009.
Filed September 11, 2009.
Amended January 12, 2010.
Second Amendment June 3, 2010.
Third Amendment November 10, 2011.
*710 Kelley J. Henry, Nashville, TN, for the petitioner-appellant.
Jon G. Anderson, Phoenix, AZ, for the respondent-appellee.
Before: MARY M. SCHROEDER, STEPHEN REINHARDT and SUSAN P. *711 GRABER,[**] Circuit Judges.

ORDER
PER CURIAM:
The second amended opinion filed June 3, 2010 is hereby amended. The amended opinion is filed concurrently with this order.
Absent further order of the court, no further petitions for rehearing or rehearing en banc will be considered.

OPINION

I. Overview
Edward Harold Schad was convicted in Arizona state court in 1979 of the murder of Lorimer Grove, and sentenced to death. After his first conviction and sentence were reversed by the Arizona Supreme Court on collateral review, Schad was retried in 1985, and was again convicted of first-degree murder and sentenced to death. His direct appeal and state habeas proceedings from his second trial lasted for the next twelve years, and his federal habeas proceedings in district court for nine years after that. After the district court denied Schad's federal habeas petition on all grounds, he filed this appeal in 2007.
Schad's appeal raises seven principal contentions. Three pertain to his conviction and four to the imposition of the death sentence. The challenges to the conviction include a claim of a Brady violation in the state's failure to disclose impeachment material relating to the credibility of a prosecution witness; a claim of ineffective assistance during the guilt phase of trial; and a challenge to the sufficiency of the evidence in support of first-degree murder.
Schad's four challenges to the sentence include claims of ineffective assistance during the penalty phase, application of an unconstitutionally narrow standard for determining the admissibility of mitigating evidence, improper use of a prior conviction to establish two aggravating factors, and insufficiency of the evidence underlying a third aggravating factor.
With respect to the conviction, the important issue involves the state's admitted failure to produce letters written in 1979 by a detective and a prosecutor to assist the state's witness, Duncan, in an unrelated California prosecution. With respect to the sentence, the key issue is whether the district court erred by denying the claim of ineffective assistance of counsel at the penalty phase without holding an evidentiary hearing to consider substantial additional mitigating evidence. The district court ruled Schad failed to exercise diligence in bringing the new evidence out during his state habeas proceedings.
We affirm the district court's denial of habeas relief for the conviction and sentence.

II. Facts and Procedural Background
This is a case with strong circumstantial evidence pointing to the defendant's guilt and to no one else's. The victim, Lorimer Grove, a 74-year-old resident of Bisbee, Arizona, was last seen on August 1, 1978, when he left Bisbee driving his new Cadillac, coupled to a trailer, to visit his sister in Everett, Washington. Grove may have been carrying up to $30,000 in cash.
On August 9, 1978, Grove's body was discovered in thick underbrush down a steep embankment off the shoulder of U.S. Highway 89, several miles south of Prescott, Arizona. The medical examiner determined that the cause of death was ligature *712 strangulation accomplished by means of a sash-like cord, still knotted around the victim's neck. According to the medical examiner, Grove had been strangled using a significant amount of force, resulting in breaking of the hyoid bone in his neck and the reduction of his neck circumference by approximately four inches. The time of death was estimated to be four to seven days prior to discovery of the body.
No physical evidence at the crime scene implicated Schad in Grove's murder, and there was no evidence of a prior connection between the two men. There was, however, ample evidence establishing Schad's presence in Arizona at the time of the crime and his possession, after the date Grove was last seen, of Grove's property, including his Cadillac, credit cards and jewelry.
On August 3, 1978, two days after Grove left Bisbee, and six days before his body was discovered, an Arizona highway patrolman found an abandoned Ford Fairmont sedan alongside Highway 89, approximately 135 miles north of where Grove's body was discovered. The Ford was unlocked, except for the trunk, and its license plates were missing. A check of the Fairmont's VIN revealed that Schad had rented the car from a Ford dealership in Utah in December 1977, had failed to return it, and that the dealership had reported it as stolen.
According to Schad's girlfriend, Wilma Ehrhardt, she and Schad, along with Ehrhardt's children, had driven the car from Utah to New York, Florida, and Ohio between December 1977 and July 1978. In late July, Schad told Ehrhardt he was going to look for work and left Ohio with the Ford. Ehrhardt and the children remained in Ohio, but later returned to Utah.
When police impounded the Ford on August 3, 1978, they found in it, among other things, three Arizona newspapers dated July 31 and August 1, 1978, the days just before the estimated date of Grove's murder, as well as a special mirror device later identified by witnesses as an object Grove invented to help him couple his trailer to his Cadillac.
According to credit card records, on August 2, 1978, Schad began driving the Cadillac from Arizona eastward, using Grove's credit cards to make purchases in numerous cities along the way. On August 2, Schad used Grove's credit card to purchase gasoline in Benson, Arizona. On August 3, Schad used the card to purchase gas in Albuquerque, New Mexico. For approximately the next month, Schad continued traveling the country in the Cadillac and using Grove's credit card. Schad also used Grove's checkbook to forge a check to himself from Grove's account, which he cashed on August 7, 1978, in Des Moines, Iowa.
In New York state on September 3, 1978, Schad, still driving Grove's Cadillac, was stopped for speeding by a New York state highway trooper. Schad told the trooper he was delivering the car to New York on behalf of a "rather elderly" man named Larry Grove. Schad could not produce the car's registration, and instead gave the trooper the registration for Grove's trailer. The trooper issued Schad a citation and let him go.
Schad then drove back across the country, reuniting with Ehrhardt in Salt Lake City, Utah, on September 7, 1978. A man who was living with Ehrhardt at the time, John Duncan, contacted Salt Lake City police the same day to report that Schad had told him the Cadillac was stolen. Schad was arrested in Salt Lake City on September 8.
After Schad's arrest, Salt Lake City police impounded and searched the Cadillac. *713 From the Cadillac's title application, found in the car, the police learned that the vehicle belonged to Grove. Schad told police that he had obtained the Cadillac four weeks before in Norfolk, Virginia, after meeting "an elderly gentleman who was with a young girl" and who asked Schad to trade vehicles temporarily so that he and the girl would not be recognized. Schad also told the Utah police that he "was supposed to leave [the Cadillac] at the New York City port of entry at a later date for the man to pick up." Police found in the Cadillac's trunk a set of Utah license plates issued to Ehrhardt. Schad had previously installed these plates on the stolen Ford. He left the Cadillac's original plates on the car while he was driving it across the country.
After Schad's arrest, Ehrhardt went to the Salt Lake City jail and retrieved Schad's wallet. Duncan then searched the wallet and found the credit card receipts and the New York traffic citation. He again contacted the Salt Lake City police. When Detective Halterman came to Ehrhardt's home to collect the wallet and the documents, Ehrhardt also handed over a diamond ring she said her daughter had found in the glove compartment of the Cadillac. Witnesses later identified the ring as belonging to Grove. Duncan also visited Schad in jail. Duncan testified that during the visit Schad talked about lying about his presence in Arizona at the time of the crime and destroying evidence of the crime.
On October 5, 1979, the jury found Schad guilty of first-degree murder, and the court sentenced Schad to death. The Arizona Supreme Court affirmed the conviction and death sentence. State v. Schad, 129 Ariz. 557, 633 P.2d 366, 383 (1981). The United States Supreme Court denied Schad's petition for certiorari. Schad v. Arizona, 455 U.S. 983, 102 S.Ct. 1492, 71 L.Ed.2d 693 (1982). Schad then petitioned for habeas relief in the state courts and obtained a reversal of his conviction on the ground that the trial court improperly instructed the jury on the elements of felony murder. State v. Schad, 142 Ariz. 619, 691 P.2d 710, 711-12 (1984).
In Schad's 1985 retrial, he was again convicted of first-degree murder on materially the same evidence, and sentenced to death. The Arizona Supreme Court again affirmed on direct appeal. State v. Schad, 163 Ariz. 411, 788 P.2d 1162, 1174 (1989). The United States Supreme Court granted certiorari to resolve two questions: (1) whether a first-degree murder conviction is unconstitutional when it does not require the jury to agree on whether the murder was premeditated murder or felony murder; and (2) whether capital defendants are entitled to jury instructions on all lesser included offenses. Schad v. Arizona, 501 U.S. 624, 111 S.Ct. 2491, 115 L.Ed.2d 555 (1991). The Court answered both questions in the negative and affirmed the conviction and sentence. Id.
Schad again sought collateral review in state court. The trial court denied the state habeas petition after four years in which Schad's counsel sought repeated extensions to file his supplemental petition detailing his claims, particularly with respect to mitigating sentencing evidence. The Arizona Supreme Court denied review.
Schad filed his federal habeas petition in the District of Arizona in August 1998, raising nearly thirty claims. In a published opinion dated September 28, 2006, the district court denied habeas relief. Schad v. Schriro, 454 F.Supp.2d 897 (D.Ariz. 2006). With respect to the challenges to the conviction, the court ruled that the state's failure to disclose impeachment material had not resulted in prejudice, that counsel was not ineffective at the guilt *714 phase, and that the evidence was sufficient to support the conviction. With respect to sentencing, the court denied Schad's request for an evidentiary hearing to present new mitigating evidence in support of his claim of ineffective assistance at the penalty phase, finding that Schad was not entitled to a hearing because he was not diligent in developing the evidence in question during state habeas proceedings. Id. at 955-56. The district court also said that the evidence presented in district court did not render trial counsel's performance deficient because the evidence did not support the strategy of presenting the positive image that trial counsel had pursued at trial. Id. at 941-44. This appeal followed.

III. The Three Challenges to the Conviction

A. State's failure to disclose exculpatory material
John Duncan, a principal witness for the state, had a lengthy criminal history. As part of its efforts to gain his cooperation in the first trial, in 1979, the prosecution promised to assist Duncan with a pending, unrelated California criminal proceeding. In impeaching Duncan's credibility, the defense was able to question him at length about his criminal record and the prosecution's promises of assistance, but the defense did not know that a prosecutor and detective in 1979 had actually written letters on Duncan's behalf to California authorities. Schad's most significant challenge to his conviction is the prosecution's failure to disclose these letters as impeachment material. Schad asserts that the state's actions violated his due process rights as set forth in Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963) and Napue v. Illinois, 360 U.S. 264, 79 S.Ct. 1173, 3 L.Ed.2d 1217 (1959).
The state has conceded that it should have disclosed the letters under Brady, so the Brady issue is whether Schad was prejudiced by the omission. We agree with the district court that the omission does not justify habeas relief because it resulted in little or no prejudice, given the extensive impeachment material already available to the defense.
Duncan eventually testified in both trials that while Schad was being detained prior to trial in 1979, Duncan visited him to talk about the theft of the Cadillac, and Schad made several incriminating statements: he asked Duncan to destroy Grove's credit cards, and said that he "would deny being in any area of Arizona or the state of Arizona, particularly Tempe, Arizona and Prescott, Arizona."
In order to obtain Duncan's testimony and assistance with the Schad investigation, an investigative officer, Detective Halterman, had told Duncan he would write a letter to the judge presiding over Duncan's pending California criminal case. Moreover, the day before Duncan was set to testify at Schad's first trial in 1979, the prosecutor at that trial wrote to the California Community Release Board, stating that Duncan was "an extremely important witness for the State of Arizona" who had been "very cooperative" and "deserve[d] any consideration that can be given, including an early release, if possible." The prosecutor wrote a similar letter a few weeks later to the California judge presiding over Duncan's prosecution, stating that Duncan was "an important witness who was of material assistance to the prosecution" in Schad's case, and requesting that Duncan's "sentence be reviewed and if possible, his sentence be modified in light of his contribution to criminal justice."
Before the second trial in 1985, defense counsel unsuccessfully moved to suppress Duncan's testimony. Duncan testified at *715 that trial that Detective Halterman promised to write a letter on his behalf, but stated he did not know whether Halterman actually sent one. Halterman testified that he did offer to write a letter on Duncan's behalf, but stated he did not remember whether he actually sent a letter. Duncan further testified that he did not ask the prosecutor in Schad's first trial for any special treatment, although he did tell the prosecutor he knew of "people in the state prison that have been released early due to the fact of a state prisoner being a witness in a major or semi major crime." Duncan stated that he did not receive early release or any other lenient treatment in exchange for his testimony at Schad's first trial. At the close of the second trial, the prosecution still had not disclosed the letters so the defense could use them to impeach Duncan.
The defense was, however, able to impeach Duncan's credibility with other evidence of his lengthy criminal history, including the fact that he was currently serving a sentence for theft. Duncan admitted the advantages he asked for and some he obtained in exchange for his involvement in the Schad investigation. Detective Halterman stated on cross that although he could not remember whether he sent a letter to California authorities on Duncan's behalf, he recalled promising to do so, and "probably" did send a letter, further impeaching Duncan's credibility. Through this impeachment, the defense established Duncan had a motivation to testify falsely. The letters themselves would have provided some documentation of his motivation, but would not have provided a new or further motivation.
It is not now disputed that the letters could have been used to impeach Duncan. The prosecution's duty to disclose material, potentially exculpatory evidenceincluding impeachment evidenceto a criminal defendant was established in Brady, 373 U.S. at 86, 83 S.Ct. 1194. The state violates its obligations under Brady, and denies a criminal defendant due process of law, where the following three elements are met: (1) the evidence in question was favorable to the defendant, meaning that it had either exculpatory or impeachment value; (2) the state "willfully or inadvertently" suppressed the evidence; and (3) the defendant was prejudiced by the suppression. Strickler v. Greene, 527 U.S. 263, 281-82, 119 S.Ct. 1936, 144 L.Ed.2d 286 (1999).
The sole dispute here concerns the question of prejudice. The state's failure to disclose the letters written on Duncan's behalf was prejudicial to Schad if "there [was] a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different." Kyles v. Whitley, 514 U.S. 419, 433, 115 S.Ct. 1555, 131 L.Ed.2d 490 (1995) (citation omitted).
We conclude the state's admitted failure to turn over the letters was not prejudicial. In the first place, the letters provided no independent basis for impeaching Duncan. We are less likely to find the withholding of impeachment material prejudicial in cases in which the undisclosed materials would not have provided the defense with a new and different form of impeachment. In Barker v. Fleming, 423 F.3d 1085 (9th Cir.2005), for example, we held that the prosecution's failure to disclose evidence of a witness's four prior convictions was not prejudicial because the undisclosed evidence was duplicative of impeachment already pursued at trial. We explained that the evidence would not have "provide[d] `the defense with a new and different ground of impeachment.'" Id. at 1097 (quoting Silva v. Brown, 416 F.3d 980, 989 (9th Cir.2005)).
*716 We have also applied that test to grant relief where the undisclosed evidence would have provided a new basis for impeachment. In Horton v. Mayle, 408 F.3d 570 (9th Cir.2005), we held that the prosecution's failure to disclose an immunity deal with its key witness did prejudice the defendant, where the impeachment pursued at trial went to the witness's criminal history and participation as a getaway driver in the defendant's offense. The undisclosed Brady information was that the key witness had received immunity for his testimony; this provided an independent motive for the witness to lie and would have made his critical, uncontroverted testimony less credible. Id. at 580. We held that the undisclosed promise of immunity was material, and therefore prejudicial, because it constituted "a wholly different kind of impeachment evidence" from the lines of impeachment pursued by the defense at trial. Id.
This case is like Barker, where the undisclosed evidence related to the same motives to lie as evidence already known to and utilized by the defense. Here the jury knew that the prospect of obtaining assistance with the California case provided an incentive to lie. Moreover, Duncan was also impeached by his extensive criminal record, apart from the California case.
In addition, in this case each of the three letters was written in connection with Duncan's assistance at Schad's first trial in 1979, so that the letters would have shed little light on Duncan's motivation to testify at the second trial six years later. Duncan had already enjoyed any benefit the letters prompted, and did not receive any further assistance for his testimony in 1985.
Finally, and most important, the circumstantial evidence demonstrating Schad's guilt was powerful, and Schad did not offer any significant evidence to rebut the strong inference of guilt arising from that evidence. In light of the evidence against Schad, any additional impeachment value of the letters would not have changed the jury's verdict.
Schad is not entitled to relief on his Brady claim because of the lack of prejudice resulting from the prosecution's failure to produce the actual letters written pursuant to a promise of assistance to Duncan that, along with the history of Duncan's other transgressions, was fully known to the defense.
In a related argument, Schad asserts that the state committed prosecutorial misconduct by permitting Duncan to testify falsely in 1985 that he did not receive any assistance from the state in exchange for his cooperation. Schad relies on Napue, 360 U.S. at 269, 79 S.Ct. 1173, in which the Supreme Court held that the state violated a defendant's right to due process by doing nothing to correct a witness's false testimony that he received no promise of consideration from the prosecutor in exchange for his cooperation.
To prevail on a Napue claim, a habeas petitioner must show that "(1) the testimony (or evidence) was actually false, (2) the prosecution knew or should have known that the testimony was actually false, and (3) that the false testimony was material." United States v. Zuno-Arce, 339 F.3d 886, 889 (9th Cir.2003). Under Napue, false testimony is material, and therefore prejudicial, if there is "any reasonable likelihood that the false testimony could have affected the judgment of the jury." Hayes v. Brown, 399 F.3d 972, 984 (9th Cir.2005) (en banc) (citation omitted); see also id. at 978 ("[I]f it is established that the government knowingly permitted the introduction of false testimony reversal is virtually automatic.") (internal quotation marks and citation omitted).
*717 In this case, it is not entirely clear that Duncan lied. Although there is some indication in the record that Duncan may at some point have learned that Detective Halterman wrote a letter on his behalf, because the letter was referred to during a California proceeding in Duncan's case, it is not clear that Duncan remembered this letter in 1985 and thus lied on the stand. Even assuming he did, there is no evidence that the state knew or should have known that his testimony was false. Finally, the record before us does not reflect that the California authorities acted on Halterman's and the prosecutor's requests to benefit Duncan. Duncan's testimony that he received no assistance in his California case was not necessarily false even if he knew and remembered the letter.

B. Ineffective assistance of counsel at the guilt phase
Schad argues that his trial counsel's failure to locate and present impeachment testimony from Duncan's ex-wife, Sharon Sprayberry, amounted to ineffective assistance of counsel. Schad contends Sprayberry's testimony would have impeached Duncan's statements about his jailhouse conversation with Schad in which, according to Duncan, Schad made statements about the need to destroy incriminating evidence and stated he would deny being in the area of Arizona where the murder took place. In an affidavit submitted with Schad's state habeas petition, Sprayberry attested that she was present during the conversation and that Schad "did not make any statements relating to a homicide in Arizona."
Ineffective assistance of counsel claims require a defendant to show that counsel's performance was so deficient that it "fell below an objective standard of reasonableness," and that there is a "reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland v. Washington, 466 U.S. 668, 687-88, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
Regardless of whether Sprayberry may have provided evidence helpful to Schad's case, Schad does not attempt to establish counsel's performance was deficient. In his briefing on appeal, Schad concedes that defense counsel's efforts to locate Sprayberry were "diligent and thorough." Strickland requires both deficient performance and prejudice to make out an ineffective assistance of counsel claim. See id. at 687, 104 S.Ct. 2052. Schad's inability to show his counsel's efforts to obtain the evidence were deficient is fatal to his claim.

C. Sufficiency of the evidence
Schad's final conviction-related claim challenges the sufficiency of the evidence underlying his conviction for firstdegree murder. In reviewing a sufficiency of the evidence challenge, we ask whether, "viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (original emphasis). Because the state habeas court did not address the merits of this claim, we review de novo whether sufficient evidence exists to support Schad's murder conviction. Pirtle v. Morgan, 313 F.3d 1160, 1167 (9th Cir.2002).
Circumstantial evidence and reasonable inferences drawn from it may properly form the basis of a conviction. United States v. Jackson, 72 F.3d 1370, 1381 (9th Cir.1995). The circumstances of Grove's death, including the fact that the murder was accomplished by ligature *718 strangulation, permitted the jury to infer that the killing was intentional and premeditated, as required under Arizona law. See Ariz.Rev.Stat. § 13-1105(A). Thus, the main issue at trial was the identity of Grove's killer. To establish that Schad murdered Grove, the state introduced evidence that one day after Grove was last seen alive, Schad was in possession of Grove's property, including his vehicle, credit cards, and checkbook. Schad's description to New York authorities of Grove as an elderly man strengthened the inference that Schad had encountered Grove in person. Moreover, the state introduced evidence that would permit a rational jury to infer that Schad knew about Grove's death, including Schad's statement to Duncan that he would deny being near the scene of the crime, and request to Duncan to destroy Grove's credit cards. The evidence, taken as a whole, was sufficient to allow a rational jury to return a conviction for first-degree murder, and we therefore deny relief on this claim.

IV. Sentencing Claims

A. IntroductionThe 1985 Sentencing Proceeding
Prior to the sentencing hearing before the trial court in 1985, Schad's counsel filed a 39-page sentencing memorandum that presented the following mitigating circumstances, which focused largely on his prison conduct following his original conviction in 1979: (1) Schad was a model prisoner; (2) Schad pursued higher education while in prison; (3) Schad had numerous stable friendships; (4) the trial court gave a felony-murder instruction at Schad's trial, meaning that Schad's conduct may have been less reprehensible than a pre-meditated murder; (5) Schad had a troubled childhood with abusive parents; (6) Schad was beaten and threatened while in prison in Utah for a prior conviction; (7) Schad showed potential for rehabilitation; (8) Schad had a stable character; (9) Schad did not pose a risk of violent or dangerous behavior; (10) Schad made charitable contributions; (11) Schad did not drink or use drugs; and (12) Schad had an excellent employment record in Arizona prisons.
At the sentencing hearing, Shaw called fifteen witnesses, including correctional officers, friends, relatives and a psychiatrist. Nearly all of the testimony related to Schad's good reputation and behavior as an adult, and particularly his good behavior while in prison. A Utah prison official, John Powers, testified regarding Schad's personal development and conduct while he was incarcerated in Utah state prison after a prior offense. Powers stated that Schad "made some great strides" in the prison's group therapy program. He also testified that Schad was permitted to be near weapons while working on a renovation project because he "was an excellent security risk." Powers testified that, in general, Schad was a "model prisoner" while incarcerated in Utah, and that he recommended Schad's release because he felt Schad was not a danger to the community. One Arizona prison official, Frank Terry, testified that Schad was placed in a relatively low-security prison block because he posed no disciplinary problems or security risks, and another official, Jerry McKeand, elaborated that Schad actually assisted with other prisoners' disciplinary issues by helping to "keep[] the cell block kind of in line."
Next, several of Schad's friends and relatives testified. Janet Bramwell, a friend and fellow member of Schad's church, the King of Glory Lutheran Church in Tempe, testified that Schad requested and received instruction in the Lutheran faith while in prison, and was confirmed as a member of the church. Bramwell also testified that she, her husband, and other *719 church members wrote letters to Schad, welcoming him into the congregation and telling him about themselves and their families. Bramwell stated that after she and her husband received a letter in return, they began visiting Schad in prison approximately once per month. Bramwell described Schad as "clean and well-groomed," "likeable," and a "very intelligent person, very talented," and stated that Schad opened up to her and her husband about his difficult childhood. Bramwell's husband, Frank Bramwell, confirmed her testimony and also described Schad's educational efforts while incarcerated, including earning such good grades in his college courses that he was named to the dean's list. Another friend and fellow church member, Herb Zerbst, testified regarding his friendship with Schad. Zerbst and his wife corresponded with Schad using both written letters and audio cassettes on which they recorded messages. Zerbst and his wife also visited Schad in prison until they moved to Illinois. Zerbst described Schad as friendly and caring, and described Schad's concern for the Zerbsts' safety during their long drive to Illinois. Zerbst also stated that Schad was creative and sent him and his wife gifts, including crocheted items and paintings.
Ronald Koplitz, the chaplain at Schad's prison, stated that Schad consulted him for religious guidance due to his fear of death. He testified that Schad stood out from other prisoners because he was likeable and genuine. Koplitz described Schad as "the kind of inmate you can like, and the kind of inmate that does not play games or try to.... get extra favors by being in a religious program." He testified that despite Schad's troubled childhood, he believed Schad had a "stable personality," at least in a controlled prison setting.
The psychiatrist, Otto Bendheim, testified briefly regarding Schad's early background and mental condition. Bendheim stated that Schad "had a miserable childhood and ha[d] been delinquent since his teens" and that he "was a deprived youngster," but that despite his criminal history, Schad was "not a dangerous type," was "pleasant" and had "above average" intelligence, and Bendheim was not "a bit afraid for his own safety" when he met with Schad.
The pre-sentence report prepared by a probation officer included discussions of Schad's troubled childhood, favorable character reports from several of Schad's friends and Arizona prison officials, and Schad's good behavior and achievements in prison. The report described Schad's childhood as follows:
The defendant reported a very stormy childhood, with his father being an alcoholic and abusing the defendant on a regular basis. The defendant stated that his father would beat him with his fist as discipline. The defendant reported that he tried to protect the family from his father's abuse by allowing his father to inflict beatings on him for anger towards other members of the family. The defendant always kept his problems to himself and to this day has not dealt with the feelings he has regarding his life.
The defendant learned at an early age how to suppress his feelings, even to the point of refusing to display emotion when his father would abuse him.... The defendant stated that at age seventeen he tried to commit his father to the VA Hospital for treatment. He stated that his father was out of control due to his alcoholism. When the officials came to pick up his father, the defendant's mother changed her mind and took sides with her husband. The defendant stated that when the officials left he experienced the worst beating of his life. The *720 defendant described his decision to commit his father as the hardest thing he ever did in his life.
The defendant stated that in addition to the abuse his father would never allow him to socialize with others; consequently, the defendant was a very shy, withdrawn adolescent.
At the sentencing hearing, defense counsel praised the pre-sentence report's discussion, but did not present additional evidence regarding Schad's troubled childhood. Counsel did not, for example, present testimony or affidavits from Schad's relatives to provide first-hand descriptions of the abuse Schad suffered as a child, nor did counsel seek a comprehensive psychiatric evaluation to assess the negative effects of that abuse.
After the sentencing hearing, the court rendered a special verdict discussing the aggravating and mitigating factors. First, the court took into account Schad's positive record since his arrest and incarceration. The court found that the most persuasive mitigating circumstance was the fact that Schad was "a model prisoner, a student and a religious man with many supportive friends since being incarcerated." The court observed that Schad was "helpful, charitable and appears to care for people," that he did not abuse drugs or alcohol or have any discipline problems, and that he took many college courses while in prison and earned good grades. The court said, however, that although Schad's "good, stable character" and "signs of rehabilitation" constituted a mitigating factor, this factor was "not particularly weighty of view of [Schad's] length of incarceration."
Next, the court noted Schad's "unfortunate childhood," but concluded it was not a "persuasive mitigating circumstance." The sentencing court determined that the mitigating circumstances presented by Shaw were insufficient "to overcome any one of the aggravating circumstances," and imposed a sentence of death. After conducting an independent review of the aggravating and mitigating evidence, the Arizona Supreme Court affirmed, concluding that the mitigating factors were "insufficient to outweigh a single aggravating factor." Schad, 788 P.2d at 1174.
The aggravating factors applied by the sentencing court related to a prior conviction and to the circumstances of the murder. The court relied on a 1968 Utah second-degree murder conviction to impose aggravating factors for having a prior conviction punishable under Arizona law by a life sentence or by death, and for having a prior conviction of a crime of violence. The court also found that Grove's murder was committed for the purpose of pecuniary gain. On appeal, the Arizona Supreme Court affirmed the first and third of these aggravating factors, and declined to reach the issue of whether the violent crime aggravator was sufficient to support imposition of the death penalty. Id. at 1170.

B. The Protracted State Court Post-Conviction Proceedings
After Schad was sentenced to death, he initiated state post-conviction proceedings in 1991 in which he was represented by a new attorney. In Schad's preliminary state habeas petition, filed on December 16, 1991, he argued the sentencing court failed to give proper weight to mitigating evidence of his troubled family background, but he did not raise a claim of ineffective assistance of counsel. The state court ordered Schad to file a supplemental petition by February 18, 1992, and Schad's legal team requested and obtained seventeen successive extensions of that deadline. During that time, post-conviction counsel obtained appointment of an *721 investigator to look into Schad's family history.
In January 1994, Schad was appointed a new post-conviction attorney. The court granted her request for further investigative services, as well as more than ten motions for an extension of the deadline to file Schad's supplemental state habeas petition. In March 1995, counsel obtained appointment of a mitigation expert. The court denied counsel's request for disclosure of Schad's prison file and for contact visits to allow the mitigation expert to interview Schad.
After the court ruled that no additional extensions of time would be granted, counsel filed Schad's supplemental petition on October 19, 1995. The supplemental petition included a general claim that Schad's sentencing counsel was ineffective for failing to discover and present mitigating evidence regarding Schad's family background. Attached to the supplemental petition was an affidavit from the expert in which she stated that the presentence report used at Schad's sentencing hearing did not adequately address the extent of the abuse Schad had suffered as a child. The affidavit described the physical and psychological abuse inflicted by Schad's father, including beating Schad with a belt or fists, refusing to allow Schad's mother to show him any affection, and isolating Schad from other children. The expert recommended that a comprehensive psychological evaluation be performed, and stated that she could compile a thorough profile only through further interviews with Schad and his relatives.
The state habeas court denied the ineffective assistance claim in June 1996 without holding an evidentiary hearing. The court described Schad's request for a hearing as amounting to nothing more than a "fishing expedition." Schad filed a motion for rehearing along with another expert affidavit. That affidavit indicated that she had performed additional interviews with Schad and obtained more information about his life history, but did not describe the new information or include any supporting affidavits or other documents. The trial court denied the motion for rehearing, and in 1997 the Arizona Supreme Court denied Schad's petition for review.

C. Federal Habeas Proceedings
By the start of federal habeas proceedings in 1998, Schad's counsel had obtained a great deal more information about his early and abusive childhood experiences. Schad asserted that he received ineffective assistance of counsel at the penalty phase of trial when his attorney, Shaw, failed to investigate and present mitigating evidence regarding Schad's troubled childhood, and instead relied on the brief discussion of Schad's childhood contained in the psychiatrist's testimony and in the presentence report. During proceedings before the district court, Schad sought an evidentiary hearing in order to present a significant amount of evidence regarding his abusive childhood, which he contends his sentencing counsel should have presented at the sentencing hearing.
The district court held that Schad was not entitled to an evidentiary hearing because he was not diligent in attempting to develop the evidence during his state habeas proceedings. The court denied Schad's ineffective assistance claim without holding an evidentiary hearing.
Schad sought to present mitigating evidence not submitted during sentencing or during his state post-conviction proceedings, including extensive mental health records of his mother, father, and brother, as well as several declarations discussing Schad's childhood and its effect on his mental health. The first declaration, from psychologist Charles Sanislow, provided an *722 extremely detailed discussion of the psychological impact of Schad's abusive childhood. The second declaration, from psychologist Leslie Lebowitz, discussed the mental health history of Schad's parents, including his mother's struggle with prescription drug addiction and his father's affliction with post-traumatic stress disorder due to spending eighteen months in a German POW camp during World War II. Declarations from Schad's mother and aunt provided details regarding Schad's father's severe alcoholism and the abuse he inflicted upon his family. The final declaration, from a paralegal employed by the office of the Federal Public Defender, described interviews with Schad's sister and aunt regarding Schad's childhood.
The district court held, however, that Schad was not entitled to expansion of the record or to an evidentiary hearing because he was not diligent in developing the proffered evidence in state court. The district court also held that even if the evidence were considered in federal court, the evidence did not show that sentencing counsel was deficient in failing to present it. The court ruled the strategy counsel pursued was competent and that the newly proffered evidence could not have affected the result.

D. Schad's Claims

1. Additional Mitigating Evidence
The state habeas court ruled that Schad's claim of ineffective assistance of counsel at sentencing lacked merit because he was unable to present any significant mitigating evidence. Although Schad sought to present such evidence in the district court, the Supreme Court has now ruled that when a state court has decided an issue on the merits, the federal courts may not consider additional evidence. Cullen v. Pinholster, ___ U.S. ___, 131 S.Ct. 1388, 1398, 179 L.Ed.2d 557 (2011) ("[R]eview under § 2254(d)(1) is limited to the record that was before the state court that adjudicated the claim on the merits."). It has vacated and remanded this case to us for reconsideration. Ryan v. Schad, ___ U.S. ___, 131 S.Ct. 2092, 179 L.Ed.2d 886 (2011). Accordingly the district court's denial of this claim must be affirmed.

2. State courts' consideration of mitigating evidence
Schad not only seeks to rely on mitigating evidence not presented at trial, but also challenges the standard under which the state courts evaluated the mitigating evidence that was submitted. While he makes a strong argument that the state court was following the wrong standard in other cases, we cannot conclude that the state court actually applied a standard that was too narrow in this case.
Because the state habeas court denied this claim without addressing the merits, we review de novo whether the state courts violated Schad's constitutional rights by failing to consider and give effect to the mitigating evidence of Schad's childhood. Pirtle, 313 F.3d at 1167.
We begin with the Supreme Court's decisions in Lockett v. Ohio, 438 U.S. 586, 98 S.Ct. 2954, 57 L.Ed.2d 973 (1978) and Eddings v. Oklahoma, 455 U.S. 104, 102 S.Ct. 869, 71 L.Ed.2d 1 (1982). In Lockett, a plurality of the Court struck down an Ohio statute requiring mandatory imposition of the death penalty unless certain specified mitigating circumstances applied. 438 U.S. at 607-08, 98 S.Ct. 2954. The Court held that a state's statutory scheme for capital sentencing must not preclude the sentencing court from considering any mitigating evidence offered by the defendant. Id. at 604, 98 S.Ct. 2954.
In Eddings, the Court extended Lockett, holding that an Oklahoma capital sentencer *723 acted unconstitutionally by refusing to consider evidence of the defendant's abusive childhood. The court ruled that the state court constitutionally erred in holding that only evidence which specifically negated an offense element was relevant for mitigation purposes. 455 U.S. at 108-13, 102 S.Ct. 869. The Court explained that Lockett's holding applies not only to state statutes that prevent a capital sentencing authority from considering all potentially mitigating circumstances, but also to the process by which a sentencing court conducts the sentencing proceedings: "Just as the State may not by statute preclude the sentencer from considering any mitigating factor, neither may the sentencer refuse to consider, as a matter of law, any relevant mitigating evidence." Id. at 113-14, 102 S.Ct. 869 (original emphasis).
Schad's principal contention in this case is that the state courts did not consider the evidence of his troubled childhood because they unconstitutionally required a "nexus" between his childhood abuse and his commission of Grove's murder. Schad contends the state courts applied the same test the Supreme Court rejected in Tennard v. Dretke, 542 U.S. 274, 281, 124 S.Ct. 2562, 159 L.Ed.2d 384 (2004).
In Tennard, a case involving a defendant's low mental acuity, the Court invalidated a Fifth Circuit test that rendered potential mitigating evidence of a mental condition relevant to a capital sentencing determination only if the defendant presented evidence that "the criminal act was attributable to" the mental condition. In Smith v. Texas, 543 U.S. 37, 45, 125 S.Ct. 400, 160 L.Ed.2d 303 (2004), the Court went further and rejected any "nexus test," explaining that the requirement to prove a "nexus" between mitigating evidence and the charged offense is "a test we never countenanced and now have unequivocally rejected." Tennard and Smith are retroactively applicable to the Arizona Supreme Court's 1989 decision in this case. Smith, 543 U.S. at 45, 125 S.Ct. 400; see also Graham v. Collins, 506 U.S. 461, 467, 113 S.Ct. 892, 122 L.Ed.2d 260 (1993).
Before Tennard was decided, Arizona courts recognized a nexus test, similar to that rejected in Tennard, to preclude consideration of evidence of childhood abuse unless the abuse bore a causal connection to the crime of conviction. See, e.g., State v. Djerf, 191 Ariz. 583, 959 P.2d 1274, 1289 (1998) In State v. Wallace, 160 Ariz. 424, 773 P.2d 983, 986 (1989), decided eight months before the Arizona Supreme Court's decision in this case, the Arizona Supreme Court said that "a difficult family background, in and of itself, is not a mitigating circumstance." Id. at 986.
After Tennard, however, the Arizona Supreme Court has clarified that the nexus test affects only the weight of mitigating evidence, not its admissibility. See State v. Newell, 212 Ariz. 389, 132 P.3d 833, 849 (2006) ("We do not require that a nexus between the mitigating factors and the crime be established before we consider the mitigation evidence. But the failure to establish such a causal connection may be considered in assessing the quality and strength of the mitigation evidence.") (citing Tennard, 542 U.S. at 287, 124 S.Ct. 2562). The United States Supreme Court has said that the use of the nexus test in this manner is not unconstitutional because state courts are free to assess the weight to be given to particular mitigating evidence. Eddings, 455 U.S. at 114-15, 102 S.Ct. 869.
In two recent published opinions, we granted habeas relief from Arizona murder convictions on the ground that a lower court used an unconstitutional nexus test. Styers v. Schriro, 547 F.3d 1026 (9th Cir. 2008); Lambright v. Schriro, 490 F.3d *724 1103 (9th Cir.2007). In Styers, we granted relief to a habeas petitioner whose evidence of post-traumatic stress disorder was expressly disregarded by the Arizona courts due to his failure to demonstrate a causal connection between the disorder and the crime. The Arizona Supreme Court had concluded that although evidence of post-traumatic stress disorder "could . . ., in an appropriate case, constitute mitigation," it did not constitute mitigation in the instant case because "two doctors who examined defendant could not connect defendant's condition to his behavior at the time of the conspiracy and the murder." Id. at 1035 (quoting State v. Styers, 177 Ariz. 104, 865 P.2d 765, 777 (1993)). We held that the court's imposition of a nexus requirement was contrary to the clearly established rule set forth in Eddings. Id.
In Lambright, we granted habeas relief after concluding that the district court improperly applied a preclusive nexus test and declined to consider mitigating evidence of the petitioner's post-traumatic stress disorder. We stated that the district court's approach was "fundamentally flawed" and that the court "misapplied" Tennard and Eddings. 490 F.3d at 1114-15. We explained that the court erred by refusing to consider the majority of Lambright's mitigating evidence solely on the ground that he failed to show a nexus between the mitigating evidence and the crime. Id.
In both of those cases, however, it was clear from the record that the lower court had applied the unconstitutional nexus test and had excluded mitigation evidence. By contrast, in this case, there is no indication that the state courts applied a nexus test, either as a method of assessing the weight of the mitigating evidence, or as an unconstitutional screening mechanism to prevent consideration of any evidence. Rather, the record shows that the sentencing court did consider and weigh the value of the small amount of childhood mitigation evidence that was offered, stating that it was not "a persuasive mitigating circumstance in this case." The Arizona Supreme Court stated that it had conducted an independent review of the entire record regarding the aggravating and mitigating factors. See Schad, 788 P.2d at 1172. In short, it does not appear that the state courts refused to consider any evidence Schad offered. They concluded, as Eddings allows them to do, that it did not outweigh the aggravating circumstances.
Absent a clear indication in the record that the state court applied the wrong standard, we cannot assume the courts violated Eddings's constitutional mandates. See Bell v. Cone, 543 U.S. 447, 455, 125 S.Ct. 847, 160 L.Ed.2d 881 (2005) ("Federal courts are not free to presume that a state court did not comply with constitutional dictates on the basis of nothing more than a lack of citation."). We must hold there was no constitutional error in the Arizona courts' consideration of the mitigating evidence of Schad's troubled childhood.
Schad's two remaining contentions with respect to the state courts' consideration of the mitigating evidence are easily disposed of. First, Schad challenges the state courts' weighing of the aggravating and mitigating evidence. It is well-established, however, that state courts have the discretion to assess the appropriate weight of sentencing-related evidence. See Harris v. Alabama, 513 U.S. 504, 512, 115 S.Ct. 1031, 130 L.Ed.2d 1004 (1995) ("[T]he Constitution does not require a State to ascribe any specific weight to particular factors, either in aggravation or mitigation, to be considered by the sentencer."). It was well within the state courts' discretion to determine that the mitigating evidence *725 presented in Schad's case did not outweigh the aggravating evidence.
Next, Schad challenges the state courts' failure specifically to address each of the categories of mitigating evidence he presented at his sentencing hearing. State courts imposing or reviewing capital sentences are not required to provide an exhaustive discussion of all the mitigating evidence presented, as long as it is clear from the record that they reviewed the evidence. See Moormann v. Schriro, 426 F.3d 1044, 1055 (9th Cir.2005) ("[T]he trial court need not exhaustively analyze each mitigating factor as long as a reviewing federal court can discern from the record that the state court did indeed consider all mitigating evidence offered by the defendant.") (internal quotation marks and citation omitted). Moreover, where, as here, the sentencing court states that it has considered all the mitigating evidence offered, we may not second-guess its actions. See id. ("This court may not engage in speculation as to whether the trial court actually considered all the mitigating evidence; we must rely on its statement that it did so.").

3. State courts' application of aggravating factors
Schad challenges the state courts' determinations regarding the aggravating circumstances present in his case. Most importantly, he challenges the sufficiency of the evidence underlying the pecuniary gain aggravating factor, the only aggravating factor connected to this crime. Schad contends that application of the aggravating factor was improper because there was insufficient evidence to prove robbery was a motive for Grove's murder.
Under Arizona law, "[a] court may find pecuniary gain as an aggravating factor if the expectation of pecuniary gain is a motive, cause, or impetus for the murder and not merely a result of the murder." State v. Hyde, 186 Ariz. 252, 921 P.2d 655, 683 (1996). In applying the pecuniary gain factor, the sentencing court in this case emphasized that the state had proved that Schad was in possession of Grove's credit cards and his vehicle within a day of the murder and immediately began using the vehicle and the cards, as well as his check book. Grove's vehicle was a new Cadillac, while Schad abandoned his stolen Ford. In affirming the application of the factor, the Arizona Supreme Court held that these facts constituted "strong circumstantial evidence that the purpose of the murder was pecuniary gain." Schad, 788 P.2d at 1171. We review this determination under AEDPA standards that require us to give a presumption of correctness to a state court's factual determinations. 28 U.S.C. § 2254(e)(1).
In essence, Schad's position is that without direct evidence of his guilt, no rational sentencer could have made any finding as to his motive. Schad's guilt, however, was established at the guilt phase through circumstantial evidence. There is nothing irrational about relying on circumstantial evidence to show motive. Nor was the application of the pecuniary motive factor arbitrary or capricious. See Lewis v. Jeffers, 497 U.S. 764, 780, 110 S.Ct. 3092, 111 L.Ed.2d 606 (1990).
It is clear that the evidence presented at trial regarding Schad's acquisition and use of Grove's vehicle, credit cards and checkbook rationally supported the application of the pecuniary gain aggravating factor. After Grove's death, Schad was living off of Grove's credit cards and his bank account. Indeed, like the district court, we find it difficult to imagine a non-pecuniary motive for the murder. See Schad, 454 F.Supp.2d at 931 ("[D]espite Petitioner's argument that the evidence could lead to contradictory inferences, it is difficult to *726 ascribe a motivation other than pecuniary gain to the offense against Mr. Grove, who was a complete stranger to Petitioner."). Accordingly, we uphold the validity of pecuniary gain as an aggravating factor.
The state courts concluded that, under state law, a single aggravating factor was sufficient to support imposition of the death penalty in this case. Because we conclude that the pecuniary gain factor was rationally supported by the evidence presented, and not arbitrarily imposed, we do not reach the challenges to other aggravating factors.

V. Conclusion
We affirm the district court's denial of habeas relief on all claims related to Schad's conviction and sentence.
AFFIRMED.
NOTES
[*]  Charles L. Ryan is substituted for his predecessor Dora B. Schriro as Director of the Arizona Department of Corrections. See Fed. R.App. P. 43(c)(2).
[**]  Judge Graber was drawn to replace Judge Rymer.
