POSNER, Circuit Judge.

In 1980, Walter Stewart pleaded guilty in an Illinois state court to two murders committed earlier that year in the course of his robbery of a suburban jewelry store, and was sentenced to death. After exhausting his state remedies, People v. Stewart, 101 Ill.2d 470, 79 Ill.Dec. 123, 463 N.E.2d 677 (1984); 123 Ill.2d 368, 123 Ill.Dec. 927, 528 N.E.2d 631 (1988), Stewart sought federal habeas corpus. The district judge, concluding from his study of the record in the state court that "Stewart's guilty plea violated his [Fourteenth Amendment] due process rights because the record does not affirmatively show that the plea was voluntary and intelligent," ordered the state either to release Stewart or to let him plead over. 770 F. Supp. 416 (N.D.Ill. 1991).

By pleading guilty a defendant waives a number of federal constitutional rights, such as the right to a jury trial and the right to confront his accusers. Boykin v. Alabama, 395 U.S. 238, 243, 89 S.Ct. 1709, 1712, 23 L.Ed.2d 274 (1969). These are important rights, and reviewing courts want to be sure that the defendant knows what he is doing when he gives them up. So they insist not only that the defendant made the plea without coercion but also that he appreciated its consequences — that is, that he understood the options he was surrendering. Brady v. United States, 397 U.S. 742, 748-50, 756-58, 90 S.Ct. 1463, 1468-70, 1472-73, 25 L.Ed.2d 747 (1970); Evans v. Meyer, 742 F.2d 371, 375 (7th Cir. 1984); Morgan v. Israel, 735 F.2d 1033, 1036 (7th Cir. 1984). The defendant must not only want to plead guilty; he must have adequate knowledge of what the plea entails as well as the intelligence to bring that knowledge, along with all other pertinent knowledge, to bear on his decision. And the satisfaction of these requirements (compendiously, the requirement that the plea be "voluntary") may not be inferred from the bare fact that the defendant pleaded guilty. Boykin v. Alabama, supra. He might not have known what he was giving up by pleading guilty.

No one doubts that Walter Stewart wanted to plead guilty; nor that he had the intelligence to make an effective plea, for he was 25 years old, had a long criminal record (arguing familiarity with the criminal justice system), and was not retarded, intoxicated, or insane. The question is whether he had adequate knowledge — not knowledge that he might be executed, for the judge told him repeatedly that a guilty plea would not preclude the death penalty; not knowledge that he was, indeed, giving up his right to a jury trial, his right to put on a defense, and his right to cross-examine the state's witnesses, and so on, for these things were made clear to him too; but knowledge of the value that those rights might have in the particular case. A defendant must be allowed to choose with undistorted vision. If he is led to believe that the procedural rights that he will be surrendering by pleading guilty are worthless to him because he has no defense to the state's charges, when actually they are not worthless because he does have a defense, his plea of guilty will not be based on a realistic assessment of the probable consequences, and thus a vital component of voluntariness will be missing. Brady v. United States, supra, 397 U.S. at 756-57, 90 S.Ct. at 1472-73; United States v. Frye, 738 F.2d 196, 199 (7th Cir. 1984); Haase v. United States, 800 F.2d 123, 127 (7th Cir. 1986). A rational choice is a choice among rationally understood probabilities.

The district judge found that Stewart had not made a voluntary waiver of his trial rights, and we should consider first what the scope of our review of such a determination is. While reserving the question, we suggested in Hanrahan v. Greer, 896 F.2d 241, 244 (7th Cir. 1990), that our review of a district court's determinations of issues that turn on the application of a legal standard to facts — issues sometimes referred to as "mixed questions of fact and law" or "ultimate questions of fact," such as whether an error is harmless, or a guilty plea voluntary, or whether a party was negligent or had possession — should be deferential in habeas corpus cases just as it is in other types of cases. Mucha v. King, 792 F.2d 602, 605 (7th Cir. 1986); United States v. McKinney, 919 F.2d 405, 419 (7th Cir. 1990) (concurring opinion). See also Sotelo v. Indiana State Prison, 850 F.2d 1244, 1253-55 (7th Cir. 1988) (concurring opinion). It is true that when, as in this case, the district judge does not hold an evidentiary hearing, his determination is based on a pure paper record equally available to us. Yet we were told in Anderson v. City of Bessemer, 470 U.S. 564, 574, 105 S.Ct. 1504, 1511, 84 L.Ed.2d 518 (1985), that the clearly erroneous rule applies to appellate review of a district judge's finding of fact even when the finding is based purely on documentary evidence. See also Mucha v. King, supra, 792 F.2d at 605-06. Why should this not be true in a habeas corpus case as well? The other circuits that have considered the question, however, believe that in such a case appellate review of the district judge's finding of voluntary (or, as here, involuntary) waiver should be plenary. Lesko v. Lehman, 925 F.2d 1527, 1536 (3d Cir. 1991); McBee v. Abramajtys, 929 F.2d 264, 266-67 (6th Cir. 1991); Schlup v. Armontrout, 941 F.2d 631, 637-38 (8th Cir. 1991); Bailey v. Cowley, 914 F.2d 1438, 1440 (10th Cir. 1990) (per curiam). We need not take sides today. Either way Stewart must lose. The district judge's error was a clear one.

The transcript of the plea hearing takes up 94 double-spaced typed pages. It begins with the calling of the case for trial, followed by a motion by the prosecutor to drop 5 of the 18 counts — some of the lesser crimes with which Stewart had been charged, such as armed violence and aggravated battery. This is followed by Stewart's waiving his right to a jury trial. He does not contend that this waiver was involuntary.

Stewart's principal lawyer (he had two lawyers) requested a five-minute recess to talk to his client. The request was granted. In judicial parlance a "five-minute recess" is a break of short but indefinite length. According to the lawyer's uncontradicted affidavit he had only one conversation with his client that day and it took half an hour; it could only have been during the recess.

When court resumed, the lawyer reported that after Stewart had discussed the matter with him and had spoken by phone with his mother and sister, and in recognition of the prosecutor's having dropped "those five counts for which we felt there was a defense," Stewart had decided that "no useful purpose would be served by proceeding with an actual denial of guilt in regard to the pending charges" even though the lawyer had made clear to him that a guilty plea would not prevent the state from seeking the death penalty. The lawyer asked Stewart in open court whether this summary of their discussion was accurate, and he said it was. By this time it was noon and the judge said he would take the guilty plea after the lunch recess, but before adjourning he "advise[d] Mr. Stewart of certain possibilities in connection with this case, that he may wish to consider over the lunch hour." By pleading guilty Stewart would be giving up not only his right to a jury trial but his right to any trial. "I merely hear a statement from the prosecutors as to what the facts are. If you and your lawyers agree there is a finding of guilty and judgment of guilty on those findings. Do you understand that?" Stewart said yes. The judge also told Stewart that upon the plea of guilty the state would in all likelihood seek the death penalty, "and the fact that you plead guilty would not necessarily obviate the imposition of such a penalty." Stewart may not have known what the word "obviate" means because later, at the penalty hearing, when the judge used the word again, Stewart asked him what it meant. But at the guilty-plea hearing the judge repeated in simple language that Stewart's pleading guilty would not prevent the state from asking for the death penalty.

The judge added that if the state sought the death penalty it would have to prove — to a jury if Stewart wanted one — "that there were certain aggravating factors." Stewart said he understood. He also acknowledged in response to a question by his lawyer that the lawyer had indeed told him that a guilty plea would not prevent (no "obviate" here) the state from seeking the death penalty.

When court reconvened after lunch the judge asked Stewart whether he had "had a chance to think over what we have talked about," and when Stewart said yes the judge asked, "You so wish to insist [persist?] in your plea of guilty or do you wish to change it?" "No, sir." "You wish to have me hear the case?" "Yes, sir, I think it would be fair." Taken in isolation, the words "You wish to have me hear the case?" could mean that the judge was asking Stewart whether he wanted a trial — and Stewart said yes. The alternative interpretation is that the judge was asking whether Stewart wanted the case resolved by the judge in the manner he had sketched before lunch ("I merely hear a statement from the prosecutors as to what the facts are. If you and your lawyers agree there is a finding of guilty and judgment of guilty on those findings") rather than by a jury in a trial. The alternative interpretation is the only plausible one. Stewart had just said he didn't wish to change his plea. He had been told before lunch that he should think over whether he really wanted to plead guilty, and the thrust of the questions after lunch was to ascertain whether he wanted to persist in that course of action, as plainly he did. Stewart must have understood that he was being asked whether he adhered to the decision he had made before the lunch recess to plead guilty and did not want a jury trial. And three times after the garbled exchange that we have quoted Stewart was asked in plain language whether he still wanted to plead guilty and each time he said yes.

So what did Stewart mean when he said that he thought it would be fair for the judge to hear the case? After the state, as expected, requested a death-penalty hearing, Stewart waived his right to have a jury determine whether the penalty should be imposed. The decision to waive that jury may well have been made before the guilty plea was made — this is suggested by the affidavit of Stewart's trial lawyer in which he said that the decision to plead guilty had been based on a feeling that this judge would not sentence Stewart to death — in which event, in telling the judge that he thought it would be fair to have the judge hear the case, Stewart would have been looking ahead to the death-penalty hearing and hoping that a plea of guilty would help persuade the judge not to sentence him to death. This is conjecture, and in a death case to have to conjecture is disturbing. But the only immediately pertinent fact is not in the realm of conjecture: it is that Stewart wanted to plead guilty.

The judge later asked whether the defendant was pleading guilty to all the remaining counts and Stewart's lawyer said yes, "whatever counts are still left." The prosecutor suggested itemizing the counts and asking the defendant how he pleaded to each one, but the defendant's lawyer insisted that was unnecessary, that the plea "encompass[es] one event, the armed robbery and the subsequent deaths of two people in the jewelry store." The judge then announced, "Plea of guilty, jury waived."

The prosecutor suggested that after the stipulation of facts was read into the record the court make a finding concerning the factual basis for each count to which the defendant was pleading guilty. The judge said to Stewart, "I don't want you to be misled. I don't want you to think that be entering a plea of guilty and saving the State and the Court the time involved in a trial that that would mean that it would have a great deal of effect, a bearing on the question of what the penalty would be. Do you understand that?" "Yes, sir." The prosecutor added that there had been no plea negotiations. Stewart's lawyer confirmed this and added "we are entering plea of guilty to the charges remaining because of the facts if they were brought to trial that the Defendant would be guilty of those charges." He then asked the judge to inform Stewart of his rights before the stipulation was read. The judge explained to Stewart that by pleading guilty Stewart was giving up his right to a jury trial and to cross-examination. He then asked Stewart, "And knowing all of that do you still wish to continue, that is, persist in your plea of guilty?" Stewart again said "Yes, sir."

The prosecutor then stated that he and Stewart's lawyer had stipulated "that the facts in evidence in this case would show the following," but later Stewart's lawyer clarified his understanding of the stipulation to be that it was a stipulation of the state's evidence. Seventy-four pages of transcript follow summarizing the physical exhibits and the testimony that the state would have presented had the case gone to trial:

Linda Manzano was the proprietor of a jewelry store in Berwyn, Illinois. One Sunday in February 1980, she was in the store with her brother, Danilo Rodica, and her boyfriend, Thomas Pavlopoulos, an employee named Laura Landsinger, and Rodica's nine-year-old daughter. Stewart, posing as a customer, first entered the store at 1:30 p.m., asked to be shown various items of jewelry, and left. He returned between 4:30 and 5:00, drew a revolver, and announced a stickup. After completing the robbery, the defendant gestured with his gun for the two men and Linda Manzano, who were standing in front of him, to move to the side (Laura Landsinger and the child were in the back room). The men didn't move, but Linda Manzano took one step backward — whereupon Stewart shot her in the abdomen. The two men, assisted by the wounded woman, jumped Stewart in an attempt to prevent his firing any more shots. The attempt failed. Stewart fired four shots, hitting both men, and shoved the woman to the ground. Rodica's body was twitching on the floor, and Stewart shot him again. He then raced to the back room, pointed his gun at Linda Landsinger's face, and pulled the trigger, but there was only a click, because the gun was empty. Meanwhile Landsinger (who had hidden the child) had pushed the holdup button, and by the time Stewart left the store the police had arrived, and they arrested him. Stewart told them, "I shot them because they jumped me." Rodica and Pavlopoulos were dead. Manzano recovered and identified Stewart at a lineup. She said, "You killed my brother." He replied, "So what. I wish it was your mother."

After the reading of the stipulation from which the above summary is drawn, the judge, without further colloquy with Stewart, announced a finding of guilty on each of the remaining counts, and the state requested a death-penalty hearing. At the hearing, many of the witnesses who would have testified at a trial testified about the circumstances of the killings. The penalty hearing occupies some 600 pages of transcript, most of them devoted to the circumstances of the robbery and killings. Stewart's counsel tried through cross-examination and in his closing argument to suggest that Stewart had killed in self-defense. Although a robber has no right of self-defense, Ill.Rev.Stat. ch. 38, ¶¶ 7-1, 7-4(a); People v. Austin, 133 Ill.2d 118, 126, 139 Ill.Dec. 819, 822, 549 N.E.2d 331, 334 (1989); People v. Moore, 95 Ill.2d 404, 411, 69 Ill.Dec. 640, 643, 447 N.E.2d 1327, 1330 (1983), counsel wished to make Stewart's actions seem less cold-blooded. He also presented evidence that Stewart was high on drugs at the time of the robbery.

Stewart argues that the guilty-plea hearing was rushed, sloppy, and confused, but in so arguing he confuses the requirements of the federal and state rules governing guilty-plea proceedings with the constitutional requirement, which is that the record show an effective waiver — one that appears to be deliberate, uncoerced, understanding, and intelligent. As many cases illustrate, such as United States v. DeForest, 946 F.2d 523, 526 (7th Cir. 1991); United States v. Henry, 933 F.2d 553, 560 (7th Cir. 1991); United States v. Gallman, 907 F.2d 639, 643 (7th Cir. 1990), and Haase v. United States, supra, 800 F.2d at 127, there is no fixed colloquy, no set sequence or number of questions and answers, no minimum length of the hearing, no talismanic language that the judge is required to use. The Constitution does not enact Rule 11 of the Federal Rules of Criminal Procedure, United States v. Frye, supra, 738 F.2d at 199; Haase v. United States, supra, 800 F.2d at 127, let alone its Illinois counterpart. Ill.Rev.Stat. ch. 110A, ¶ 402. So we do not ask whether the guilty-plea proceeding in this case was in substantial compliance with that rule. We focus instead on the particular omissions that Stewart contends are critical. Some plainly are not. For example, he complains that the judge never asked him whether the plea was uncoerced. In eleven years of post-trial proceedings Stewart has never contended that it was coerced, so the failure of the judge to ask that question could not have been material. Cf. United States ex rel. Cyburt v. Rowe, 638 F.2d 1100, 1104 (7th Cir. 1981).

Potentially significant omissions are the following. Stewart did not, after the reading of the stipulation of facts, state that it was accurate; in fact he never directly admitted that he had committed the crimes with which he was charged. The judge did not explain to Stewart the elements of the offenses with which he was charged, nor is it certain from the transcript that his lawyer did. And the judge never told him what the minimum sentence for murder was. There were other omissions but these are the only conceivably material ones, and neither singly nor together do they permit an inference that Stewart's plea was involuntary.

The first and third are weak. There is no requirement that for a guilty plea to be effective, the defendant must admit his guilt. North Carolina v. Alford, 400 U.S. 25, 36-37, 91 S.Ct. 160, 166-67, 27 L.Ed.2d 162 (1970); United States v. Musa, 946 F.2d 1297, 1302 (7th Cir. 1991). A guilty plea is no more involuntary because the defendant believes he is innocent than the settlement of a civil lawsuit is involuntary because the defendant refuses to admit liability and may believe in all sincerity that he is not liable in the least. Stewart's lawyer made plain to the judge that while the defense had stipulated to the contents of the state's case, it did not accept the truth of every bit of testimony and had the case gone to trial would have tried to chip away at the state's case through cross-examination. Nevertheless Stewart wanted to plead guilty and that was his right. We add lest there be any misunderstanding of the significance of Stewart's failure to acknowledge his guilt explicitly that the transcript of the penalty hearing dispels any doubt of that guilt.

As for the judge's failure to inform Stewart that the minimum sentence for murder was 20 years, we do not understand the materiality of this omission (even less do we understand the materiality of the judge's failure to inform Stewart of the minimum and maximum sentences for armed robbery and for attempted murder). Stewart argues that he thought the minimum sentence for murder was imprisonment for his natural life, but we don't see how, if that is indeed what he assumed, it could have persuaded him to plead guilty. On the contrary, the lower the perceived minimum sentence, the more the defendant could be expected to want to curry favor with the judge by pleading guilty. He would have had more to gain from pleading guilty if he had thought he could be sentenced to only 20 years than if he thought that the only concession he could wring from the court would be a sentence of imprisonment for the rest of his life.

We said earlier that for a plea of guilty to be voluntary the defendant must know the value to him of the rights he is giving up, and in particular he must know what the state would have to prove if he insisted on his right to a trial. Stewart's strongest argument is that the judge, by failing to advise him of the elements of murder, misled him about the prospects for an acquittal of the charges that would place him in gravest risk of the death penalty. Under Illinois law at the time of the robbery, "a person who kills an individual without lawful justification commits murder if, in performing the acts which cause the death," he "intends to kill or do great bodily harm to that individual or another, or knows that such acts will cause death to that individual or another," or "knows that such acts create a strong probability of death or great bodily harm to that individual or another," or "is attempting or committing a forcible felony other than voluntary manslaughter." Ill.Rev.Stat. ch. 38, ¶¶ 9-1(a)(1), (2), (3). All three offenses are murder but to be subject to the death penalty the murderer must have been at least 18 years old when he committed the crime and must (so far as relevant to this case) have murdered two or more persons, "provided the deaths occurred as the result of . . . either an intent to kill more than one person or of separate premeditated acts." ¶ 9-1(b)(3). Stewart pleaded guilty to all three versions of first-degree murder, that is, to the offenses in ¶¶ 9-1(a)(1), (2), and (3), and he argues that by pleading guilty to both murders under ¶ (1) he automatically exposed himself to the death penalty by thus acknowledging, in effect, that "the deaths occurred as the result of. . . an intent to kill more than one person." He would not have automatically exposed himself to the death penalty had he pleaded guilty only under ¶ (3). You can be guilty of felony murder without intending to kill anybody, so had Stewart pleaded guilty only to that crime the state would have had to prove at the penalty hearing that he had intended to kill both of his victims (or some other statutory aggravating factor). And likewise if he had pleaded guilty under ¶ (1) as to only one of his victims and under ¶ (3) as to the other. These subtleties, he claims, were not explained to him, and as a result he unknowingly forfeited a crucial issue at sentencing.

It is true that the judge did not instruct Stewart on the differences among the subsections of the murder statute, but that is not required. It is enough if defense counsel informed Stewart of the differences, and it is presumed that he did. Henderson v. Morgan, 426 U.S. 637, 647, 96 S.Ct. 2253, 2258, 49 L.Ed.2d 108 (1976); Marshall v. Lonberger, 459 U.S. 422, 436-37, 103 S.Ct. 843, 851-52, 74 L.Ed.2d 646 (1983). The cases establishing this presumption may seem inconsistent with Boykin, which Stewart interprets as insisting that, as part of the requirement that the voluntariness of the guilty plea must appear in the record of the plea hearing, the elements of the crime be stated on the record. If there is any inconsistency, the later decisions control. But we do not think there is any. In Boykin "the judge asked no questions of the petitioner concerning his plea, and petitioner did not address the court." 395 U.S. at 239, 89 S.Ct. at 1710; see also id. at 245 n. 1, 89 S.Ct. at 1713 n. 1 (dissenting opinion). Any presumption that the petitioner knew what he was doing would have rested on air. There is much to support an inference that Stewart knew what he was doing. There is the 94-page transcript of the guilty-plea hearing which includes among other things the statement by his counsel that "We have at length with the Court's permission advised the Defendant of the consequences" of his pleading guilty. Stewart was repeatedly warned that his plea of guilty might expose him to a sentence of death, which it could do (so far as relevant to this case) only if he pleaded guilty to killing intentionally. If counsel failed to advise Stewart of the elements of capital murder, he was incompetent. There is no argument that he was incompetent. Nor does Stewart ask for an evidentiary hearing in order to explore, by means of testimony from Stewart and his trial counsel, what exactly Stewart was told. It is true that his trial counsel's affidavit in the postconviction proceedings speaks only of advising Stewart of the consequences of a guilty plea, not of the elements of the crime. But the affidavit is limited to the discussion between lawyer and client on the day of the guilty plea. It was not the first time they had discussed the case. Stewart's current counsel, whose ability and dedication cannot be questioned, has made no offer to prove that trial counsel failed to provide Stewart with all the information he needed in order to make an intelligent plea. The argument is limited to omissions in the transcript of the guilty-plea hearing. The argument might be telling if the question were compliance with Rule 11. It is not.

We see no escape from the inference that Stewart was fully advised of the nature and consequences of his plea. We might hesitate to rest decision in so grave a matter on an inference of this character if we thought it even remotely possible that Stewart might have had a defense to capital murder and forgone it out of ignorance of the elements of that crime. It is not even remotely possible. Even if he was high on drugs at the time of the crimes, there can be no serious contention — we do not understand Stewart to be contending — that he was so high that he could not form an intent to kill or do great bodily harm, which is the only possible relevance of intoxication in the criminal law of Illinois. Evans v. Meyer, supra, 742 F.2d at 373-74; People v. Primmer, 111 Ill.App.3d 1046, 67 Ill.Dec. 593, 444 N.E.2d 829 (1983); People v. Moon, 107 Ill.App.3d 568, 572, 63 Ill.Dec. 174, 176, 437 N.E.2d 823, 825 (1982) (intoxication "so extreme as to suspend all reason"). He fired six shots. Four hit their mark, felling three people. Stewart shot one man a second time after the man had fallen gravely wounded from a previous shot. He aimed at a fourth person and pulled the trigger. The fact that the two men he killed had jumped him did not give him a lawful justification to shoot them, and therefore was not a defense under the statute, while the circumstances that we have reviewed negate any suggestion that the killings were unintentional. The killings were not the work of an automation or a sleepwalker. Cf. Greider v. Duckworth, 701 F.2d 1228, 1237 (7th Cir. 1983) (concurring opinion). At all events these matters were gone into in the penalty hearing at length. The same judge who accepted the guilty plea sentenced Stewart to death, although Stewart had waived a jury at the sentencing hearing because he and his lawyer believed that this judge was unlikely to impose the death sentence.

Against this background the fact that had Stewart pleaded guilty only to felony murder he would have thrust a greater burden of proof on the state at the penalty hearing has only academic significance. If he had pleaded guilty only to armed robbery, there would have been no death-penalty hearing at all. The fact is that he was plainly guilty of all three forms of first-degree murder. He knew it, his lawyer knew it, and the state knew it.

We are not saying that any error in the guilty-plea proceeding was harmless because the outcome of a trial would have been a forgone conclusion. Almost any trial error will be disregarded if harmless, Arizona v. Fulminante, ___ U.S. ___, 111 S.Ct. 1246, 1264-66, 113 L.Ed.2d 302 (1991) (Rehnquist, C.J., speaking for a majority of the Court on this point), but this is not a case of trial error — there was no trial — and a defendant cannot be forced to give up his right to a trial by a demonstration that a trial would be a waste of time. Walberg v. Israel, 766 F.2d 1071, 1074 (7th Cir. 1985); United States v. Kerley, 838 F.2d 932, 938 (7th Cir. 1988); cf. Tumey v. Ohio, 273 U.S. 510, 535, 47 S.Ct. 437, 445, 71 L.Ed. 749 (1927). We cannot find a case which states that compelling a defendant to plead guilty against his will cannot be disregarded even if he obviously is guilty, but we think the reason for the absence of such cases is simply that no one would argue such a proposition. The relevance of the fact that this was an open and shut case of capital murder is to demonstrate the rationality of Stewart's action in pleading guilty without a guaranty that his life would be spared. He had no chance of being acquitted. His only hope was to throw himself upon the judge's mercy. He did so. He took a calculated and informed risk that failed. The outcome did not deny him due process of law. Brady v. United States, supra, 397 U.S. at 756-57, 90 S.Ct. at 1472-73.

The most singular feature of the procedures in this case should not go unremarked. Stewart's main argument, it will be recalled, is that by pleading guilty to a form of murder that requires intent to kill, he placed his head in the noose because, since there were two murders and anyone who murders two people intending to murder both of them can be sentenced to death, the state in order to "qualify" Stewart for death had only to prove, which no one disputed, that he was at least 18 years old when he committed the murders. But then why does the transcript of the penalty hearing take up 600 pages? The answer is that the state shouldered the burden all over again of proving that Stewart really did intend to kill both his victims. Illinois law required the state to prove the existence of an "aggravating" factor, that is, a factor that makes the defendant subject to a death sentence, beyond a reasonable doubt. Ill.Rev.Stat. ch. 38, ¶ 9-1(f); People v. Simms, 143 Ill.2d 154, 157 Ill.Dec. 483, 488, 572 N.E.2d 947, 952 (1991). One factor, we know, and the one the state relied on, is that the defendant intentionally killed at least two persons. So the state set about to prove this beyond a reasonable doubt, although, as Stewart now points out, the state might well have taken the position that Stewart's intention to kill both his victims had been established by his guilty plea, so that the only remaining issue was whether there might be some mitigating factors. The state did not take that position, and as a result Stewart not only put the state to its proof but also had a full opportunity to contest the state's case, which he did both through cross-examination of the state's witnesses and through his own witnesses. He had in fact the full trial he would have received had he pleaded not guilty, and before his preferred trier of fact — a judge and not a jury.

Stewart's counsel reminds us that judicial review in capital cases must be exacting. To condemn to death unjustly is a terrible thing, and few modern Americans will take much comfort in the reassurance of William Paley that "He who falls by a mistaken sentence, may be considered as falling for his country." "Moral and Political Philosophy," in 3 Works of William Paley 1, 315 (1838 ed.). But the state is entitled to justice too, and perfection is no more to be expected in a capital case than in any other human endeavor. There were irregularities in the proceedings in this case, but the principal one favored the defendant — he got, in effect, a full trial on guilt after pleading guilty and waiving his right to a trial. This court's authority is limited to the correction of federal constitutional errors. We find none, and therefore reverse with directions to deny the petition for habeas corpus.

REVERSED.

ORDER

In the last sentence of the panel opinion issued on February 27, the judgment of the district court is "reversed with directions to deny the petition for habeas corpus." The petition for rehearing points out, and the state's response confirms, that the petitioner had presented in the district court alternative grounds for habeas corpus which the district judge had not passed on. (Neither of the parties had mentioned the existence of these unresolved grounds in their briefs, or at the oral argument.) The better practice in habeas corpus death cases is for the judge to rule on all the grounds presented in the petition, so that the appellate court can decide the entire case in one round, without the interminable delays that characterize postconviction proceedings in such cases. King v. McCotter, 795 F.2d 517 (5th Cir. 1986) (per curiam); cf. Thigpen v. Smith, 792 F.2d 1507 (11th Cir. 1986). Unfortunately that was not done here, and we hereby modify our decision to make it a simple reversal and remand for further proceedings consistent with our opinion, thus leaving it to the district judge to decide in the first instance what further proceedings are proper in this case. In all other respects the petition for rehearing is denied.