EASTERBROOK, Chief Judge.
A jury concluded that Michael Over-street kidnapped, raped, and murdered Kelly Eckart. The jury recommended that he be executed for these offenses, and the state judge imposed a death sentence. The Supreme Court of Indiana affirmed Overstreet’s convictions and sentence, 783 N.E.2d 1140 (2003), and affirmed an order denying his petition for post-conviction relief, 877 N.E.2d 144 (2007). The only issues in this collateral attack under 28 U.S.C. § 2254 concern the penalty. The district court denied Overstreet’s petition. 2011 WL 836800, 2011 U.S. Dist. Lexis 22175 (N.D.Ind. Mar. 4, 2011).
Overstreet contends that during the penalty proceedings his lawyers made three errors that individually or collectively amount to ineffective assistance. One supposed error is that counsel did not ask the trial judge to require spectators who wore buttons or ribbons with Eekart’s picture to remove the displays of sympathy for the victim. Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 166 L.Ed.2d 482 (2006), shows that defendants did not have any constitutional right to such a removal order at the time of Overstreet’s trial and appeal — and no decision since Carey has created such an entitlement, let alone held that it would apply retroactively. Indiana law could give defendants greater protection than the Constitution does of its own force, and counsel who failed to ensure that defendants received all of their state-law rights might fail the performance element of the ineffective-assistance standard, see Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), but Overstreet does not cite any statute, rule, or decision establishing that Indiana entitles defendants to trial in a courtroom free of symbols implying support for the victim. No juror could have doubted that Eckart had friends and family who mourned her death. That’s the message the pictures conveyed, and in the post-conviction proceedings the state trial judge found that Overstreet had not established prejudice.
His second contention is that his lawyers failed to convey “effectively” or “meaningfully” the prosecutor’s offer of a plea bargain. Overstreet contends that the prosecutor orally proposed a sentence of life in prison without possibility of parole. Missouri v. Frye, — U.S.-, 132 S.Ct. 1399, 1408-10, 182 L.Ed.2d 379 (2012), holds that failure to communicate a plea offer to the defendant is deficient performance. Overstreet’s lawyers did relay the offer to him, and he turned it down. He contends, however, that the communication was not effective because he was having a psychotic “break” at the time and could not appreciate the offer’s significance. Frye does not consider whether counsel furnish ineffective assistance by [407]*407failing to convey a plea offer “effectively”; we assume without deciding that counsel must do so. Similarly, Frye does not discuss the proper treatment of oral offers (the Court stressed that the offer to Frye was a writing that contained all material terms); we assume, again without deciding, that counsel’s duty to communicate potential bargains to their clients covers oral offers before they are term-complete.
Overstreet has mental problems. The psychiatric evidence in the record leaves little doubt that on some occasions Over-street would have lacked the ability to evaluate his legal situation rationally. The evidence is mixed about Overstreet’s mental state at the time his lawyers presented the offer for his consideration. See 2011 WL 836800 at *7-10, 2011 U.S. Dist. Lexis 22175 at *21-26. The district judge concluded that Overstreet understood the offer and discussed it intelligently with his sister; Overstreet says that the judge was mistaken, but we need not decide. After conducting a six-day hearing on Over-street’s request for collateral relief, the judge who had conducted Overstreet’s trial and imposed the death sentence issued a lengthy opinion denying his petition. The judge stated at page 82 of her decision that any shortcoming by counsel did not cause prejudice because, if Overstreet had attempted to plead guilty before trial, she would have rejected the plea. Frye holds that, to show prejudice from counsel’s failure to convey a plea offer, “defendants who have shown a reasonable probability they would have accepted the earlier plea offer must also show that, if the prosecution had the discretion to cancel it or if the trial court had the discretion to refuse to accept it, there is a reasonable probability neither the prosecution nor the trial court would have prevented the offer from being accepted or implemented.” 132 S.Ct. at 1410. Here we have a finding, by the trial judge herself, that she would not have accepted a guilty plea.
The due process clause permits judges to accept guilty pleas from defendants who do not admit the factual basis of the charge against them, when the judge nonetheless has an adequate basis for finding that the defendant committed the crime. See North Carolina v. Alford, 400 U.S. 25, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970). But the Court added that states are not required to accept such pleas, id. at 38 & n. 11, 91 S.Ct. 160, and Indiana has chosen to forbid Alford pleas. See Carter v. State, 739 N.E.2d 126, 128-29 (Ind. 2000). A defendant who wants to plead guilty in Indiana must admit the factual basis of the plea in open court. Overstreet denies having any memory of the night when Eckart was killed and said repeatedly — to his lawyers and to the trial judge— that he could not plead guilty when he did not know himself to be guilty. This is why the state judge declared that she would not have accepted a guilty plea had Over-street attempted to enter one.
He contends that Carter allows a judge in Indiana to accept a guilty plea from an amnesiac; according to Over-street, Indiana blocks Alford pleas only when the defendant affirmatively denies culpability. But a writ under § 2254 cannot be based on a federal court’s belief that the state judiciary misunderstands state law. See, e.g., Wilson v. Corcoran, — U.S.-, 131 S.Ct. 13, 178 L.Ed.2d 276 (2010). The state trial judge has told us what she would have done, and why, had Overstreet attempted to plead guilty; given Frye’s definition of prejudice, that finding is dispositive.
Oversteet’s third line of argument is that his lawyers fell short when presenting mitigating evidence during the sentencing hearing. Given 28 U.S.C. [408]*408§ 2254(d), this is an uphill battle. See, e.g., Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1401-11, 179 L.Ed.2d 557 (2011); Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011); Wood v. Allen, 558 U.S. 290, 130 S.Ct. 841, 175 L.Ed.2d 738 (2010); Wong v. Belmontes, 558 U.S. 15, 130 S.Ct. 383, 175 L.Ed.2d 328 (2009). The Supreme Court of Indiana did not contradict any law established by the Supreme Court; it cited Strickland and accurately summarized its holding.
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EASTERBROOK, Chief Judge.
A jury concluded that Michael Over-street kidnapped, raped, and murdered Kelly Eckart. The jury recommended that he be executed for these offenses, and the state judge imposed a death sentence. The Supreme Court of Indiana affirmed Overstreet’s convictions and sentence, 783 N.E.2d 1140 (2003), and affirmed an order denying his petition for post-conviction relief, 877 N.E.2d 144 (2007). The only issues in this collateral attack under 28 U.S.C. § 2254 concern the penalty. The district court denied Overstreet’s petition. 2011 WL 836800, 2011 U.S. Dist. Lexis 22175 (N.D.Ind. Mar. 4, 2011).
Overstreet contends that during the penalty proceedings his lawyers made three errors that individually or collectively amount to ineffective assistance. One supposed error is that counsel did not ask the trial judge to require spectators who wore buttons or ribbons with Eekart’s picture to remove the displays of sympathy for the victim. Carey v. Musladin, 549 U.S. 70, 127 S.Ct. 649, 166 L.Ed.2d 482 (2006), shows that defendants did not have any constitutional right to such a removal order at the time of Overstreet’s trial and appeal — and no decision since Carey has created such an entitlement, let alone held that it would apply retroactively. Indiana law could give defendants greater protection than the Constitution does of its own force, and counsel who failed to ensure that defendants received all of their state-law rights might fail the performance element of the ineffective-assistance standard, see Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), but Overstreet does not cite any statute, rule, or decision establishing that Indiana entitles defendants to trial in a courtroom free of symbols implying support for the victim. No juror could have doubted that Eckart had friends and family who mourned her death. That’s the message the pictures conveyed, and in the post-conviction proceedings the state trial judge found that Overstreet had not established prejudice.
His second contention is that his lawyers failed to convey “effectively” or “meaningfully” the prosecutor’s offer of a plea bargain. Overstreet contends that the prosecutor orally proposed a sentence of life in prison without possibility of parole. Missouri v. Frye, — U.S.-, 132 S.Ct. 1399, 1408-10, 182 L.Ed.2d 379 (2012), holds that failure to communicate a plea offer to the defendant is deficient performance. Overstreet’s lawyers did relay the offer to him, and he turned it down. He contends, however, that the communication was not effective because he was having a psychotic “break” at the time and could not appreciate the offer’s significance. Frye does not consider whether counsel furnish ineffective assistance by [407]*407failing to convey a plea offer “effectively”; we assume without deciding that counsel must do so. Similarly, Frye does not discuss the proper treatment of oral offers (the Court stressed that the offer to Frye was a writing that contained all material terms); we assume, again without deciding, that counsel’s duty to communicate potential bargains to their clients covers oral offers before they are term-complete.
Overstreet has mental problems. The psychiatric evidence in the record leaves little doubt that on some occasions Over-street would have lacked the ability to evaluate his legal situation rationally. The evidence is mixed about Overstreet’s mental state at the time his lawyers presented the offer for his consideration. See 2011 WL 836800 at *7-10, 2011 U.S. Dist. Lexis 22175 at *21-26. The district judge concluded that Overstreet understood the offer and discussed it intelligently with his sister; Overstreet says that the judge was mistaken, but we need not decide. After conducting a six-day hearing on Over-street’s request for collateral relief, the judge who had conducted Overstreet’s trial and imposed the death sentence issued a lengthy opinion denying his petition. The judge stated at page 82 of her decision that any shortcoming by counsel did not cause prejudice because, if Overstreet had attempted to plead guilty before trial, she would have rejected the plea. Frye holds that, to show prejudice from counsel’s failure to convey a plea offer, “defendants who have shown a reasonable probability they would have accepted the earlier plea offer must also show that, if the prosecution had the discretion to cancel it or if the trial court had the discretion to refuse to accept it, there is a reasonable probability neither the prosecution nor the trial court would have prevented the offer from being accepted or implemented.” 132 S.Ct. at 1410. Here we have a finding, by the trial judge herself, that she would not have accepted a guilty plea.
The due process clause permits judges to accept guilty pleas from defendants who do not admit the factual basis of the charge against them, when the judge nonetheless has an adequate basis for finding that the defendant committed the crime. See North Carolina v. Alford, 400 U.S. 25, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970). But the Court added that states are not required to accept such pleas, id. at 38 & n. 11, 91 S.Ct. 160, and Indiana has chosen to forbid Alford pleas. See Carter v. State, 739 N.E.2d 126, 128-29 (Ind. 2000). A defendant who wants to plead guilty in Indiana must admit the factual basis of the plea in open court. Overstreet denies having any memory of the night when Eckart was killed and said repeatedly — to his lawyers and to the trial judge— that he could not plead guilty when he did not know himself to be guilty. This is why the state judge declared that she would not have accepted a guilty plea had Over-street attempted to enter one.
He contends that Carter allows a judge in Indiana to accept a guilty plea from an amnesiac; according to Over-street, Indiana blocks Alford pleas only when the defendant affirmatively denies culpability. But a writ under § 2254 cannot be based on a federal court’s belief that the state judiciary misunderstands state law. See, e.g., Wilson v. Corcoran, — U.S.-, 131 S.Ct. 13, 178 L.Ed.2d 276 (2010). The state trial judge has told us what she would have done, and why, had Overstreet attempted to plead guilty; given Frye’s definition of prejudice, that finding is dispositive.
Oversteet’s third line of argument is that his lawyers fell short when presenting mitigating evidence during the sentencing hearing. Given 28 U.S.C. [408]*408§ 2254(d), this is an uphill battle. See, e.g., Cullen v. Pinholster, — U.S. -, 131 S.Ct. 1388, 1401-11, 179 L.Ed.2d 557 (2011); Harrington v. Richter, — U.S. -, 131 S.Ct. 770, 178 L.Ed.2d 624 (2011); Wood v. Allen, 558 U.S. 290, 130 S.Ct. 841, 175 L.Ed.2d 738 (2010); Wong v. Belmontes, 558 U.S. 15, 130 S.Ct. 383, 175 L.Ed.2d 328 (2009). The Supreme Court of Indiana did not contradict any law established by the Supreme Court; it cited Strickland and accurately summarized its holding. And, like the district court, we do not think that the state judiciary acted unreasonably in holding not only that counsel’s performance was within the bounds of competence, but also that Over-street did not show prejudice from any shortcoming.
Counsel retained the services of three mental-health professionals: Eric Engum, a neuropsychologist; Robert Smith, a clinical psychologist; and Philip Coons, a forensic psychiatrist. Engum testified at the sentencing hearing that Overstreet had a “schizotypal personality disorder”, which he told the jury was “among the most severe of the personality disorders.” He also testified that Overstreet had a “severely disturbed personality structure”. Smith testified in the post-conviction hearing that, had he been called, he would have testified that Overstreet had a “schizoaffective disorder”, which Smith defined as a combination of schizophrenia and depression. It is unclear whether Coons, had he testified at the sentencing hearing, would have agreed with Engum, with Smith, or offered a third view.
Overstreet contends that counsel should have called Smith as well as Engum, the better to impress on the jury his mental problems, or should have called Smith alone, because schizotypal personality disorder is just a “personality disorder” on Axis II of the American Psychiatric Association’s Diagnostic and Statistical Manual of Mental Disorders, while schizophrenia is a more serious Axis I “clinical disorder”. The Supreme Court of Indiana doubted that jurors would have seen much difference, writing: “it is not at all clear that a lay jury would necessarily appreciate the subtle and nuanced distinction between a schizoaffective disorder and a schizotypal personality disorder.” 877 N.E.2d at 156. Overstreet replies that this shows that the Supreme Court of Indiana did not understand the evidence, because Smith would have testified to schizophrenia. If five appellate judges, after full briefing, didn’t see the difference between Engum’s approach and Smith’s, it is unlikely that a lay jury would have done so. But Overstreet is wrong about the state court’s appreciation of the evidence; the court expressly related, ibid., that to Smith “schizoaffective disorder is a combination of schizophrenia and depression.”
In this court Overstreet’s lawyers harp on the theme that an Axis I “clinical disorder” is worse than an Axis II “personality disorder” and assert the difference surely would have affected the jury. But it was not clear to the state judiciary, see 877 N.E.2d at 156, and is not clear to us, that psychiatric terminology affects juries. The point of showing a jury that the defendant has a mental disorder is to reduce blameworthiness, because juries are more likely to think capital punishment appropriate when a defendant is morally responsible. See Michelle E. Barnett, Stanley L. Brodsky & Cali Manning Davis, When Mitigation Evidence Makes a Difference: Effects of Psychological Mitigating Evidence on Sentencing Decisions in Capital Trials, 22 Behavioral Sciences & the Law 751 (2004). Overstreet’s lawyers put on evidence that he has a serious mental abnormality and contended that he is not blameworthy. Engum and Smith agreed [409]*409about Overstreet’s symptoms; they just attached different labels. Whether his condition is called “schizotypal personality disorder” or schizophrenia plus depression does not change the nature of this mitigating strategy.
Smith testified at the post-conviction hearing that his diagnosis was not close to Engum’s; he views the difference between Axis I and Axis II as substantial. Engum, by contrast, testified that there is very little difference between the diagnoses. (He explained that “if there is a dividing line between ... psychosis and nonpsychosis, schizotypal is just on the nonpsychotic side. You’re close, but you’re not quite there.”) The state judiciary was entitled to accept Engum’s view and to think that what would have affected jurors was not the formal classification but the symptoms the two reported — and if there was any difference in the way the two described Overstreet’s symptoms, it is hard to discern.
Hallucinations, for example, are among the distinctions between Axis I and Axis II disorders — yet the line is not some hallucinations versus none, but their frequency. Engum diagnosed Overstreet not only with a schizotypal personality disorder that includes “perceptual distortions” (in Over-street’s case, “seeing shadows out of the corner of his eyes,” Engum testified) but also with occasional psychotic breakdowns such as the one Engum witnessed. Engum testified that stresses probably had caused Overstreet to experience similar episodes in the past. Periodic episodes of psychosis entail hallucinations (and Engum so testified); Smith likewise diagnosed Overstreet with a disorder that involves periodic hallucinations. This is a difference, but not the sort of difference that marks the line of moral responsibility. Engum testified emphatically that he viewed Overstreet’s ability to “conform his conduct to the requirements of law” as “significantly impaired”.
To get around the state court’s finding that jurors probably would not have seen much difference between Engum’s and Smith’s assessments, Overstreet needs more than his current lawyers’ say-so. His trial lawyers testified at the post-conviction hearing that they put Engum but not Smith on the stand for two reasons: first, Engum saw Overstreet have a psychotic episode and could tell the jury what happened, while Smith had not seen such an episode; second, given the decision to have Engum testify, counsel believed that it would have been imprudent to put Smith on the stand, because then the jurors would have learned that mental-health professionals disagreed about Overstreet’s condition and might have discounted the testimony of both men.
Overstreet’s current lawyers pooh-pooh these rationales and insist that their view — that testimony about schizophrenia beats testimony about schizotypal personality disorder, even from a neuropsychologist who has seen the defendant undergo a psychotic episode — is the only sensible approach. Strickland tells us, however, that tactical decisions by trial counsel cannot be declared ineffective just because a different set of lawyers would have handled things differently. Overstreet’s trial counsel made an informed choice, quite unlike the situation in Wiggins v. Smith, 539 U.S. 510, 123 S.Ct. 2527, 156 L.Ed.2d 471 (2003), where counsel had not done an investigation; Overstreet’s lawyers decided how to proceed only after receiving the views of three mental-health professionals.
To undermine trial counsel’s choices, and the state judiciary’s findings about prejudice, Overstreet needs more than lawyers’ talk. He needs evidence showing that no reasonable lawyer would have thought Engum the better witness, and [410]*410that jurors would be less likely to recommend death for a defendant who has schizophrenia — and that both of these propositions are so strongly supported that the contrary decision by the state judiciary is unreasonable. But the brief does not point to any such evidence; it relies entirely on current counsel’s certitude. If we must choose between the belief of the state judiciary that Engum and Smith would have left pretty much the same impression on the jurors, and the belief of Over-street’s current lawyers that the two would have had a materially different effect, both § 2254(d) and § 2254(e) tell us that the federal judiciary must prefer the conclusions of the state judiciary. It takes clear and convincing evidence to upset a state court’s factual finding, see § 2254(e)(1), and lawyers’ beliefs, however confident and sincere counsel may be, are not “evidence” at all.
In the state post-conviction hearing, Overstreet’s new lawyers did not present evidence from an expert in jury psychology, or a statistician, that capital juries are more favorably disposed toward defendants whose condition is called schizoaffective disorder than when the same condition is called schizotypal personality disorder. Overstreet’s briefs do not cite any studies in the medical or psychological literature about how different psychiatric terms affect juries. We asked at oral argument whether counsel knew of such a study; the answer was no. We looked and could not find one. A few studies find that the man in the street has different impressions of different psychiatric conditions. See Melody S. Sadler, Elizabeth L. Meagor & Kimberly E. Kaye, Stereotypes of Mental Disorders Differ in Competence and Warmth, 74 Social Science & Medicine 915 (2012); Bruce G. Link, Jo C. Phelan, Michaelene Bresnahan, Ann Stueve & Bernice A. Pescosolido, Public Conceptions of Mental Illness: Labels, Causes, Dangerousness, and Social Distance, 89 Am. J. Pub. Health 1328, 1330 (1999). But these studies do not concern the behavior of jurors after being informed by testimony; they take untutored public beliefs as givens rather than evaluating laypersons’ responses to evidence. So the contest boils down to the beliefs held by Overstreet’s current lawyers, versus the beliefs held by his trial lawyers and Indiana’s judiciary. Under Strickland and the AEDPA, trial counsel and the state judiciary must prevail.
Overstreet has some other arguments about the evidence presented in mitigation, but they pale beside the one we have addressed and do not require discussion.
Affirmed.