
537 F.3d 1062 (2008)
Eric John KING, Petitioner-Appellant,
v.
Dora B. SCHRIRO, Director, of the Arizona Department of Corrections, Respondent-Appellee.
No. 06-99006.
United States Court of Appeals, Ninth Circuit.
Argued and Submitted July 10, 2007.
Filed August 11, 2008.
*1064 Daniel D. Maynard, Maynard, Cronin, Erickson, Curran & Sparks, P.L.C., Phoenix, AZ, for the appellant.
John P. Todd, Assistant Attorney General, Phoenix, AZ, for the appellee.
Before: ALEX KOZINSKI, Chief Judge, ANDREW J. KLEINFELD, and RICHARD C. TALLMAN, Circuit Judges.
KLEINFELD, Circuit Judge:
This is a death penalty case. King robbed a convenience store. During the robbery, he murdered the clerk and the security guard. After his conviction for two first degree murders and armed robbery, appeals in the Arizona courts,[1] and denial and appeal of his petition for post-conviction relief in the Arizona courts, he petitioned unsuccessfully for a writ of habeas corpus in the United States District Court,[2] and now appeals. Two grounds for appeal have been certified: prosecutorial misconduct by vouching for one witness and implying that another witness was scared of King, and ineffective assistance of counsel at sentencing. At trial, the defense argued (King did not testify) that the jurors ought to have had a reasonable doubt about whether King really was the murderer or whether the person who was with him had done it.

FACTS
King committed the robbery and murders just after midnight. Security cameras caught the robbery and murder of the convenience store clerk, Ron Barman, on tape. Though the video did not clearly show King's face, it did show his distinctive diamond-patterned sweater. Also, despite the late hour, numerous individuals saw parts of the events, and several described the sweater pattern.
A Mr. Madden had driven into the parking lot of a restaurant behind the convenience store. He saw two men in the convenience store parking lot, one wearing a blue or black and white sweater with "some kind of pattern like pyramids," and the other wearing a "green sweatshirt." Hearing gunshots, he drove to the convenience store, got out, and saw the security guard, Richard Butts, lying on the ground, his holster empty. Mr. Butts was not yet dead, bleeding from the gut, and moaning. Mr. Madden dialed 911. As he dialed, he saw the man in the distinctive sweater go over to the security guard, wipe his holster and belt off with a white cloth, and leave.
Two more witnesses, Mr. Harris and Mr. Dils, heard the gunshots as they drove nearby. Mr. Harris saw two men running from the store, one carrying a gun. Mr. Harris and Mr. Dils stopped, and Mr. Harris saw the guard lying on the ground, *1065 entered the store, and saw the clerk, shot in the stomach and shoulder but not yet dead, yelling into the telephone. Mr. Dils checked the guard for a pulse, but found none. These two witnesses stayed and tried to help the clerk until the ambulance came.
Three more witnesses pulled into the convenience store parking lot. One noticed the guard on the ground, and another saw a man in a dark sweater with a white "logo" bend over the security guard and wipe off his holster with a white cloth before running away.
A Phoenix police officer got a radio call directing him to go to the convenience store and providing a description of the suspects. He saw two men more or less fitting the description, got out of his car, and told them to halt. One did (Michael Page Jones, whose testimony we describe below); the other, a man wearing a distinctive sweater, ran away.
Two more witnesses, Ms. Hill and Ms. Smith, were walking nearby. Ms. Hill was at that time Jones's girlfriend, and had known King for years. She saw King throw a plastic bag, containing a gun and a distinctive sweater she had seen him wearing earlier that night, into a dumpster. Ms. Hill called the police and identified King after seeing his picture, taken from the security camera, on television. The police then apprehended him.
At trial, King's lawyer skillfully brought out various discrepancies among the many witnesses' descriptions of King, his sweater, and the gun. Jones, the man with King at the time of the murders whom police caught right away, testified that he had stayed outside the store and heard the gunshots. He said he saw King leave the store with the gun in his hand and saw the security guard lying on the ground with an empty holster, though earlier that evening Jones had seen the security guard with a large handgun in his holster. Though Jones was at first charged with the crime, the charges against him had been dismissed by the time of King's trial. King's lawyer brought out on cross examination that the dismissal was without prejudice and that Jones understood that he could be charged again.
The prosecutor planned to put Jones and Ms. Hill on the witness stand, but was not confident that they would testify in accord with what they had told the police. In the prosecutor's opening statement, when he summarized the evidence he intended to put before the jury, he made the remarks that give rise to the certified claims of prosecutorial misconduct. Specifically, King contends that the prosecutor improperly vouched for Jones and implied that King or King's family had threatened Ms. Hill to keep her from testifying. Defense counsel had expected Jones not to testify for the prosecution, or to testify that he did not remember the events:

I hadn't expected Jones to be here, but since he is here, I think we need to have a determination before his direct examination, though I don't think either Paul or I knows what he's going to say. I think we have narrowed it down to two or three possibilities, and I think we need to know before he begins direct in what way the Court is going to allow Mr. Rood to impeach him. I think the most likely answer is I don't remember anything, and if that's the answer, it's my position that he cannot be impeached with a prior inconsistent statement, and I just would like a ruling from the Court on that issue before we begin. [Emphasis added.]
Before opening statements, in the hearing on in limine motions, defense counsel stated that even though Jones had been subpoenaed by the prosecutor, "I'm not sure he can produce him." She said this arguing for an in limine order to preclude the *1066 prosecutor from telling the jury what Jones would testify to since in her view he might not. Thus, the prosecutor had reason to prepare the jury for the possibility that Jones might not show up and testify to what he had previously said.
During his opening statement, the prosecutor said that he could not guarantee what Jones would say on the witness stand, but "if he testifies truthfully," that is, in accord with what he had told the police, he would implicate King:
You will hear from a man by the name of Michael Page Jones. Mr. Jones was with Eric King that night. In fact, at one time Mr. Jones was charged as an accomplice. The case was later dismissed. Michael Jones was with Mr. King. He told the police officers later in December exactly what happened. I can't guarantee you what Mr. Michael Page Jones is going to say when he gets on the stand, ladies and gentlemen, but he was there that night and he has information, and I suggest to you that if he testifies truthfully as he should, he will implicate the defendant, Eric King, without a doubt. [emphasis added]
Also during his opening statement, the prosecutor explained that he would put Ms. Hill on the witness stand, but that she did not want to testify and "is scared to death":
Who else? Renee Hill is here. Renee Hill at one time was the girlfriend of Michael Jones. Renee Hill currently lives in the Projects. She is on welfare, and she is scared to death. She comes to Court today not voluntarily, but because Detective House managed to go out and find her over the last 24 or 36 hours and bring her to the Court. She is scared. Whether she should be or whether she shouldn't be, ladies and gentlemen, it doesn't matter, because in her own mind she is scared. She does not want to testify. She does not want to come into this courtroom under any circumstances. Ladies and gentlemen, she will be brought into this courtroom, and you will hear her testify. [Emphasis added.]
Defense counsel did not object to the prosecutor's comments at the time they were made, but after the prosecutor had completed his opening statement, defense counsel moved for a mistrial on the basis of the "if he tells the truth" statement about Jones. The trial judge denied the motion for three reasons: it was not "clear vouching under the circumstances," the court had instructed the jurors that the statements of counsel were not evidence, and the jurors would be so admonished again in the instructions at the end of the trial. The court offered to give the admonition again, but wondered whether defense counsel wanted the jury to be reminded that what the lawyers say is not evidence just before she gave her opening statement. Defense counsel responded "I don't want you to."
Defense counsel did not, during the prosecutor's opening statement, or in her motion for a mistrial immediately after the opening statement, raise any question with regard to the remarks in the opening statement about Ms. Hill. The prosecutor's statement that Ms. Hill was "scared to death" went unobjected to and unraised in the motion. But after Ms. Hill had testified, defense counsel moved for a mistrial based on the combination of Ms. Hill's testimony and the prosecutor's remarks. The trial judge denied the motion, finding that the prosecutor's remark was supported by Ms. Hill's demeanor, which showed that she was a reluctant witness who did not want to be there and was afraid, and that there was no indication that her fear came from anything King said or did:
[Ms. Hill's] demeanor obviously indicated she did not want to be there. She *1067 was a very reluctant witness. It was obvious she was under a great deal of stress and anxiety and fear, and she never indicated that fear was coming from any specific individual or defendant or anybody else from his family.
As counsel had expected, Jones claimed memory problems. When he was asked which direction he was going when the policeman stopped him half a block from the convenience store, he said, "I don't actually remember," and when asked whether he was coming back from the convenience store, he said, "I really don't know. I was very intoxicated at the time." Subsequent police testimony was that they did not smell alcohol on his breath. Jones then admitted that he had been at the convenience store some time that evening with King, but when asked whether he was there earlier he said, "I don't remember." As the questions proceeded he said, "I don't really remember much."
But then Jones admitted that he had talked to one of the police officers and that he did indeed go to the convenience store more than once with King that evening. He had told the policeman he did not go into the store, but that he was there when the murders were committed. As the prosecutor continued asking detailed questions, Jones conceded that he looked in the direction of the store because he had heard two gunshots, and that he then saw King coming out of the store with a gun in his hand. Jones testified that he saw the security guard lying on the ground, and he ran away because he was scared.
After the murders, but before trial, King changed his appearance by shaving off his beard and sideburns. Jones testified he could not identify the person in the picture shown to him on the stand, but then conceded that it seemed like King. Asked whether he had told the police officer the truth at the time of his arrest, he said, "I do not lie very often." Jones also said he was telling the truth on the stand when he said King was at the convenience store with a gun in his hand when he heard two shots. When asked whether he had any idea where the gun in King's hand came from, he testified "My guess is it was the security guard's," because previously the security guard had had a gun that looked like a .44 Magnum or a .357 in his holster. On cross examination, defense counsel elicited that the murder and robbery charges against Jones had been dismissed, but that they could be filed again. The policeman who had interrogated Jones also testified that Jones had told him approximately the same story that Jones told on the witness stand.
King also appeals a second certified issue of ineffective assistance of counsel at sentencing. For the reader's convenience, we state the facts related to this claim below, where we consider it.

ANALYSIS
This is a petition for a writ of habeas corpus from a state conviction, governed by the limitations on our review under 28 U.S.C. § 2254. Accordingly, though we review the district court's decision de novo,[3] our review of the state court is highly deferential.[4] The Antiterrorism and Effective Death Penalty Act of 1996 (AEDPA)[5] provides that we cannot impose our view of what federal constitutional law requires on the state system unless the state court decision was contrary to or *1068 unreasonably applied federal law clearly established by the United States Supreme Court:
An application for a writ of habeas corpus on behalf of a person in custody pursuant to the judgment of a State court shall not be granted with respect to any claim that was adjudicated on the merits in State court unless the adjudication of the claim
(1) resulted in a decision that was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States.[6]
Thus, all we can decide regarding these remarks by the prosecutor is whether the Arizona Supreme Court acted contrary to or unreasonably applied Supreme Court holdings when it decided not to vacate the conviction.[7]
Appellant's brief does not cite any Supreme Court decision that the Arizona Supreme Court acted contrary to or unreasonably applied regarding the prosecutor's remarks in his opening statement, and the only decision of the Supreme Court cited in appellant's brief on the ineffective assistance claim is Strickland v. Washington.[8] The Arizona Supreme Court's decision denying relief may be set aside only if it acted contrary to or unreasonably applied the Supreme Court's holdings, regardless of whether it decided as we would have.[9] For the "contrary to" clause, appellant would have to demonstrate that the state court decision "`arrives at a conclusion opposite to that reached by [the Supreme Court] on a question of law,'"[10] or when faced with "materially indistinguishable" facts.[11] The "unreasonable application" clause requires not merely that we disagree with the state court's application,[12] but beyond that, that the state court decision is objectively unreasonable.[13] Even if we think the state court erred, the state court decision stands if the error was not an unreasonable application of Supreme Court holdings. State court factual determinations stand, even if we would not reach them on the same record, unless there is "clear and convincing evidence" that they are "objectively unreasonable."[14] Thus, our analysis in a case governed by § 2254 is quite confined.

I. Prosecutorial Misconduct

A. Jones's Testimony
The Arizona Supreme Court considered whether in context the prosecutor's "if he testifies truthfully" remark placed the prestige of the government behind Jones's testimony or suggested that information not presented to the jury supported Jones's testimony.[15] These were the right factors to consider, under the *1069 Supreme Court's decision in United States v. Young.[16] As to the first factor, far from giving the jury the government's assurance that Jones was honest, the prosecutor was revealing doubts about whether he would testify honestly. As the Arizona Supreme Court explained, the prosecutor was "preparing the jury for the possibility that Jones might testify otherwise" than the account he gave to the police officer who interrogated him.[17] As to the second Young factor, suggesting that the prosecutor knew something that the jury did not, the prosecutor put the police officer on the stand to testify about what Jones had told him and got Jones to admit (after considerable memory difficulties) what he had previously told the police officer. The implication was that the prosecutor knew what Jones told the police, nothing more, and the jury heard the testimony of the police about what Jones told them.
What controls the outcome of this case is whether the Arizona Supreme Court unreasonably concluded that, taken in context, the prosecutor's comments neither placed the government's imprimatur on Jones's testimony nor implied that information not in evidence showed what the truth really was, such that the "fairness, integrity or public reputation of the judicial proceedings"[18] were seriously affected.[19] A cautious prosecutor may well wish to avoid saying anything that implies that he knows what is actually the truth. And an epistemologically sensible prosecutor may realize that he does not, since he was not at the scene of the crime and relies on what others of varying credibility say they saw or heard and on arguable inferences from the circumstantial evidence. Even the criminals, victims, and witnesses are often unsure or mistaken. In this case, the Arizona Supreme Court's application of the Supreme Court's holding in Young was not unreasonable, so we must deny relief.[20]

B. Hill's Testimony
King's theory regarding the prosecutor's "she's scared to death" remark about Ms. Hill is that it implied facts not in evidence, showing that King or King's family had threatened to kill her if she testified. But defense counsel did not object when the prosecutor made the remark. Even when moving for a mistrial at the end of the prosecutor's opening statement because of the "if he testifies truthfully" statement about Jones, the defense did not move for a mistrial or otherwise object to the "scared to death" language about Ms. Hill. King did raise the matter, finally, after Ms. Hill had completed her testimony and left the witness stand, in another motion for mistrial.
The Arizona Supreme Court rejected King's argument on alternative grounds.[21] First, under Arizona law, "the defendant must voice his objection to arguments that are objectionable, and failure to do so constitutes a waiver of any right to review."[22] The court cited a well established *1070 body of Arizona law to that effect.[23]
Second, the Arizona Supreme Court rejected the argument on the merits because Ms. Hill's fear was obvious from her demeanor, and her "unwillingness to testify goes directly to her credibility."[24] The court explained that the prosecutor rightly wanted to prepare the jury for Ms. Hill's demeanor, and even if the prosecutor's remarks were "improper but colorful hyperbole,"[25] they had no significant effect:
Hill testified that she called the police after seeing the surveillance pictures broadcast on television. She admitted that she identified defendant as the person in the picture. When asked whether defendant was the person depicted in the surveillance photograph, however, she repeatedly stated that the person in the picture did not look like defendant. Her fear and anxiety over testifying certainly served to bolster her earlier identifications over her trial testimony.[26]
The court concluded that there was no plain error and no prejudice in King's case. Ms. Hill testified that "I don't want to testify. I am being held against my will, something I don't want to do. . . . I got my own troubles and worries." The Arizona Supreme Court thus agreed with the trial court's conclusion that Ms. Hill's fear was obvious from her testimony, so the prosecutor's remark did not have the effect of denying King a fair trial.
The Arizona Supreme Court also evaluated the statement in context and concluded that "the prosecutor had no idea what Ms. Hill would say once she was on the stand," but "rightly anticipated that he would have to provide the jury some explanation for Hill's eventual refusal to identify defendant."[27] In fact, after trying to get off the witness stand before direct was even completed, Ms. Hill testified that the surveillance photograph shown on television, which had prompted her to call the police, did not look like King after all.
On appeal to us, King argues that the failure to object arose because defense counsel expected there to be evidence of a threat and saw no prejudice until it was clear no such evidence would be presented. But there is no evidence or authority before us showing how that speculation would bear on the question of whether the Arizona Supreme Court acted contrary to or unreasonably applied Supreme Court holdings.
We have no supervisory authority over Arizona court proceedings,[28] and it is plain from Ms. Hill's own testimony that she was scared of something. The state trial judge's finding that her demeanor showed fear is not "based on an unreasonable determination of the facts in light of the evidence presented in the State court proceeding," so we cannot reject it.[29] It is clear that she was scared, though neither the prosecutor's statement nor Ms. Hill's testimony says who or what was the cause. She could have been scared of a threat, or a reputation as a "snitch," or social ostracism from King's friends, or something unrelated to this case that might be exposed on cross examination, or merely involvement with the police and the judicial system. In evaluating a claim of prosecutorial misconduct, "a court should not lightly infer that a prosecutor intends an *1071 ambiguous remark to have its most damaging meaning or that a jury, sitting through lengthy exhortation, will draw that meaning from the plethora of less damaging interpretations."[30] Appellant has not brought to our attention any Supreme Court holding that would have required the Arizona Supreme Court to follow another course in this case. Since the Arizona Supreme Court did not act contrary to or misapply Supreme Court holdings, we must deny relief.[31]

II. Ineffective Assistance of Counsel
King's second certified claim is that he received ineffective assistance of counsel at sentencing. The only authority he cites is Strickland v. Washington.[32]
The lawyer initially appointed to represent King was public defender Mr. Roland J. Steinle, III. He moved to withdraw because his office represented several individuals who might become witnesses. The trial court granted this motion to withdraw for conflict of interest, and appointed Ms. Mary Wisdom, from the private bar, to represent King. She represented King through trial, and the certified issues do not include any claim of ineffective assistance by her through trial and the verdicts of guilty on all counts.
After he lost his case, King personally asked the trial court to appoint replacement counsel. Ms. Wisdom filed a "motion to determine counsel," based on a handwritten letter from King to the judge. King claimed in his letter that the evidence was not sufficient to convict him, Jones should not have been allowed to testify, and the transcripts would "reveal the bias and prejudice conduct of state and my own counsel, was part of this conspiracy to convict not on provided information submitted to grand jury but only because of my ethnic background in order to satisfy society."
At the hearing on this motion on October 30, 1990, Ms. Wisdom advocated reappointing Mr. Steinle, since her client no longer trusted her, and Mr. Steinle no longer had a conflict of interest (none of the witnesses his office represented had testified). The judge was reluctant to change attorneys and lose the virtues of continuity, but King insisted. He said to the judge "I want new counsel." Besides complaining about Ms. Wisdom's lack of success and some things he felt she ought to have done, King said more broadly "I just don't feel that she did her best, and I feel I got railroaded." The judge remained reluctant, and asked Ms. Wisdom to comment. She said that King "will not cooperate with me in what evidence we ought to present to the Court in mitigation. . . and I'm somewhat dependent upon my client to present mitigation." The reason King would not cooperate was that "[h]e's alleged that I conspired to ensure his conviction because he's black, Your Honor." The judge asked King if he stood by that allegation, and King said, "Yes."
The judge accordingly granted King's request, reappointed the public defender's office, and stated his expectation that he would continue the sentencing hearing. Two months later, in early January 1991, the court held a status conference, at which King's original lawyer, Mr. Steinle, appeared. The court arranged for sentencing to be six weeks thence, 3 months after Mr. Steinle's substitution for Ms. *1072 Wisdom. A further continuance moved the sentencing hearing to March 1, 1991, a full four months after the substitution of counsel.
King makes several arguments for ineffective assistance of counsel in sentencing. First, he argues (without citation) that "there needs to be continuity of representation." This has little force, because King himself demanded the discontinuity, and the court gave substitute counsel four months to prepare (and he did not request more time). Next, King argues that counsel was ineffective for not requesting a second attorney or a "mitigation specialist," but he cites no authority for the proposition that counsel should have done so, and makes no showing of prejudice from not doing so.
Finally, King argues that counsel did not adequately prepare for the mitigation hearing. The only evidence in the record that King points to in support of this claim is an affidavit by a Ms. Mary Patricia Durand. Ms. Durand states that she is a private investigator. She sets out a number of things that she thinks ought generally to be done in death penalty mitigation investigations and states her opinion that no adequate investigation was performed for King. Ms. Durand does not explain how any of the inquiries she recommends might have benefitted King. Nor does she recite any investigation she has done or anything she found in any such investigation that might have benefitted King and was not brought out at King's sentencing hearing.
Ms. Durand criticizes the reports King's attorney obtained from two doctors of psychology as being based on insufficient foundation and investigation, but does not say what the additional investigation she advocates might have turned up.
The district court noted that before King demanded that she be replaced, Ms. Wisdom had obtained funding for a mental health examination, disclosure of his school records and prison file (he committed the robbery and murders four months after serving seven years for rape and kidnapping), and interviewed several family members. Only one psychologist had examined King and prepared a report at the time of sentencing, and defense counsel presented testimony from him. The second psychologist did not prepare his report until 1996, five years after King was put on death row. But, as the district court noted, the two psychologists say approximately the same thing in their reports.
At sentencing, the defense psychologist testified that he had interviewed King on a number of occasions, gathered a history including the psychological report from the state department of prisons, performed psychological tests, interviewed family members, and studied the trial transcript. Though he found no indication in any of the tests of any organic brain damage, he opined that King had a very significant post traumatic stress disorder. While some of the trauma was of little value for mitigation (King's parents were divorced when he was a small child, his father died of a heart attack when he was eleven, the family spent seven years battling over the father's estate in court), some was extremely serious. The most severe, which counsel brought out effectively, was that when King was ten, he misbehaved and left the house without permission. His mother was not content with having his brothers go get him and bring him home. "[S]he put a gun to his head and told him that she would kill him if he misbehaved again."
Other information elicited was that after his father died, his mother commenced "living with a man who periodically beat her." One of King's brothers said that "he was beating and battering their mother to the point where she at one time he started to beat on her and she had to pull out a gun shoot him [sic] to stop him doing *1073 that," and another time "one of the brothers had to put a knife to his throat one time to stop, to warn him not to do that anymore." Then all the brothers, including King, moved out (King was fifteen) because "[t]hey had just got to the point where somebody was going to get hurt." Subsequently, King began abusing alcohol and drugs, which the psychologist attributed to "self-medicating" to drown out the trauma. Also, when King was serving his time for the rape and kidnapping, there was a riot in which an acquaintance of King's was killed.
The psychologist opined that trauma such as King had endured can cause "some insensitivity to the needs of others . . . consistent . . . with an anti-social kind of orientation." King had normal intelligence and no learning disorder, and had made good grades in school until he dropped out. The psychologist thought King had a "much much greater chance of successfully undergoing some treatment regime" in prison, because he would not miss appointments, and his life would be given structure and rules. He thought King "would be able to profit" from treatment, was fairly intelligent, and that the risk of violence would decline as he aged.
As this mitigation testimony proceeded into cross examination, King said "I don't want to be here." The judge emphasized to him his right to be present, but King said "I did not commit the crime. No evidence, no effect. . . . You will give me the death penalty or life. I feel either way you go and I want to leave." Then King left.
On cross examination, the prosecutor brought out that the interviews showed King perceived others to be threatening "and has worked very hard to be insensitive and hardened to any kind of emotional reaction because it can re-trigger the trauma." King viewed the world, as a result of his trauma, as a jungle where the strong took from the weak. Asked whether King would take from others to be strong rather than weak, the psychologist replied that "[w]hen he feels threatened or in a potentially threatening kind of situation for him, then that would be his defense."
The sentencing judge accepted substantially all of the mitigation evidence, except for the psychologist's speculation that King might have been drunk when he committed the armed robbery and murders. He expressly considered the mitigation factors that the psychologist and defense counsel had brought out, and noted the mother's letter that said she loved her son.[33] He accepted the testimony that King suffered from posttraumatic stress on account of the abuse he suffered as a child. But he concluded that the mitigating factors were outweighed by the aggravating factors: that King murdered Robert Barman and Richard Butts to facilitate his escape and keep the $72.84 taken from the cash register and that the murders were premeditated and depraved, as evidenced by the facts that King killed the two men so that they could not testify against him, wiped his fingerprints off the gun, and got rid of his clothes and gun to avoid capture.
King's brief does not suggest that he ought to have received an evidentiary hearing. All he presents to support his argument that his lawyer should have done more to establish mitigation is the private *1074 detective's affidavit stating that in her opinion, more ought to have been done.
Even if we were to assume (without deciding) that the private investigator was right, and that counsel's performance was deficient, Strickland v. Washington[34] also requires a showing that "there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different."[35] We "need not determine whether counsel's performance was deficient before examining the prejudice suffered by the defendant as a result of the alleged deficiencies."[36]
The district court concluded, and we agree, that King made no showing of prejudice. The private detective's affidavit, though it opined that more investigation should have been done, "does not . . . contain any information suggesting what the results of a more complete social and medical history of Petitioner would have revealed."[37] In his post-conviction relief proceedings, King did produce the second psychologist's report, obtained five years after sentencing. But that report does not say anything substantially different or more helpful than the first psychologist's report.
The second psychologist says that after being on death row for several years, King displayed an "overall mood of mild depression." The psychologist described additional abuse by his mother, whipping him with telephone cords and extension cords and limbs from an oleander tree, as well as putting the gun to his head, but said King "had no hard feelings concerning this." The tension on death row when the state started executing people was very stressful for King, and for a while (two years before the psychological examination) he was hearing voices because "this place will drive you crazy at times." He had headaches from the stress. This psychologist's examination of King showed "no signs of hallucinations and/or delusions." He concluded that "[a]t the present time, Mr. King is not a cold, callous individual," but because of his traumatic home environment, "he has never learned to love himself nor to believe that he is worthy of anyone's consideration." His release from prison after he had served his time for the rape and kidnapping "left [him] to his own faulty resources, which resulted in a continuation of excessive drug and alcohol dependency," and "this type of benign neglect played a central role in Mr. King's behavior and subsequent crime."
Like the district judge, we are unable to see how any of this would have changed the outcome of King's sentencing. The second psychologist's report is the only evidence in the record that shows what might have been turned up if his defense attorney had done more investigation. The test we are required by Strickland to apply is whether "there is a reasonable probability that . . . the result of the proceeding would have been different."[38] There is not.

III. Uncertified Issues
King also raises six issues that have not been certified for appeal. We have carefully examined each of them, applying the liberal Miller-El v. Cockrell[39]*1075 standard, which requires that a "`petitioner must demonstrate that reasonable jurists would find the district court's assessment of the constitutional claims debatable or wrong.'"[40] We agree with the district court's determination that the uncertified claims do not meet this standard.[41]
AFFIRMED.
NOTES
[1]  See State v. King, 180 Ariz. 268, 883 P.2d 1024 (1994).
[2]  See King v. Schriro, 2006 WL 1735247 (D.Ariz. June 22, 2006).
[3]  See Nulph v. Cook, 333 F.3d 1052, 1056 (9th Cir.2003).
[4]  See Lindh v. Murphy, 521 U.S. 320, 334 n. 7, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).
[5]  28 U.S.C. § 2254; see Lindh v. Murphy, 521 U.S. 320, 334 n. 7, 117 S.Ct. 2059, 138 L.Ed.2d 481 (1997).
[6]  28 U.S.C. § 2254(d).
[7]  See Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 653-54, 166 L.Ed.2d 482 (2006).
[8]  466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
[9]  See Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 653-54, 166 L.Ed.2d 482 (2006).
[10]  Stenson v. Lambert, 504 F.3d 873, 881 (9th Cir.2007) (alteration in original) (quoting Williams v. Taylor, 529 U.S. 362, 405, 120 S.Ct. 1495, 146 L.Ed.2d 389 (2000)).
[11]  Id.
[12]  Cooks v. Newland, 395 F.3d 1077, 1080 (9th Cir.2005) ("The `unreasonable application' clause requires the state court decision to be more than incorrect or erroneous." (quoting Lockyer v. Andrade, 538 U.S. 63, 75, 123 S.Ct. 1166, 155 L.Ed.2d 144 (2003))).
[13]  Id.
[14]  Miller-El v. Cockrell, 537 U.S. 322, 340, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003).
[15]  State v. King, 180 Ariz. 268, 883 P.2d 1024, 1032-33 (1994).
[16]  470 U.S. 1, 7 n. 3, 11-12, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985).
[17]  State v. King, 180 Ariz. 268, 883 P.2d 1024, 1033 (1994).
[18]  United States v. Young, 470 U.S. 1, 15, 105 S.Ct. 1038, 84 L.Ed.2d 1 (1985) (quoting United States v. Atkinson, 297 U.S. 157, 160, 56 S.Ct. 391, 80 L.Ed. 555 (1936)); see Darden v. Wainwright, 477 U.S. 168, 180-81, 106 S.Ct. 2464, 91 L.Ed.2d 144 (1986).
[19]  See Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 653, 166 L.Ed.2d 482 (2006).
[20]  28 U.S.C. § 2254(d); Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 653, 166 L.Ed.2d 482 (2006).
[21]  State v. King, 180 Ariz. 268, 883 P.2d 1024, 1033-34 (1994).
[22]  Id. at 1033.
[23]  See id. (citing State v. Holmes, 110 Ariz. 494, 520 P.2d 1118, 1120 (1974)).
[24]  Id. at 1033-34.
[25]  Id. at 1034.
[26]  Id.
[27]  Id. at 1033.
[28]  See Donnelly v. DeChristoforo, 416 U.S. 637, 647-48, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974).
[29]  28 U.S.C. § 2254(d)(2).
[30]  Donnelly v. DeChristoforo, 416 U.S. 637, 647, 94 S.Ct. 1868, 40 L.Ed.2d 431 (1974).
[31]  28 U.S.C. § 2254(d); Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 653, 166 L.Ed.2d 482 (2006).
[32]  466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
[33]  Though this is how the sentencing judge interpreted the letter, King's mother focused on sufficiency of the evidence rather than her feelings or her son's virtues. The mitigation information she provided was that King had had "only 12 weeks of freedom" before being arrested for the murders. The remainder of her letter complains that the evidence against King was not strong enough, because Jones should not have been believed and the identification evidence was inadequate.
[34]  466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
[35]  Id. at 694, 104 S.Ct. 2052.
[36]  Id. at 697, 104 S.Ct. 2052.
[37]  King v. Schriro, 2006 WL 1735247, at *22 (D.Ariz. June 22, 2006).
[38]  Strickland v. Washington, 466 U.S. 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984).
[39]  537 U.S. 322, 123 S.Ct. 1029, 154 L.Ed.2d 931. We treat the briefing of uncertified issues on appeal as a motion to expand the certificate of appealability, see 9th Cir. R. 22-1(e), and so apply the same standard used to evaluate a request for a certificate of appealability in the first instance, see Doe v. Woodford, 508 F.3d 563, 567 (9th Cir.2007).
[40]  Miller-El v. Cockrell, 537 U.S. 322, 338, 123 S.Ct. 1029, 154 L.Ed.2d 931 (2003) (quoting Slack v. McDaniel, 529 U.S. 473, 484, 120 S.Ct. 1595, 146 L.Ed.2d 542 (2000)).
[41]  The uncertified issues include: (1) failure to grant an evidentiary hearing, not on ineffective assistance at sentencing, but on whether Jones had an undisclosed deal and whether alibi evidence should have been put on; (2) whether his right to confrontation was violated because Jones's statements to the police interrogator were brought out to impeach Jones (although the police interrogator was sworn and subject to cross examination); (3) whether consideration of the robbery in sentencing for each of the murders amounted to double jeopardy; (4) whether the Arizona death penalty statute unconstitutionally failed to adequately channel discretion; (5) whether he received ineffective assistance of counsel because his lawyer did not put on an alibi defense (for which King has offered no evidence); (6) whether his conviction violated due process because of various claims that King did not exhaust in state court, viz., that Jones lied and the prosecutor knew it, that the interrogating officer did not preserve the handwritten notes upon which he had based his report, that the remaining jurors were not interrogated about what they heard after a juror who had talked to someone about the case was dismissed, that witnesses should not have been allowed to identify King from the videotape because they were laymen, that Ring v. Arizona, 536 U.S. 584, 122 S.Ct. 2428, 153 L.Ed.2d 556 (2002), was not applied retroactively, that the Arizona death penalty violates the equal protection clause, etc.
