POSNER, Circuit Judge.

In 1997 a jury in an Indiana state court convicted petitioner Stephenson of three murders. The judge sentenced him to death. After exhausting his state remedies, see Stephenson v. State, 742 N.E.2d 463 (Ind.2001) (affirming his conviction and sentence), and 864 N.E.2d 1022 (Ind.2007) (affirming denial of post-conviction relief), he sought a writ of federal habeas corpus. The district judge ruled that he had been denied effective assistance of counsel during both the guilt and penalty phases of the trial (and so she vacated both the conviction and the sentence), because his counsel had failed to object to the state's making him wear a stun belt in the courtroom. In affidavits and a deposition introduced in the state postconviction proceedings, four jurors said they were aware that he was wearing a stun belt.

Stephenson argued other grounds for relief as well, but the district judge didn't rule on any of them. That may have been a mistake, considering how protracted capital cases are. It means that if we reject the ground on which the court did rule, we must reverse and remand for consideration of the other grounds, while if those grounds for relief had been before us we might have agreed with one of them and thereby spared the parties a further proceeding in the district court, possibly followed by a further appeal.

One of those grounds, moreover, was that Stephenson's counsel had rendered ineffective assistance at the penalty phase of his trial by failing to obtain and present mitigating evidence; had the judge addressed that ground, we would have a better sense of counsel's performance as a whole. In Williams v. Lemmon, 557 F.3d 534, 538 (7th Cir.2009) (per curiam), we answered the "question ... whether single oversights by counsel violate the sixth amendment ... no. The Supreme Court insists that judges must not examine a lawyer's error (of omission or commission) in isolation. See, e.g., Strickland [v. Washington], 466 U.S. [668], 690-96, 104 S.Ct. 2052, 80 L.Ed.2d 674 [(1984)]. It is essential to evaluate the entire course of the defense, because the question is not whether the lawyer's work was error-free, or the best possible approach, or even an average one, but whether the defendant had the `counsel' of which the sixth amendment speaks." But Williams goes on to explain that of course the Supreme Court "has allowed for the possibility that a single error may suffice `if that error is sufficiently egregious and prejudicial,' Murray v. Carrier, 477 U.S. 478, 496, 106 S.Ct. 2639, 91 L.Ed.2d 397 (1986)," as contended in this case.

It was Stephenson who requested that the district judge review the stun belt claim separately from his other claims for relief. He may have been playing a delay game (common enough in capital cases, for obvious reasons); the judge was not required to join him in his play.

The Indiana Supreme Court had ruled in Stephenson's state post-conviction case that "prevailing norms at the time of Stephenson's trial required counsel to object to visible restraints where there is no evidence suggesting escape, violence, or disruptive behavior," 864 N.E.2d at 1035, but that if Stephenson's lawyer had objected, the objection would have been overruled. And rightly so, the court thought, because "these three murders were contended by both the defendant and the prosecution to have been related to organized drug activity. The murders appeared to have been premeditated and had characteristics of an assassination. There was testimony that the defendant had threatened to kill a critical witness." Id. at 1040-41.

It's not easy to reconcile the two crucial statements that we have just quoted. If the objection to the stun belt would rightly have been overruled, how could a failure to make the objection be thought unprofessional? See, e.g., Rodriguez v. United States, 286 F.3d 972, 983-85 (7th Cir.2002); Hough v. Anderson, 272 F.3d 878, 898 and n. 8 (7th Cir.2001); United States v. Sanders, 404 F.3d 980, 986 (6th Cir.2005); Koch v. Puckett, 907 F.2d 524, 527 (5th Cir. 1990). Overlooking the contradiction, the state doesn't challenge the ruling that competent counsel would have objected to Stephenson's being required to wear a stun belt.

Stephenson had turned himself in after hearing that the police were looking for him in connection with the murders, and he had been a model prisoner ever since— a period of six months before the trial. Although the sheriff said that the stun belt had been chosen as the best way to get Stephenson in and out of the courtroom without the jury seeing him in shackles or handcuffs, he could have been brought in before the jury entered and taken out after the jury left, and then no physical restraint would have been visible to the jurors. None of the security personnel explained why any physical restraint (as distinct from just the normal complement of armed guards) would have been necessary once the defendant was seated at the defense table. Apart from the murders themselves, the fact that they had grown out of a dispute among drug dealers, the capital nature of the case, and the state's contention that after the murders Stephenson had threatened a possible accomplice with death if he spilled the beans—the factors mentioned by the Indiana Supreme Court in ruling that an objection to the stun belt would rightly have been overruled—there was no reason to think that the defendant would have been likely to try to flee the courtroom or cause any other disturbance during the trial.

The factors relied on by the court to uphold the use of the stun belt were insufficient in light of the case law both then and now. Well before 1996, when Stephenson's trial began, the U.S. Supreme Court had said that shackling was "the sort of inherently prejudicial practice" that "should be permitted only where justified by an essential state interest specific to each trial." Holbrook v. Flynn, 475 U.S. 560, 568-69, 106 S.Ct. 1340, 89 L.Ed.2d 525 (1986) (emphasis added); cf. Estelle v. Williams, 425 U.S. 501, 503-06, 96 S.Ct. 1691, 48 L.Ed.2d 126 (1976) (defendant in prison garb); Illinois v. Allen, 397 U.S. 337, 344, 90 S.Ct. 1057, 25 L.Ed.2d 353 (1970) (defendant shackled and gagged). But Stephenson doesn't argue that extending the Holbrook dictum, and the holding of the other two Supreme Court cases that we've just cited, to stun belts was "clearly established Federal law, as determined by the Supreme Court of the United States," 28 U.S.C. § 2254(d)(1) (emphasis added), in 1996 and therefore a ground for obtaining relief in a federal habeas corpus proceeding. Gagging is a lot more extreme than a stun belt, and forcing a defendant to wear prison garb serves no security interest, though once in a while a defendant will prefer to appear in court to prison garb to reassure the jurors that they are safe from him, to evoke their sympathy, or out of sheer obstreperousness. Stephenson's argument is that the use of the stun belt was sufficiently questionable that, as federal and state law then stood, an objection to his being forced to wear it during his trial without a showing that he presented a security risk would, or at least should, have been granted, and so counsel was deficient in failing to make the objection.

The "clearly established Federal law, as determined by the Supreme Court of the United States," that is relevant to this case is thus not that forcing a defendant to wear a stun belt deprives him of his constitutional right to a fair trial unless necessity for a physical restraint be shown. It could be argued that, read together, Holbrook, Estelle, and Allen had by 1996 established a rule determined by the Supreme Court (and therefore a ground of federal habeas corpus) against unnecessary visible restraints that was broad enough to include the stun belt. But that is not the principle that Stephenson invokes. He can't, because his counsel failed to invoke it in objecting to the stun belt at trial—counsel made no objection on any ground to Stephenson's having to wear a stun belt—and didn't try to raise the issue on direct appeal. The principle Stephenson invokes is that of Strickland v. Washington, supra, 466 U.S. at 686-87, 104 S.Ct. 2052, entitling criminal defendants to effective assistance of counsel.

By 1996, as Deck v. Missouri, 544 U.S. 622, 626-29, 125 S.Ct. 2007, 161 L.Ed.2d 953 (2005), and cases cited there make clear, the law was well settled, though perhaps not in the U.S. Supreme Court, that placing any kind of visible restraint on a defendant's movement during a criminal trial was permissible only if the particular defendant was too dangerous to be allowed in the courtroom without such a restraint—that is, only if less conspicuous security measures, such as seating one or two guards near but not too near the defendant, would be insufficient to ensure the safety of the persons in the courtroom and prevent the defendant from escaping. See United States v. Fountain, 768 F.2d 790, 794 (7th Cir.1985); Harrell v. Israel 672 F.2d 632, 635 (7th Cir.1982) (per curiam); Marquez v. Collins, 11 F.3d 1241, 1243-44 (5th Cir.1994); United States v. Hack, 782 F.2d 862, 867 (10th Cir.1986); Evans v. State, 571 N.E.2d 1231, 1238 (Ind.1991); Coates v. State, 487 N.E.2d 167, 168-69 (Ind.App.1985), overruled on other grounds by Hahn v. State, 533 N.E.2d 618 (Ind.App.1989). These decisions were based primarily on a concern, which continues to be expressed, see Deck v. Missouri, supra, 544 U.S. at 626-29, 125 S.Ct. 2007; United States v. Cooper, 591 F.3d 582, 587-88 (7th Cir.2010); Gardner v. Galetka, 568 F.3d 862, 890-91 (10th Cir.2009); Hatten v. Quarterman, 570 F.3d 595, 603 (5th Cir.2009), that jurors might infer from a visible restraint that the defendant was especially dangerous. That might lead them to prejudge his guilt, particularly in a trial for violent crimes—and an inference of guilt derived from a gratuitous visible restraint would infringe his constitutional right to a fair trial.

The Indiana Supreme Court seems to have thought that the requirement of evidence of a security threat specific to the defendant rather than to the crime could be relaxed when a defendant is on trial for multiple murders and the prosecution is seeking the death penalty. But that would produce the paradox that capital defendants would have less protection from the prejudice that visible restraints might induce in jurors than persons convicted of lesser crimes and facing milder punishment. The cases thus hold that the nature of the crime with which a defendant is charged, however heinous, is insufficient by itself to justify visible restraints. See Deck v. Missouri, supra, 544 U.S. at 634-35, 125 S.Ct. 2007; Wrinkles v. Buss, 537 F.3d 804, 807-08, 813-15 (7th Cir.2008); Cox v. Ayers, 2010 WL 2853764, at *2, *5 (9th Cir. July 22, 2010); Lakin v. Stine, 431 F.3d 959, 965 (6th Cir.2005).

Even when a visible restraint is warranted by the defendant's history of escape attempts or disruption of previous court proceedings, as in Williams v. Norris, 2010 WL 2772676, at *11-13 (8th Cir. July 15, 2010); United States v. Honken, 541 F.3d 1146, 1162-64 (8th Cir.2008), and Bigby v. Dretke, 402 F.3d 551, 573 (5th Cir.2005), it must be the least visible secure restraint, such as, it is often suggested, leg shackles made invisible to the jury by a curtain at the defense table. See United States v. Brooks, 125 F.3d 484, 502 (7th Cir.1997); United States v. Brazel, 102 F.3d 1120, 1157-58 (11th Cir.1997); cf. Lemons v. Skidmore, 985 F.2d 354, 358-59 (7th Cir.1993). (There should of course be a curtain at the prosecution table as well, lest the jury quickly tumble to the purpose of the curtain at the defense table.)

But while curtained leg shackles might seem less conspicuous than a stun belt, actually this is unclear and underlines the difficulty of reconciling the interest in courtroom security with the interest in a fair trial for the defendant, and casts doubt on the ruling of the Indiana Supreme Court that Stephenson's counsel should have objected to the stun belt. The clanking of leg chains is audible, and even without hearing it jurors may guess what the curtain is for. And when there is a sidebar in a criminal trial the defendant is entitled to participate, and if his legs are shackled there is no way he can join the sidebar without revealing his shackling to the jury. So the jury would have to be sent out of the courtroom every time there was a sidebar, which would slow down the trial and might irritate the jurors. The problem would be particularly acute in older courthouses that do not have good facilities for jurors. We have been told nothing about the size or floor plan of the Indiana state courthouse in which Stephenson was tried.

The stun belt is of course inaudible, and worn under the defendant's shirt is visible only as a slight bulge at his back and thus does not reveal its purpose. But we know from juror affidavits solicited by Stephenson's postconviction counsel that one juror guessed that he was wearing a stun belt because the juror had seen a stun belt in a television show, and another juror inferred it from the bulge at Stephenson's back and the absence of handcuffs; he apparently thought that Stephenson had to be physically restrained in some way. One of these jurors may have reported their discoveries to the other two jurors whose affidavits state that they thought the defendant was wearing a stun belt; but this is speculation.

So the stun belt is not the perfect solution to the security/fair trial dilemma but neither, as we said, are leg shackles, or a crowd of armed guards. This court has said that the stun belt is a method of restraint that minimizes the risk of prejudice, United States v. Brooks, supra, 125 F.3d at 502; Stevens v. McBride, 489 F.3d 883, 899 (7th Cir.2007), though several years after the trial in this case the Indiana Supreme Court disapproved its use. Wrinkles v. State, 749 N.E.2d 1179, 1194-95 (Ind.2001). Guards remain the preferred alternative to any physical restraint, Holbrook v. Flynn, supra, 475 U.S. at 568-69, 106 S.Ct. 1340; Lakin v. Stine, supra, 431 F.3d at 964; Hellum v. Warden, 28 F.3d 903, 908 (8th Cir.1994), but too many guards can create the same impression of a dangerous defendant as a physical restraint.

Not knowing the size or shape of the courtroom in which Stephenson was tried, we find it difficult to place ourselves in the position of his counsel in deciding whether to object to the stun belt. Counsel might have considered it superior to leg shackles; and as for additional guards, a lot would depend on the size of the courtroom: the smaller it is, the more that additional guards would create an impression that the defendant was dangerous. If a defendant's lawyer went for broke and objected to any security beyond what would be required in a prosecution for kiting checks, he might be disserving his client by making the jury nervous to be confronting an accused triple murderer with no protection against his acting up. The lawyer might even be afraid of his client.

Yet apart from the nature of the defendant's crime, the only justification suggested by the Indiana Supreme Court for the stun belt was Stephenson's having threatened to kill a prospective witness. But the prospective witness was a possible accomplice, told by Stephenson (naturally enough—if he was the murderer!) to shut up about the crime, and the threat was made before he turned himself in. That is different from a threat uttered in the course of a legal proceeding, a verbal act that the judge might fear would presage disruptive behavior in the courtroom. So given the case law as it had evolved in 1996, the state may be correct to concede that the defense should have objected to the stun belt. We have our doubts but will still them and move on to the issue of prejudice—in a moment, because there are two further wrinkles to smooth out.

Suppose that had counsel objected to the stun belt the judge would have overruled the objection, and suppose that had he done so, it would have been an error. The state supreme court, we know from its later decision, might have affirmed the ruling; and suppose that had it done so, that it would have been an error too. The test of ineffective assistance is not whether the court system would have ruled correctly on a valid objection or other defense tactic; it is whether the existing law would have required the courts to uphold the objection. "The assessment of prejudice should proceed on the assumption that the decisionmaker is reasonably, conscientiously, and impartially applying the standards that govern the decision. It should not depend on the idiosyncrasies of the particular decisionmaker, such as unusual propensities toward harshness or leniency." Strickland v. Washington, supra, 466 U.S. at 694, 104 S.Ct. 2052; see also Fountain v. United States, 211 F.3d 429, 434 (7th Cir.2000); Wrinkles v. Buss, supra, 537 F.3d at 813-15.

Another issue would have to be considered before one could conclude that an objection to the stun belt, had it been made, should have been sustained. To be timely, the objection would have had to be made before the trial began and the jurors saw the defendant. Conceivably the judge would have ruled that the stun belt was insufficiently conspicuous to be visible to them. We don't know what the defendant looked like with the stun belt on; the jurors who said they thought he was wearing a stun belt may have been guessing. Had the objection been overruled on the narrowly factual ground, based on the trial judge's direct observation, that the stun belt was not visible, the appellate courts might have been justified in affirming his ruling. If so, there would have been no harm from defense counsel's failure to object, although had it become known by the time of the appeal that some jurors had been aware of the stun belt the appellate court would have realized that the trial judge's ruling had been based on an erroneous factual assumption.

The state has not made the argument that we've just sketched against a finding of prejudice. It argues rather that the fact that several jurors realized that Stephenson was wearing a stun belt is unlikely to have "so prejudiced his defense that it deprived him of a fair trial," Roche v. Davis, 291 F.3d 473, 483 (7th Cir.2002), or in simpler terms to have changed the outcome of the trial. See Strickland v. Washington, supra, 466 U.S. at 687, 693-94, 104 S.Ct. 2052; Wrinkles v. Buss, supra, 537 F.3d at 812-13, 815; Fountain v. United States, supra, 211 F.3d at 434-36; Marquard v. Secretary for Dept. of Corrections, 429 F.3d 1278, 1313-14 (11th Cir. 2005); Wilkerson v. Whitley, 16 F.3d 64, 68 (5th Cir.1994).

Had Stephenson challenged the stun belt on direct appeal, the state would have had to prove beyond a reasonable doubt that the stun belt had not influenced the verdict. Hatten v. Quarterman, supra, 570 F.3d at 603-04. But because he alleges only that his counsel was ineffective in failing to challenge the stun belt, he must show that he was prejudiced by counsel's error. And the burden of proving prejudice is on him, because to prevail on a claim of ineffective assistance a defendant must show not only that counsel's performance fell below minimum professional standards but also that the subpar performance harmed the client. Strickland v. Washington, supra, 466 U.S. at 687, 104 S.Ct. 2052; Wrinkles v. Buss, supra, 537 F.3d at 812-13; Roche v. Davis, supra, 291 F.3d at 482; Marquard v. Secretary for Dept. of Corrections, supra, 429 F.3d at 1313-14; Wilkerson v. Whitley, supra, 16 F.3d at 68. He must demonstrate "a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." United States v. Banks, 405 F.3d 559, 569 (7th Cir.2005). "If a court erroneously shackles a defendant, the jury receives a powerful image contradicting the presumption of innocence. As a result, `The state must prove beyond a reasonable doubt that the shackling error complained of did not contribute to the verdict obtained.' However, on collateral review of a state court conviction, federal courts apply a more lenient standard, only granting a writ when an error had a `substantial and injurious effect or influence in determining the jury's verdict'" Hatten v. Quarterman, supra, 570 F.3d at 603-04 (emphasis added, citations omitted). (We take "substantial and injurious" to mean the same as prejudicial.)

The jurors' affidavits might seem the best evidence of the prejudicial effect (if any) of juror awareness of the stun belt. But they merely establish awareness. Two jurors thought the purpose of the stun belt was to control the defendant's behavior, and specifically, one thought, to prevent him from running away. There is no suggestion that the jurors considered the stun belt to be evidence of guilt. So far as we can tell, they thought it routine that a criminal defendant would be physically restrained in some fashion. They may, indeed, have felt more secure, and hence less fearful of and hostile toward the defendant, than if there had been no visible restraint.

To protect jurors from harassment and intimidation and enhance the finality of jury verdicts, jurors are not permitted to impeach their verdict. Fed. R.Evid. 606(b); Tanner v. United States, 483 U.S. 107, 121-25, 107 S.Ct. 2739, 97 L.Ed.2d 90 (1987); United States v. Muthana, 60 F.3d 1217, 1223 (7th Cir.1995); Gacy v. Welborn, 994 F.2d 305, 312-14 (7th Cir.1993); United States v. Benally, 546 F.3d 1230, 1239-40 (10th Cir.2008); Ind. R. Evid. 606(b); Griffin v. State, 754 N.E.2d 899, 902-03 (Ind.2001); Johnson v. State, 700 N.E.2d 480, 480-81 (Ind.App. 1998). They are, however, permitted to testify about "whether extraneous prejudicial information was improperly brought to the jury's attention," Fed.R.Evid. 606(b); United States v. Fozo, 904 F.2d 1166, 1171 (7th Cir.1990); United States v. Lloyd, 269 F.3d 228, 237 (3d Cir.2001); United States v. Hall, 85 F.3d 367, 370-71 (8th Cir.1996); Ind. R. Evid. 606(b); Griffin v. State, supra, 754 N.E.2d at 902-03, because such an impropriety is a ground for reversal. But as these cases make clear, they may not testify about the effects of such outside influences on their deliberations.

A visible restraint on a defendant might seem a good example of prejudicial material improperly (if there was no adequate reason for the restraint) brought to the jurors' attention. But to allow jurors to be interrogated about such observations would mean that in any trial in which a physically restrained defendant was convicted, the defendant could challenge the verdict by obtaining affidavits from jurors concerning what they thought—even if the reasons for the restraint had been compelling. Yet if those reasons had been compelling, the jurors' reactions are irrelevant, and if they had not been compelling, the defendant is entitled to a new trial—provided, to repeat, that the error was prejudicial. But the state has not objected to the juror affidavits, maybe because they don't prove prejudice but only realization by several jurors that the defendant was wearing a stun belt.

Courtroom security is necessary during a trial for a crime of violence. The sheriff testified that there were two uniformed guards in the courtroom throughout the trial. One sat near Stephenson; the other, who had the controls for the stun belt, sat in the back of the courtroom, next to the door. Additional guards were not needed because the officer at the back could trigger the stun belt, delivering a 50,000-volt shock for eight seconds and thus incapacitating the defendant. Shelley A. Nieto Dahlberg, Comment, "The REACT Security Belt: Stunning Prisoners and Human Rights Groups Into Questioning Whether Its Use Is Permissible Under the United States and Texas Constitutions," 30 St. Mary's L.J. 239, 246-48 (1998). Had there been no stun belt, more guards might have been needed and so the question is whether the stun belt, visible only as a bulge in Stephenson's back, made the jury more likely to think him guilty than additional armed guards in the courtroom would have done. This is unclear and it is a reason we gave earlier for skepticism about the state supreme court's ruling that Stephenson's counsel failed to adhere to minimum professional standards when he did not object to the stun belt. It also bears on the issue of prejudice.

We doubt that either mode of restraint—stun belts or more guards—would have influenced this jury's verdict. The charge of multiple murders and the state's urging the death penalty made the trial a fraught event and created an expectation of heightened security whether Stephenson was guilty or innocent. He might be guilty, obviously, and the possibility would make everyone in the courtroom assume there would be ample security against his attempting to disrupt the proceedings.

We find it significant that the trial stretched over eight months, with three months of trial days. The trial was so protracted because the lead defense attorney put up a no-holds-barred defense for which he billed the state, according to media reports, $500,000—the largest amount ever spent on the defense of a capital case in Indiana. "No Expense Spared in Stephenson Case," Evansville Courier & Press, Oct. 26, 2001, p. A12; see also Garret Mathews, "After 16 Years, Warrick Prosecutor Off the Case," id., Feb. 13, 2010, p. A4. It's difficult to believe that the jurors who guessed that the defendant was wearing a stun belt thought it a significant clue to his likely guilt, compared to evidence generated over months of testimony and cross-examination. As the Supreme Court had explained in Holbrook, because "jurors are quite aware that the defendant appearing before them did not arrive there by choice or happenstance," courts "have never tried, and could never hope, to eliminate from trial procedures every reminder that the State has chosen to marshal its resources against a defendant to punish him for allegedly criminal conduct. To guarantee a defendant's due process rights under ordinary circumstances, our legal system has instead placed primary reliance on the adversary system and the presumption of innocence. When defense counsel vigorously represents his client's interests and the trial judge assiduously works to impress jurors with the need to presume the defendant's innocence, we have trusted that a fair result can be obtained." 475 U.S. at 567-68, 106 S.Ct. 1340 (emphasis added). No one can doubt the vigor, the tenacity, the thoroughness of Stephenson's defense. This would not (as the Court in Holbrook went on to make clear) have rebutted a claim of prejudice from binding and gagging a defendant, but the restraint in this case was far less extreme.

The speculative nature of the inquiry into prejudice, combined with the fact that the evidence of Stephenson's guilt (summarized in the decision of the Supreme Court of Indiana affirming the conviction), although powerful, was not overwhelming, may make this seem a close case. It would be helpful if the effect of visible restraints on jurors had been subjected to careful empirical studies rather than left to judicial speculation. There are rigorous empirical studies of jury behavior. See, e.g., Jeffrey S. Neuschatz et al., "The Effects of Accomplice Witnesses and Jailhouse Informants on Jury Decision Making," 32 Law & Human Behavior 137 (2007); Dennis J. Devine et al., "Deliberation Quality: A Preliminary Examination in Criminal Juries," 4 J. Empirical L. Stud. 273 (2007); Theodore Eisenberg et al., "Judge-Jury Agreement in Criminal Cases: A Partial Replication of Kalven and Zeisel's The American Jury" 2 J. Empirical L. Stud. 171 (2005); Stephen P. Garvey, "Aggravation and Mitigation in Capital Cases: What Do Jurors Think?," 98 Colum. L.Rev. 1538 (1998); Theodore Eisenberg & Martin T. Wells, "Deadly Confusion: Juror Instructions in Capital Cases," 79 Cornell L.Rev. 1 (1993). As pointed out in Gacy v. Welborn, supra, 994 F.2d at 313, "social science has challenged many premises of the jury system." But no studies that the parties have cited or that we have found address the impact of visible restraints on jury deliberations. Nevertheless we conclude that Stephenson has failed to carry his burden of proving prejudice, even on the dubious premise that his counsel should have objected to the stun belt—dubious because the alternatives might have been worse.

We have thus far been considering prejudice only at the guilt phase of the trial. The same jury that had determined guilt recommended the death penalty, and Stephenson continued to wear the stun belt in the penalty hearing. As the law then stood, the judge was not bound by the jury's recommendation though required to consider it in making his own, independent determination, Ind.Code § 35-50-2-9(e) (1996); Dye v. State, 717 N.E.2d 5, 23 (Ind.1999); Wrinkles v. State, 690 N.E.2d 1156, 1171-72 (Ind.1997), But we have been given no reason to doubt that he gave the recommendation significant weight.

Stephenson's brief in this court, while stating that had it not been for the stun belt he would not have been convicted and sentenced to death, does not argue that he might have been convicted but not sentenced to death if only no juror had been aware that he was wearing it. But remember that an unrelated challenge to his death sentence is pending in the district court. And in the sentencing hearing his counsel had argued against the death penalty on the ground that a "residual doubt" of Stephenson's guilt had been created by his alibi witnesses and by witnesses who testified that they heard another person admit involvement in the murders. Remember too that the district judge found ineffective assistance of counsel at the penalty stage as well as the guilt stage, though she did not discuss that aspect separately.

Whether "residual doubt" is appropriate for consideration in a death-penalty hearing was left open by the Supreme Court in Oregon v. Guzek, 546 U.S. 517, 525-26, 126 S.Ct. 1226, 163 L.Ed.2d 1112 (2006), and we called it "questionable" in United States v. Corley, 519 F.3d 716, 729 (7th Cir.2008). It is unlikely that a jury would convict a defendant in a death case if it doubted his guilt. Jurors aware of the stun belt at the guilt phase might be confused or alarmed at its absence at the penalty hearing, and the jury as a whole might be scratching its collective head if (the stun belt having been discarded) there were more guards at the penalty stage than at the guilt stage. Such a change might actually prejudice the defendant in the eyes of jurors unaware of the stun belt; seeing more guards they might conclude that he was even more dangerous than they had thought in finding him guilty of three murders. But the district judge did not discuss the "residual doubt" issue in her opinion, and we do not know her thoughts on it.

Marquez v. Collins, supra, 11 F.3d at 1244, suggests a different ground from "residual doubt" for challenging a visible restraint in a death-penalty hearing even though "when the complained of restraint comes only in the sentencing phase of a capital charge, a jury has just convicted of a violent crime—so the risk of prejudice is lessened from the risk of such events during the guilt phase. At the same time, the defendant's life turns on the same jury's answer to the question of future dangerousness, so the risk, although less, is not eliminated. Restraint at trial may carry a message that a defendant continues to be dangerous" (emphasis in original). And in Roche v. Davis, supra, 291 F.3d at 484, we held, without reference to the doctrine of residual doubt, that the defendant's counsel had rendered ineffective assistance of counsel by failing to object, at the penalty phase of a capital case, to the defendant's being shackled. The question of prejudice from Stephenson's having been required to wear the stun belt at the penalty hearing will require the further consideration of the district court on remand.

REVERSED AND REMANDED.