POSNER, Chief Judge.
In 1979, James P. Free, Jr. was convicted of a felony murder committed the previous year and was sentenced to death. After exhausting his state remedies, see People v. Free, 94 Ill.2d 378, 69 Ill.Dec. 1, 447 N.E.2d 218 (1983), 112 Ill.2d 154, 97 Ill.Dec. 396, 492 N.E.2d 1269 (1986), 122 Ill.2d 367, 119 Ill.Dec. 325, 522 N.E.2d 1184 (1988), he sought habeas corpus in federal district court. The district judge, concluding on the basis of a study by the late Hans Zeisel that the instructions to the jury at the hearing on whether to sentence Free to death had been so confusing as to be constitutionally infirm, ordered the state to resentence Free. United States ex rel. Free v. Peters, 778 F.Supp. 431 (N.D.Ill.1991), 806 F.Supp. 705 (N.D.Ill.1992). The state appeals. Free cross-appeals. The judge’s order allows the state to request another death-sentence hearing, since the only infirmity in the previous one was the instructions. Free argues that reim-position of the death penalty is barred regardless of the instructions. So he is not just defending the judge’s order on other grounds, and the cross-appeal is therefore proper. We begin our discussion with it.
At the time of the murder Illinois’ felony-murder statute authorized capital punishment if “the murdered individual was killed in the course of ... rape.” Ill.Rev. Stat. ch. 38 ¶ 9-l(b)(6)(e) (1977). Free murdered his victim in the course of an attempted rape, and it was not until 1982, four years after the murder, that the Supreme Court of Illinois held that “in the course of’ includes attempts. People v. Walker, 91 Ill.2d 502, 64 Ill.Dec. 531, 535-536, 440 N.E.2d 83, 87-88 (1982). (The statute has now been amended to make that explicit. 720 ILCS 5/9-1(b)(6)(c).) Free argues that the statute failed to give him fair warning that his conduct might expose him to a death sentence, and therefore that the sentence was a denial of due process. A failure to provide fair warning in the statute itself is not curable by a judicial decision rendered after the defendant acted. Bouie v. City of Columbia, 378 U.S. 347, 84 S.Ct. 1697, 12 L.Ed.2d 894 (1964). But the statute was sufficiently open to the interpretation that it included attempted as well as completed felonies to provide Free with all the notice to which the Constitution entitled him. As the statutory words “in the course of’ imply, the felony-murder rule punishes as a murderer one who kills while committing a felony. It is an unimportant detail whether the killing occurs before or after the last! act necessary to complete the felony. In the case of rape the felony is not complete until the penetration of the victim by the rapist, 720 ILCS 5/12-13, but we cannot imagine a reason for differentiating punishment according to whether the rapist killed his victim shortly before penetration or shortly after. It would carry legal fiction to offensive lengths to speculate that Free was inveigled by the Illinois legislature into killing his victim when he did because he reasonably believed that he could not be punished for capital felony murder. Although the interpretive issue was not re[703]*703solved definitively until the state supreme court decided Walker, it is not as if until then the course of judicial interpretation had run the other way; there were no published decisions supporting Free’s interpretation.
Evidence was presented at the sentencing hearing concerning the impact of the killing on the victim’s family. Eight years later the U.S. Supreme Court held that “victim impact” evidence is inadmissible in a capital case. Booth v. Maryland, 482 U.S. 496, 107 S.Ct. 2529, 96 L.Ed.2d 440 (1987). Four years after that,'the Supreme Court, overruled Booth. Payne v. Tennessee, — U.S.-,-, 111 S.Ct. 2597, 2609-11, 115 L.Ed.2d 720 (1991). Free argues that Booth did not create a new rule, and therefore under Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), was applicable to his sentencing hearing, but that Payne did, and therefore was inapplicable. The argument fails at its first step. The Supreme Court deems Teague a one-way street: designed as it is to protect the state’s interest in the finality of criminal' convictions, it entitles the state, but not the petitioner, to object to the application of a new rule to an old case. Lockhart v. Fretwell, — U.S. -,-, 113 S.Ct. 838, 844, 122 L.Ed.2d 180 (1993). We add that Booth plainly stated a new rule under the expansive criteria that the Court uses for deciding this question. See, e.g., Gilmore v. Taylor, — U.S.-, 113 S.Ct. 2112, 124 L.Ed.2d 306 (1993).
The other issues presented by the cross-appeal do not require discussion; they were adequately dealt with by the district judge. We move on to the state’s appeal. By way of background, we point out that in Illinois a death-sentence hearing has two stages. In the first, the jury is asked whether the state has proved beyond a reasonable doubt the existence of at least one of the statutory circumstances that makes the defendant eligible for the death sentence, such as killing in the course of rape. 720 ILCS 5/9-l(g). If the jury finds beyond a reasonable doubt (§ 9 — 1(f)) that at least one such circumstance was present, it proceeds to the second stage, where it is required to consider aggravating factors (including but not limited to the “eligibility” factors) and mitigating factors. “Mitigating factors may include but need not be limited to the following....” Five factors are listed; they include: defendant has no significant criminal history; defendant acted under “extreme mental or emotional disturbance”; and defendant was riot present in person when the victim was killed. § 9-l(c). “If the jury determines unanimously that there are no mitigating factors sufficient to preclude the imposition of the death sentence, the court shall sentence the defendant to death.” § 9-l(g). At this second stage, where the jury is comparing aggravating and' mitigating factors, there is no burden of persuasion. The prosecutor has the burden of producing evidence of aggravating factors and the defendant has the burden of producing evidence of mitigating factors, but if both parties satisfy these burdens the burden of proof drops out. People v. Simms, 143 Ill.2d 154, 157 Ill.Dec. 483, 495, 572 N.E.2d 947, 959 (1991). Later Simms says that “the State must ... persuade the jury that there are no mitigating factors,” id. 157 Ill.Dec. at 496, 572 N.E.2d at 960, but it is evident from its citation to People v. Bean, 137 Ill.2d 65, 147 Ill.Dec. 891, 560 N.E.2d 258 (1990), that the court was, not attempting to speak with legal precision. For in that case, decided only one year earlier, the court had been explicit that both parties bear the burden.of persuasion, id. 147 Ill.Dec. at 924-25, 560 N.E.2d at 291-92, which is the equivalent of saying that neither does. At all events, Fred’s briefs do not challenge the proposition that there is no burden of persuasion once the state has proved beyond a reasonable doubt the defendant’s “eligibility” for the death sentence.
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POSNER, Chief Judge.
In 1979, James P. Free, Jr. was convicted of a felony murder committed the previous year and was sentenced to death. After exhausting his state remedies, see People v. Free, 94 Ill.2d 378, 69 Ill.Dec. 1, 447 N.E.2d 218 (1983), 112 Ill.2d 154, 97 Ill.Dec. 396, 492 N.E.2d 1269 (1986), 122 Ill.2d 367, 119 Ill.Dec. 325, 522 N.E.2d 1184 (1988), he sought habeas corpus in federal district court. The district judge, concluding on the basis of a study by the late Hans Zeisel that the instructions to the jury at the hearing on whether to sentence Free to death had been so confusing as to be constitutionally infirm, ordered the state to resentence Free. United States ex rel. Free v. Peters, 778 F.Supp. 431 (N.D.Ill.1991), 806 F.Supp. 705 (N.D.Ill.1992). The state appeals. Free cross-appeals. The judge’s order allows the state to request another death-sentence hearing, since the only infirmity in the previous one was the instructions. Free argues that reim-position of the death penalty is barred regardless of the instructions. So he is not just defending the judge’s order on other grounds, and the cross-appeal is therefore proper. We begin our discussion with it.
At the time of the murder Illinois’ felony-murder statute authorized capital punishment if “the murdered individual was killed in the course of ... rape.” Ill.Rev. Stat. ch. 38 ¶ 9-l(b)(6)(e) (1977). Free murdered his victim in the course of an attempted rape, and it was not until 1982, four years after the murder, that the Supreme Court of Illinois held that “in the course of’ includes attempts. People v. Walker, 91 Ill.2d 502, 64 Ill.Dec. 531, 535-536, 440 N.E.2d 83, 87-88 (1982). (The statute has now been amended to make that explicit. 720 ILCS 5/9-1(b)(6)(c).) Free argues that the statute failed to give him fair warning that his conduct might expose him to a death sentence, and therefore that the sentence was a denial of due process. A failure to provide fair warning in the statute itself is not curable by a judicial decision rendered after the defendant acted. Bouie v. City of Columbia, 378 U.S. 347, 84 S.Ct. 1697, 12 L.Ed.2d 894 (1964). But the statute was sufficiently open to the interpretation that it included attempted as well as completed felonies to provide Free with all the notice to which the Constitution entitled him. As the statutory words “in the course of’ imply, the felony-murder rule punishes as a murderer one who kills while committing a felony. It is an unimportant detail whether the killing occurs before or after the last! act necessary to complete the felony. In the case of rape the felony is not complete until the penetration of the victim by the rapist, 720 ILCS 5/12-13, but we cannot imagine a reason for differentiating punishment according to whether the rapist killed his victim shortly before penetration or shortly after. It would carry legal fiction to offensive lengths to speculate that Free was inveigled by the Illinois legislature into killing his victim when he did because he reasonably believed that he could not be punished for capital felony murder. Although the interpretive issue was not re[703]*703solved definitively until the state supreme court decided Walker, it is not as if until then the course of judicial interpretation had run the other way; there were no published decisions supporting Free’s interpretation.
Evidence was presented at the sentencing hearing concerning the impact of the killing on the victim’s family. Eight years later the U.S. Supreme Court held that “victim impact” evidence is inadmissible in a capital case. Booth v. Maryland, 482 U.S. 496, 107 S.Ct. 2529, 96 L.Ed.2d 440 (1987). Four years after that,'the Supreme Court, overruled Booth. Payne v. Tennessee, — U.S.-,-, 111 S.Ct. 2597, 2609-11, 115 L.Ed.2d 720 (1991). Free argues that Booth did not create a new rule, and therefore under Teague v. Lane, 489 U.S. 288, 109 S.Ct. 1060, 103 L.Ed.2d 334 (1989), was applicable to his sentencing hearing, but that Payne did, and therefore was inapplicable. The argument fails at its first step. The Supreme Court deems Teague a one-way street: designed as it is to protect the state’s interest in the finality of criminal' convictions, it entitles the state, but not the petitioner, to object to the application of a new rule to an old case. Lockhart v. Fretwell, — U.S. -,-, 113 S.Ct. 838, 844, 122 L.Ed.2d 180 (1993). We add that Booth plainly stated a new rule under the expansive criteria that the Court uses for deciding this question. See, e.g., Gilmore v. Taylor, — U.S.-, 113 S.Ct. 2112, 124 L.Ed.2d 306 (1993).
The other issues presented by the cross-appeal do not require discussion; they were adequately dealt with by the district judge. We move on to the state’s appeal. By way of background, we point out that in Illinois a death-sentence hearing has two stages. In the first, the jury is asked whether the state has proved beyond a reasonable doubt the existence of at least one of the statutory circumstances that makes the defendant eligible for the death sentence, such as killing in the course of rape. 720 ILCS 5/9-l(g). If the jury finds beyond a reasonable doubt (§ 9 — 1(f)) that at least one such circumstance was present, it proceeds to the second stage, where it is required to consider aggravating factors (including but not limited to the “eligibility” factors) and mitigating factors. “Mitigating factors may include but need not be limited to the following....” Five factors are listed; they include: defendant has no significant criminal history; defendant acted under “extreme mental or emotional disturbance”; and defendant was riot present in person when the victim was killed. § 9-l(c). “If the jury determines unanimously that there are no mitigating factors sufficient to preclude the imposition of the death sentence, the court shall sentence the defendant to death.” § 9-l(g). At this second stage, where the jury is comparing aggravating and' mitigating factors, there is no burden of persuasion. The prosecutor has the burden of producing evidence of aggravating factors and the defendant has the burden of producing evidence of mitigating factors, but if both parties satisfy these burdens the burden of proof drops out. People v. Simms, 143 Ill.2d 154, 157 Ill.Dec. 483, 495, 572 N.E.2d 947, 959 (1991). Later Simms says that “the State must ... persuade the jury that there are no mitigating factors,” id. 157 Ill.Dec. at 496, 572 N.E.2d at 960, but it is evident from its citation to People v. Bean, 137 Ill.2d 65, 147 Ill.Dec. 891, 560 N.E.2d 258 (1990), that the court was, not attempting to speak with legal precision. For in that case, decided only one year earlier, the court had been explicit that both parties bear the burden.of persuasion, id. 147 Ill.Dec. at 924-25, 560 N.E.2d at 291-92, which is the equivalent of saying that neither does. At all events, Fred’s briefs do not challenge the proposition that there is no burden of persuasion once the state has proved beyond a reasonable doubt the defendant’s “eligibility” for the death sentence.
An instruction alleged to be confusing is constitutionally defective if there is a “reasonable likelihood” that it misled the jury into sentencing the defendant to death. Boyde v. California, 494 U.S. 370, 380, 110 S.Ct. 1190, 1198, 108 L.Ed.2d 316 (1990). The district judge invalidated two of the instructions given at Free’s sentencing hearing under this standard. The first concerned the burden of persuasion (or rather lack thereof) in the jury’s determination whether to impose the death penalty upon consideration of the aggravating and mitigating fae-[704]*704tors. The jury had been told: “If, from your consideration of the evidence and after your due deliberation, there is at least one of you who finds that there is at least one mitigating factor sufficient to preclude the imposition of the death sentence then you should return a verdict that the Defendant be sentenced to imprisonment. On the other hand, if from your consideration of the evidence- and after your due deliberation you unanimously find that there are no mitigating factors sufficient to preclude the imposition of the death sentence then you should return a verdict that the Defendant be sentenced to death.” Free argues that the words “sufficient to preclude”- gave the jury insufficient guidance to how to weigh mitigating, against aggravating factors.
The other instruction also concerned mitigating factors: “If you unanimously find from your consideration of all the evidence that there are no mitigating factors sufficient to preclude the imposition of a sentence of death then you should return a verdict imposing a sentence of death. If, on the other hand, you do not unanimously find that there are no mitigating factors sufficient to preclude the imposition of a sentence of death then you should return a verdict that the sentence of death should not be imposed.” Free objects that the jury was not told it was free to consider mitigating factors other than the five listed in the statute.
If we disregard for a moment Professor Zeisel’s research, it is difficult to see what is confusing about these instructions when they are placed in the context of the entire set of instructions plus the closing- arguments of the lawyers. Since there is no burden of persuasion in the comparison of mitigating and aggravating factors — an absence that Free does not claim violates the Constitution — it really is up to the jury to decide whether a mitigating factor or factors is (are) “sufficient to preclude the imposition of a sentence of death.” There isn’t much more to say on the subject. To instruct that there is no burden of persuasion would be as likely to confuse the jurors as to say nothing. Free argues that the jury should have been told that it was to weigh the aggravating against the mitigating factors, but we do not see how the metaphor of a scale would have aided the jury’s reasoning. It is obvious that when one is.asked to consider pro and con considerations one is being asked to compare and thus in a sense weigh them. Belaboring the obvious is not a reliable formula for enlightenment; and as we have pointed out in deprecating efforts to define “beyond a reasonable doubt” for jurors, there is a point at which definition ceases to be enlightening and becomes confusing. United States v. Hall, 854 F.2d 1036, 1038 (7th Cir.1988).
As for whether the second instruction may have confused the jury about the possibility of sparing Free’s life on the basis of mitigating factors not listed in the statute, we point out that the judge instructed the jury that “mitigating factors include but are not limited to the following circumstances” (the two factors — lack of significant criminal history and defendant acting under the influence of extreme mental or emotional disturbance — on the statutory list that Free argued were present in his case) and that the jury should consider not only these mitigating factors but also “any other mitigating factors [that] are present in this case.” Both the prosecutor and the defense counsel plainly stated to the jurors that they should consider other mitigating, factors as well as those listed in the statute. , In evidence and argument, defense counsel cited as mitigating factors obviously not found in the statute that Free had served without incident in the armed forces and that he had always been employed; and the prosecutor, while questioning the substantiality of these factors in relation to aggravating factors that included not only the deliberate killing in the course of rape but also the attempted murder of an eyewitness, never suggested that the jury should not consider them. Considering the instructions as a whole and in the context of the entire sentencing hearing, we do not think there is a reasonable likelihood that the jury could have misunderstood the statutory scheme.
But, we have yet to consider the Zeisel evidence, which persuaded the district judge that there was a reasonable likelihood of confusion. In a previous case, a different panel of this court expressed its more than [705]*705skepticism concerning the quality and even the relevance of the evidence. Gacy v. Welborn, 994 F.2d 305, 308-10 (7th Cir.1993). Free calls that discussion dictum, and the state calls it holding. It hardly matters. For there is more to. Gacy. If the Zeisel study is properly classified not as new evidence in support of an old rule but rather as the basis for a new rule, it is barred to Free by Teague. Gacy holds in identical circumstances — Gaey’s efforts to use the Zeisel study to overturn his own death sentence— that Zeisel’s study is properly classified as the basis for a new rule and is therefore inadmissible to upset a judgment that had become final before the study was conducted. Id. at 310-11. Therefore, unless we overrule .Gacy, that decision requires us to reverse the district court’s decision in the present ease.
We are unwilling to overrule Gacy. Indeed, we are unwilling even to consider overruling Gacy, because, even if we did overrule it, that would make no difference to the outcome of the present case. So deficient is Professor Zeisel’s study that, even if Teague created no obstacle to the district court’s consideration of it, the study would not support the conclusion that the instructions given the sentencing jury in Free’s cáse were so confusing as to be constitutionally defective.
Zeisel, a professor of law and sociology who had conducted extensive research on juries, proceeded as follows. He picked at random a number of persons who had been summoned for jury duty in the circuit court of Cook County but not picked for a jury. He administered to them a written test which summarized the evidence at Free’s trial, recited the instructions that had been given to the jury concerning aggravating and mitigating circumstances, and then asked 18 true-or-false questions about the reasoning of hypothetical jurors confronted with those instructions. Question 2, for example, asks whether a juror would have been following the judge’s instructions if the juror, though persuaded that the defendant’s having been a good boy was a mitigating factor sufficient to preclude the death penalty, decided that she must nevertheless vote for the death penalty because the judge had not mentioned that factor specifically and it was not comparable to the mitigating factors that he had mentioned. The instructions, drawn from Illinois Pattern Instructions, were not identical to the instructions given in Free’s case; but in a subsequent similar study Zeisel substituted the Free instructions. (The two tests are appended to the district judge’s second opinion.)
The test takers did not do well. On Question 2, for example, 56 percent of the responses on the first test and 40 percent of those on the second were incorrect, and there were even higher flunk rates on some of the other questions. From this the district judge inferred that there is a high probability that the jurors at Free’s sentencing hearing were seriously confused, since the instructions to the test takers were identical or nearly so to the instructions that Free’s jury had received.
The tests have, however, two fatal flaws. The first is lack of comparability between the test setting and the setting of the sentencing hearing. The second is the lack of a control group consisting of persons administered a test containing what Zeisel (or Free’s lawyers) would consider adequately clear instructions.
A group of people who thought they were going to serve on a jury were instead given a written examination on what to them was an imaginary ease. They were instructed to read - several pages summarizing evidence and jury instructions and then to answer written questions about the reasoning process of hypothetical jurors. People are not summoned for jury duty on the basis of their skill in taking written examinations and most American adults have not taken a written examination since they were in school and shudder at the thought of having to do so. If jurors were adept exam takers we could dispense with trials and submit cases to them on the basis of summaries of evidence, instructions, and argument — a reform we have not heard proposed. There is little a priori reason to think that the results of such an examination offer insight into the ability of a real jury, which has spent days or weeks becoming familiar with the case and has had the benefit of oral presentations by witness[706]*706es, lawyers, and the judge, and which renders a verdict after discussion rather than in the isolation of an examination setting. We could of course be wrong and the examination setting accurately simulate the experience of being a real juror, but it is a sufficiently remote possibility to require some evidence to substantiate it, for example a comparison between “jurors” administered the Zeisel test after seeing a mock sentencing hearing and those who had seen only the written summary of evidence and instructions. Zeisel attempted no such comparison.
Even if the problem of comparability were not fatal, the absence of a control group would be. And it was such an easy problem to solve. All Zeisel would have had to do was administer his test to another randomly selected group of “jurors,” only this time altering the instructions so that they were clearer. Suppose that it turned out, as we think it well might (because the cause of the complexity of the instructions may be Illinois’s constitutionally sanctioned system for determining whether to impose the death penalty in a particular case rather than the articulation of that system- in the challenged instructions), that the failure rate was as high or almost as high when the instructions were reworded to satisfy Zeisel’s standards for clarity. Then it would be apparent that either the high failure rate had been generated by the examination setting or the entire American jury' system is hopeless because Americans can’t understand even simple jury instructions. The lack of comparability between the examination setting and the trial setting would make it impossible to choose between these hypotheses, but as no one proposes to jettison the jury system it would be plain that Zeisel’s study had failed to invalidate the instructions given in Free’s case. If the test takers scored much higher when given clear instructions, the problem of comparability would remain but at least there would be some- reason to believe that clearer instructions might make a difference in jury verdicts. No effort at this elementary form of control was made.
Zeisel was a respected researcher, and other reputable social scientists testified in the district court in support of the validity of his results. But ultimately it is judges who must decide whether a piece of social science research has sufficient reliability to provide a permissible basis for upsetting a jury verdict. Witherspoon v. Illinois, 391 U.S. 510, 517-18, 88 S.Ct. 1770, 1774-75, 20 L.Ed.2d 776 (1968); McCleskey v. Kemp, 481 U.S. 279, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987); cf. Rhodes v. Chapman, 452 U.S. 337, 348 n. 13, 101 S.Ct. 2392, 2400 n. 13, 69 L.Ed.2d 59 (1981); Dunagin v. City of Oxford, 718 F.2d 738, 748 n. 8 (5th Cir.1983) (en banc). Appellate judges, not trial judges. The district judge did not find as a fact that -the jury in Free’s cases was confused; he held that a sentence of death imposed by any jury that is given the Illinois Pattern Instructions or some variant thereof is invalid; that is why Gacy was able to use the Zeisel study in his case. The district judge announced a rule; and appellate review of rules, and therefore (it follows) of the social scientific or other data on which the rules are based, is plenary. See John Monahan & Laurens Walker, “Social Authority: Obtaining, Evaluating, and Establishing Social Science in Law,” 134 U.Pa.L.Rev. 477 (1986). If the proper standard for evaluating the confusion quotient of Illinois Pattern Instructions were “clear error,” one could imagine a situation in which the identical set of jury instructions would be held unconstitutional in a habeas corpus proceeding before one district judge and constitutional in a proceeding before another — even though there were no pertinent factual differences between the cases — simply because the two judges evaluated the facts differently; and on appeal both decisions would have to be affirmed. Such disparity in treatment would be intolerable.
The skepticism that we have expressed about the validity of Zeisel’s study was presaged in the Gacy opinion (see 994 F.2d at 312) and pressed at the argument of this appeal in colloquy between the bench and Free’s able counsel. Neither in his brief nor at argument was counsel able to explain how Zeisel’s results can be taken seriously in light of the extraordinary vulnerability of his method.
The judgment of the district court is affirmed in part and reversed in part and the [707]*707case is remanded with directions to dismiss the application for habeas corpus.