delivered the opinion of the court:
Following a jury trial in the circuit court of Cook County, the defendant, Derrick E. King, was convicted of murder and armed robbery. Sitting without a jury, the trial judge sentenced the defendant to death for his murder conviction. Sentence was stayed (87 Ill. 2d R. 609(a)) pending direct review by this court (Ill. Const. 1970, art. VI, sec. 4(b); 87 Ill. 2d R. 603), and we now affirm the judgment of the circuit court.
The offenses occurred in the evening of December 19, 1979, at a record and candy store named “Pleasures Unlimited,” located at 1943 West 79th Street in Chicago. The victim, Dwayne Miller, was employed at the store as a salesclerk; he was shot once in the back of the head, and he died from the wound. There were two cash registers in the store, and the drawers of both were found open and empty of paper money. Various items, including phonograph records and change, were scattered on the floor. The victim was found behind a counter in the store.
On February 23, 1980, the defendant was arrested in connection with the murder and armed robbery. Under questioning, he made several inculpatory statements, culminating in a signed confession to the crimes. Following that, the defendant was charged by information with murder, armed violence, and armed robbery; before trial, the State nol-prossed the armed-violence charge.
The defendant’s statements were introduced into evidence at trial, and they supplied the primary evidence of his guilt. Following his arrest, the defendant was first questioned by robbery investigators about an armed robbery that occurred at a Church’s Chicken restaurant on *522December 22, 1979; the restaurant was located across the street from the Pleasures Unlimited store. After that, he was interrogated by Officer Robert Dwyer, a homicide investigator, about the murder in question here. Dwyer told the defendant that bullets fired at the two businesses had been shown to have come from the same gun. Initially, the defendant said that he waited outside Pleasures Unlimited and that another person, Summage, had shot the victim. The defendant also said that a third person, Coleman, was involved too and that Summage and Coleman would try to implicate him, that Summage would say that the defendant had shot the victim. The defendant then was asked whether he had in fact fired the fatal shot, and the defendant admitted that he had. He said that it was an accident, however. He explained that he was walking the victim toward the back of the store, where there was a second cash register, when the victim jerked away and the gun went off.
After the defendant gave that statement, he accompanied police officers to point out to them Coleman’s residence. Later that night, Coleman surrendered a gun to police. The defendant identified it as the murder weapon and then agreed to make a formal statement; this final interview began about 2:40 a.m. on February 24.
In the written confession, the defendant explained that he and two other persons, Donald Ray Summage and Michael Coleman, were outside the Pleasures Unlimited store in the evening of December 19, 1979. The defendant and Summage entered the store, intending to obtain money and drugs, which they believed were sold there by the owner, Demetrius Shaw. Inside the store, the defendant asked for Shaw. The youth behind the counter said that he was not in and did not know when he would return. The defendant then told the youth to give him the money in the cash register, and the youth *523complied, handing over $7. At that point the defendant was holding the youth, trying to move him toward another cash register. The youth jumped, and the defendant shot him once in the back of the head. While giving the statement, the defendant identified a gun, a .38-cali-ber revolver, as the weapon he had used in the murder and robbery. The defendant also confessed to the armed robbery at the Church’s Chicken restaurant on December 22, 1979. On that day, the defendant and Summage entered the restaurant, located at 79th and Damen, across the street from the Pleasures Unlimited store, and Summage raised the gun and announced the holdup. The defendant took about $400. As they left, Summage fired a shot into the woodwork or paneling there. After the statement was typed, the defendant had Officer Dwyer add the sentence, “I did not mean to kill the boy.”
I
The defendant first argues that the trial court erred in denying his motion to suppress his inculpatory statements. The defendant argues that they were the products of coercion inflicted on him by the police. Following an extensive hearing, the trial judge denied the motion, finding that the defendant had given the statements voluntarily.
At the suppression hearing, the defendant presented testimony regarding his condition before and after his arrest. Michael Berry, a friend, testified that the defendant spent the day of his arrest, February 23, 1980, drinking at another person’s house. In the evening, Berry, the defendant, and another left, taking a bus. While walking, the defendant was arrested by a police officer who pulled up in a car. According to Berry, the defendant was intoxicated at that time.
Darlene Harland, a cousin of the defendant, visited *524the defendant in custody on February 24, 1980, the day after he was arrested. She testified that the defendant’s eyes were very red, his face was swollen, and an arm was scratched. Harland had seen the defendant only two days before, and at that time he appeared normal. The defendant told her that he had been beaten following his arrest. Harland believed that the defendant looked worse when she saw him than he did in a photograph of a lineup that the defendant had appeared in.
The defendant testified that he spent the day of his arrest drinking at a friend’s house. That evening, while walking with two others, he was arrested. A police car pulled up, and the officer ordered the defendant to get in the car. The defendant testified that police officers questioned him about a murder case and hit him on the knees with a baseball bat 20 to 40 times; they also struck him in the chest with the bat and hit him in the head once or twice with a book. According to the defendant, the police told him to cooperate and advised him not to say anything about his mistreatment to the assistant State’s Attorney who took his confession. The defendant testified that he confessed to the crimes because of the beatings. He acknowledged that he was informed of his Miranda rights on several occasions.
Also testifying in the defendant’s behalf was Leon White, manager of the Church’s Chicken restaurant robbed by the defendant. White viewed the defendant in a lineup on February 24, 1980, at about 6 p.m. White said that at that time the defendant looked as though he had been injured: his face was swollen and an eye was bruised. White was shown a photograph taken after the lineup, and he noted that in it the defendant’s face did not appear swollen, and he could not determine from it whether an eye was bruised.
The State presented the testimony of a number of police officers who saw the defendant during the period of *525his arrest and interrogation. According to this evidence, the defendant first was taken to the sixth district police station and then later was transported to area two headquarters, where he was questioned about the murder and robbery at Pleasures Unlimited and also about the robbery at the Church’s Chicken restaurant. The various teams of police officers who questioned the defendant said that they informed him of his Miranda rights, and they denied threatening or beating him. The defendant presented in rebuttal Donald Summage, who had been questioned by police in connection with the crimes here. Summage testified that police officers said that they had beaten the defendant and Coleman and threatened him with the same treatment. This was disputed by an officer who arrested Summage.
At the conclusion of the hearing, the trial judge denied the defendant’s motion to suppress his statements. The trial judge found that coercion was not used against the defendant and that he had given his statements voluntarily.
The State has the burden of establishing the voluntariness of a defendant’s confession, and the applicable standard requires proof by a preponderance of the evidence. (People v. Caballero (1984), 102 Ill. 2d 23, 33; People v. Harper (1967), 36 Ill. 2d 398, 402; Ill. Rev. Stat. 1979, ch. 38, par. 114—11(d); see Lego v. Twomey (1972), 404 U.S. 477, 489, 30 L. Ed. 2d 618, 627, 92 S. Ct. 619, 626.) The trial court’s determination will not be reversed on appeal unless it is against the manifest weight of the evidence (People v. Davis (1983), 97 Ill. 2d 1, 20; People v. Kincaid (1981), 87 Ill. 2d 107, 117-18), and, on review, evidence presented at trial may be considered in addition to the evidence that was presented at the suppression hearing (People v. Stewart (1984), 104 Ill. 2d 463, 480; People v. Caballero (1984), 102 Ill. 2d 23, 36; People v. La Bostrie (1958), 14 Ill. 2d 617, 620-*52621).
For proof of his mistreatment at the hands of the police, the defendant relies primarily on Leon White, whose testimony the defendant believes is especially reliable: according to the defendant, White, as the manager of a store allegedly robbed by the defendant, would have had no bias in his favor. The defendant argues that White’s testimony therefore confirms Harland’s and his own regarding his injuries. The defendant believes, too, that the State failed to provide an innocent explanation for the injuries, and he points out several inconsistencies in the testimony of the officers who arrested and interrogated him.
White and Harland did not see the defendant until the afternoon of the day following his arrest, and their accounts of his appearance at that time, even if accurate, do not explain when or how the alleged injuries occurred. More important, however, the photograph taken immediately after the lineup on February 24 tends to undermine their descriptions of the defendant’s appearance on that day. Additional photographs introduced into evidence at trial support the court’s finding that the defendant’s statements were not coerced. One photograph was taken immediately after the defendant’s formal confession; the other was an intake photograph taken on February 25, 1980, when the defendant was transferred to the county jail. Harland indicated that she could detect in them some injuries suffered by the defendant, but the State’s witnesses disputed that injuries were present. Taken together, these photographs support the trial court’s finding on this matter. We conclude that its finding was not against the manifest weight of the evidence.
Next, the defendant argues that one of his witnesses was improperly impeached and that the State presented to the jury, as substantive evidence, details of a confes*527sion allegedly made by the defendant to that witness.
Testifying in the defendant’s behalf at trial, Timothy Cox denied the truthfulness of testimony that he had given to a grand jury on February 8, 1980, implicating the defendant in the robbery and murder at Pleasures Unlimited. Over the State’s objection, Cox was permitted to explain that he had given that testimony because of threats and harassment by the police. On cross-examination, Cox acknowledged that he had spoken with the defendant on December 23, 1979, four days after the murder at Pleasures Unlimited. Asked about specific parts of the earlier testimony, Cox admitted making those statements to the grand jury but denied that they were true. Specifically, Cox denied that the defendant showed him a silver .38-caliber handgun, that the defendant said that he and “Norris” robbed the Church’s Chicken restaurant, and that the defendant said that he would hold up every store on 79th Street and shoot if he were not given money. Cox also denied that the defendant told him the following about the murder and armed robbery at Pleasures Unlimited: that the defendant dragged the victim, Dwayne Miller, to a safe at the back of the store, which he knew contained contraband, that the youth resisted and the defendant hit him, that when the victim refused to open the safe, the defendant ordered him to his knees and asked him one more time to open the safe, and that the victim did not respond, so the defendant shot him in the back of the head.
This information also was revealed in the State’s presentation of a rebuttal witness at trial, assistant State’s Attorney Jacqueline Cox; she is not related to Timothy Cox. Jacqueline Cox testified that she was present at an interview with Timothy Cox on June 4, 1981, a week before the trial. During that interview, another assistant State’s Attorney questioned Timothy Cox about his *528grand jury testimony, and Timothy Cox reaffirmed it. Jacqueline Cox then recounted Timothy Cox’ statements on that occasion. At defense counsel’s request, the trial judge instructed the jury that the testimony was not evidence that the defendant had made the statements to Cox but rather could be used only as evidence that Timothy Cox had made the statements to the grand jury and later to the assistant State’s Attorneys. Essentially, Miss Cox then repeated what Timothy Cox admitted telling the grand jury but now, at the time of trial, said was false.
The defendant argues that the extensive impeachment of Timothy Cox, both through the cross-examination of that witness and in the rebuttal testimony of Jacqueline Cox, was improper and prejudicial. The defendant believes that the jury inevitably gave this evidence substantive effect, despite receiving several cautionary instructions to the contrary, and points to a part of the State’s argument in which the impeachment material was used substantively.
The defendant contends that the prior statements presented here were not proper impeachment of Timothy Cox’ trial testimony. The defendant believes that Timothy Cox’ testimony on direct examination did not damage the State’s position at trial and therefore his impeachment was unwarranted and pertained only to collateral matters. We disagree. The testimony was damaging, for it was intended to support the defendant’s theory of police coercion in connection with the investigation of this case. Moreover, that Cox admitted making the earlier statements would not preclude the State from introducing them in impeachment. People v. Bradford (1985), 106 Ill. 2d 492.
The defendant also argues that this court has forbidden the impeachment of a witness with earlier statements made outside the presence of the defendant and *529relating a confession of guilt. In support of that contention the defendant quotes People v. Bryant (1983), 94 Ill. 2d 514, 522, where the court said:
“[Statements made outside the defendant’s presence which relate his confession of guilt or innocence are not competent evidence even for impeachment purposes if likely to prejudice the jury. (People v. McKee (1968), 39 Ill. 2d 265, 271; People v. Tunstall (1959), 17 Ill. 2d 160.)”
The defendant would derive from Bryant, McKee, and Tunstall a general prohibition of the form of impeachment attempted here.
That theory originated in People v. Tunstall (1959), 17 Ill. 2d 160, and the broad “rule” announced there has had an uneven course; it has been variously repudiated and revived. (See People v. Bailey (1975), 60 Ill. 2d 37, 49-59 (Underwood, J., dissenting).) Thus, in People v. Tate (1964), 30 Ill. 2d 400, the court expressly disavowed Tunstall’s broad statement, but later, in People v. McKee (1968), 39 Ill. 2d 265, Tunstall was cited approvingly and Tate was not mentioned.
The notion that the defendant’s absence from the conversation renders it inadmissible has been rejected as a limitation on the substantive use of evidence (People v. Carpenter (1963), 28 Ill. 2d 116), and it would appear to be an equally inappropriate limit on the use of statements for impeachment. The real basis for the concern, then, expressed in Bryant and the other cases is the effect that the statements may have on the jury. Emphasis has been placed on the proper instruction of the jury, and Tate explained the results in the earlier cases as resting on the failure to instruct the jury properly. Thus, Bryant would seem to rest not on a per se prohibition, of the form of impeachment here, but rather on the desire to avoid the introduction of impeachment material that the jury is likely to misuse.
Here the jury was instructed, both during trial and at *530the close of trial, on the limited use of impeachment. We would note, too, that under current law Cox’ earlier statements, made under oath, would be admissible for substantive use. See Ill. Rev. Stat., 1984 Supp., ch. 38, par. 115—10.1.
Apart from impeachment, however, this information was admissible to contradict Timothy Cox’ allegations of police misconduct, which the defense had offered in support of its theory of coercion. Significantly, Cox acknowledged having a conversation with the defendant; he denied only that the defendant had made the incriminating remarks. Yet the detail of the statements related by Cox, the similarity of those statements to the statements made by the defendant, and the consistency, of those statements with the ballistics evidence that the same gun was used in both robberies, belied his claim that they were not true. Similarly, the assistant State’s Attorney’s account of Cox’ statements the week preceding the trial, and some four months after he testified before the grand jury, served also to contradict his claim of coercion and therefore weakened the defendant’s assertion that he too had been coerced.
Next, the defendant argues that he was denied a fair trial because of the admission of evidence concerning his participation in the armed robbery at the Church’s Chicken restaurant. Before trial the defendant moved to exclude this evidence, and the motion was granted. During the State’s case in chief, however, the prosecutor asked the trial judge to reconsider that ruling, and he did, deciding then to allow the introduction of the evidence.
Evidence of other crimes may be admitted if for some purpose other than to establish the defendant’s propensity to commit crime. (People v. Bartall (1983), 98 Ill. 2d 294.) The defendant asserted at trial that the police had coerced him into making an untrue confession to the *531crimes at Pleasures Unlimited. Evidence regarding the Church’s Chicken robbery was relevant to establish the accuracy of the confession. Moreover, the evidence bore out the validity of Timothy Cox’ original statements implicating the defendant and therefore undermined his claim of coercion.
Sergeant Vincent La Moro and Officer James Gainer testified at trial regarding their analyses of the bullets used at Pleasures Unlimited and Church’s Chicken. This comparison of the two bullets established that they had been fired from the same gun, and the defendant does not dispute that finding. That the crimes occurred only three days apart and in the same neighborhood would tend to discredit any theory that the weapon may have passed out of the control of its first users and into unknown hands. The defendant acknowledged that the particular weapon was used in the murder at the Pleasures Unlimited store. The evidence of the other crime tended to corroborate the defendant’s statements in his confession concerning the two offenses, his role in each, and the weapon. We believe that the evidence of the other crime was properly admitted. For this reason, too, no error occurred in the prosecutor’s statement in closing argument that the defendant “was going to go up and down 79th Street until he got whatever he could and the evidence clearly shows that.” The Church’s Chicken restaurant was located at 1956 West 79th Street, across and a few doors down from the Pleasures Unlimited store.
The defendant next contends that the State improperly argued to the jury that he had been identified by an eyewitness at the Church’s Chicken robbery. During trial the defendant’s hearsay objection was sustained to the testimony of a police officer that the defendant had been identified as one of the robbers by employees of the restaurant. The prosecutor mentioned the objectionable tes*532timony in his rebuttal argument, however, when, during his explanation of why the defendant had confessed, he said, “The police told him he’d been identified and — .”
The trial judge sustained the defendant’s objection to the reference to the identification, denied his motion for a mistrial, and instructed the jury to disregard the prosecutor’s statement. The trial judge’s prompt ruling on defense counsel’s objection and his instruction to the jury to disregard the statement cured whatever prejudice momentarily arose. The motion for a mistrial was correctly denied.
The defendant also argues that he was prejudiced by two remarks at trial suggesting that he had a history of criminal conduct. The first reference came in the testimony of a police officer, who explained that with his request for the listing of the defendant in the police department’s Daily Bulletin, he “submitted what is called an I.R. or identification records number which corresponds to the Defendant’s Criminal History Sheet.” Defense counsel objected, and the prosecutor agreed that his witness had offered too much. The trial judge denied the defendant’s motion for a mistrial. Because defense counsel feared that a special admonition would only emphasize the testimony, he asked that the jurors not be instructed to disregard it. Notably, the trial judge believed that the jurors probably had not noticed the remark or understood its significance. We agree that no prejudice ensued.
The second remark at trial suggesting the defendant’s criminal history came during rebuttal closing argument, when the prosecutor said that the defendant was familiar with the Miranda warnings. Arguing that the defendant gave his formal confession voluntarily, the prosecutor mentioned that the defendant was advised of his Miranda rights a number of times that day and that a copy of the rights was on the wall of the room in *533which the defendant was being held; the prosecutor then said, “Don’t you think he probably had occasion to look at those rights[?] Maybe he didn’t bother because he knew them very well and didn’t have to. He knew his rights.” Defense counsel’s objection was sustained.
This remark was less direct than the earlier reference to the criminal-history sheet; the jurors may have understood it as referring to the number of times that the defendant had been advised of his constitutional rights on the day of his arrest. In any event, the trial judge sustained contemporaneous objections to the statements, and we believe that that was sufficient to correct, or prevent, prejudice. Moreover, as the State points out, defense counsel did not raise the matters later in the post-trial motion, and therefore the defendant waived any further consideration of them (People v. Caballero (1984), 102 Ill. 2d 23, 31).
The defendant next contends that the trial judge’s decision during trial to reverse his earlier ruling and to allow evidence of the other crime — the armed robbery at the Church’s Chicken restaurant — denied him a fair trial. The defendant has already attacked the propriety of this ruling; here, he argues that the ruling was ill-timed, coming after counsel had made a strategic decision incompatible with it.
The defendant traces the problem to defense counsel’s opening statement, which included a statement to the jury that Leon White, the manager of the Church’s Chicken restaurant, would testify that the defendant appeared to have bruises on his face the day after his arrest and interrogation. Counsel also mentioned that White would dispute during trial the State’s photographic evidence of the defendant’s physical condition.
As we have said, the trial judge later decided to allow information about the Church’s Chicken robbery into evidence. During the defendant’s case in chief, defense *534counsel renewed his motion for a mistrial regarding the changed ruling. Defense counsel recited his understanding that if White were called to testify, the State would be allowed to question him concerning his identification of the defendant as one of the Church’s Chicken robbers. Because of that, counsel said that he had determined not to call White as a witness. Yet defense counsel feared that the defense would lose credibility before the jury by not fulfilling the promise, made in the opening statement, to present that evidence. The trial judge denied the motion for a mistrial but directed the prosecution not to mention to the jury defense counsel’s failure to have White testify. The State complied with that order; the missing witness was not mentioned.
The defendant argues that the importance of the promised testimony was so apparent that the jury could not have failed to notice and consider its absence. Thus, the defendant believes that the change in ruling operated to deny him a fair trial. Implicit in the defendant’s argument is the assumption that he was entitled to rely, in shaping his opening statement, on the trial judge’s original decision concerning the other-crime evidence. To be sure, prejudice may result when a decision at trial is made in reliance on an evidentiary ruling and the ruling later is changed. (See, e.g., People v. Cooper (1978), 66 Ill. App. 3d 205 (defendant testified, following trial judge’s definitive ruling barring use of conviction for impeachment, but trial judge later changed his mind and permitted the impeachment; new trial ordered).) For several reasons here, however, we are of the opinion that no error occurred and no prejudice ensued.
First, when the trial judge made his initial ruling, he intimated that it might be reconsidered later on. The judge said that he did not want the Church’s Chicken robbery “brought before the jury” and then said, “Now, if there is some information that I feel is relevant, that *535stems from the Church’s Chicken, then let’s cross that bridge when we get to it and I am sure there is some way that will be satisfactory between the two of you, so no one is hurt.” The trial judge also advised the State, “During opening I want nothing mentioned about Church’s.” Defense counsel was made aware from those remarks that information concerning the other crime might eventually be permitted.
The defendant argues, however, that the purpose of the opening statement is to advise the trier of fact— here, the jury — what the evidence will show. (People v. Warmack (1980), 83 Ill. 2d 112.) Accordingly, error may occur when the prosecution asserts in the opening statement facts or propositions on which no evidence later is presented. (People v. Whitlow (1982), 89 Ill. 2d 322.) By analogy, the defendant argues that error resulted here when the change in ruling made it inadvisable to present the promised testimony. The analogy is imperfect, however. Cases involving prosecutorial misconduct assume that the jury failed to notice the absence of evidence on a particular point that was asserted in the opening statement; here, the defendant makes the opposite assumption. Given the length of the .trial and the variety of prosecution and defense witnesses, we do not believe that any prejudice ensued from the failure by the defense to present the promised testimony. We note, too, that the defendant presented Darlene Harland’s testimony on his physical condition the day after his arrest. Thus, the jury heard the substance of what the opening statement promised, and the other witness’ absence may have gone unnoticed. For the reasons mentioned, we do not believe that the change in ruling denied the defendant a fair trial.
The defendant also argues that his arrest was not shown to have been made with probable cause. The impetus for this argument is the discrepancy or inconsis*536tency between Officer Dwyer’s explanation at the suppression hearing and the one he gave at trial regarding his reasons for placing a stop order on the defendant. The stop order was published in the police department’s Daily Bulletin on January 21, 1980. At the suppression hearing, Dwyer said that the basis for the stop order was Timothy Cox’ grand jury testimony implicating the defendant. Later, however, Dwyer gave a different explanation. At trial he testified that he had based the stop order on the ballistics evidence showing that the bullets fired at Pleasures Unlimited and the Church's Chicken restaurant had been fired from the same weapon, and on restaurant employees’ identification of the defendant as one of the robbers. Defense counsel’s objection to the statement regarding identification was sustained. Defense counsel impeached Dwyer with his testimony at the suppression hearing. Later, Dwyer acknowledged that Cox had testified before the grand jury on February 8, 1980, after the stop order had appeared in the Daily Bulletin.
The defendant now argues that there was no showing that the stop order was based on probable cause; the defendant contends that the only competent evidence that Dwyer was shown to have relied on, the findings of the ballistics examiners, could not by itself establish identity and therefore was insufficient.
We agree with the State that the defendant has waived consideration of this issue. At no time in the trial court did he challenge the basis for the stop order that appeared in the Daily Bulletin. In advance of trial, the defendant did not question the stop order in the bulletin. This is made clear from the events and arguments at the suppression hearing. Before trial, the defendant filed a motion to suppress his statements, alleging that they were products of physical coercion and that they were taken in violation of his Miranda rights. During the sup*537pression hearing, the defendant was permitted to file a motion to quash his arrest. In requesting leave to file the motion, defense counsel explained that it was in response to the testimony of Officer McKeon. McKeon had testified that he arrested the defendant soon after he was flagged down by another officer, Duffing, who described the defendant — black, male, five feet eight inches tall, 165-70 pounds — and said that he was nearby. Thus, the key paragraph in the defendant’s second suppression motion said:
“4. The police did not have probable cause to arrest petitioner. The mere facts that: 1) the police knew a warrant was outstanding for the arrest of Derrick King; and 2) the police arrest in virtually an all black community the first man in the community meeting the general physical description of five feet, eight inches tall, 160 to 170 pounds, male, and black do not constitute probable cause.”
As it developed, Lieutenant Duffing testified at the suppression hearing and said that he had arrested the defendant. Duffing knew who the defendant was, and he said that he based his arrest on the information contained in the Daily Bulletin.
In arguing the probable-cause issue at the suppression hearing, defense counsel was required to consider the inconsistent claims of who had arrested the defendant. Under the theory that McKeon had made the arrest, defense counsel argued that that officer had only a general description of the defendant and lacked sufficient facts to justify an arrest. Under the theory that Duffing had made the arrest, defense counsel said, “Obviously if he knows the man and if in fact he had a bulletin in his possession, then that would constitute probable cause. *** The arrest, if it was by McKeon, was insufficient. That is probably why Duffing took the stand because the prosecution knew that that arrest was insufficient.” The *538defendant argued that McKeon rather than Duffing should be believed. Thus, defense counsel did not question whether the stop order in the bulletin would be a sufficient basis for the arrest. Defense counsel believed that McKeon arrested the defendant, that the existence of probable cause depended entirely on the reasons stated by McKeon for making the arrest, and that those reasons were insufficient.
The trial judge found that Duffing made the arrest and had done so on the basis of the published stop order, which supplied the necessary probable cause.
At trial, then, when the explanation for the stop order was changed, the defendant did not move for reconsideration of his motion to quash the arrest. Moreover, the defendant objected on other grounds to part of the new explanation for the stop order. We conclude that the issue has been waived.
The defendant makes the related argument that he should have been permitted to present to the jury the conflict concerning which officer had actually arrested him. The State did not call either McKeon or Duffing as a witness, and during the defendant’s case in chief moved to preclude the defendant from presenting their testimony; the motion was granted, for the trial judge believed that the contradiction would not be relevant. The court noted that the defense was premised on the validity of the confession; the two officers’ roles in the case ended soon after the defendant was arrested, and they did not take part in the interrogation of the defendant. Thus, the trial judge did not believe that the conflict in their testimony was relevant.
We agree. Proof of that inconsistency would not have advanced the defense presented in this case; instead, it would have focused the jury’s attention on collateral matters. The trial judge did not abuse his discretion in barring this testimony.
*539The defendant argues next that the trial court erred in permitting a high school classmate of the victim to testify briefly about the victim. The witness, Kenneth Wilson, explained that he and the victim had played together on their school’s chess and football teams. The defendant argues that because the victim’s character went unchallenged, testimony regarding his favorable background was irrelevant and prejudicial. The State’s purpose for the testimony was to isolate the victim from the suggestions contained in the defendant’s confession that drug dealing occurred in the Pleasures Unlimited store, where the victim was employed.
Contrary to the defendant’s argument here, we believe that defense counsel acquiesced in the presentation of this testimony. After the witness identified himself and said that he and the victim had attended the same high school, the defendant objected to the evidence as irrelevant. Initially the trial judge sustained the objection. The following colloquy took place:
“THE COURT: Let’s do it this way. I don’t think at this point it is relevant because his character is not in issue. And I’m going to assume that you fellows [i.e., defense counsel] be of your word and say your position is he wasn’t there. But now if you bring in in any manner directly, indirectly or by innuendo that there was dope being dealt here—
[PROSECUTOR]: Judge, it comes in in our case. That’s one of the reasons he came in there and killed him. That’s the evidence that the jury is going to hear. All we’re trying to do, at least let us go this far and say he played football with him, he knows him from school and leave it like that.
[DEFENSE COUNSEL]: Fine. Your Honor, we’ve maintained our posture. Whatever ruling the court makes, we can roll either way This could help us.
THE COURT: All right, let him testify.”
It appears, then, that defense counsel would have agreed *540with whatever ruling the court made. Moreover, assuming that the evidence was admitted over objection and that it was error, we conclude that no prejudice could have resulted from its admission.
II
The defendant also raises a number of arguments concerning his sentencing hearing and the death penalty. The sentencing hearing was held before the trial judge alone, the defendant having waived his right to a jury. The parties stipulated that the various witnesses would give the same testimony, if called to testify, as they had at trial. The defendant’s birth certificate was admitted into evidence, and it showed that he was over the age of 18 when he committed the offenses here. The trial judge found the existence of a statutory aggravating circumstance — that the defendant killed the victim, intentionally, during the course of an armed robbery (Ill. Rev. Stat. 1979, ch. 38, par. 9—1(b)(6)). Next, the trial judge heard evidence in aggravation and mitigation; this comprised evidence of the defendant’s prior criminal conduct and testimony by his mother and an aunt. The trial judge sentenced the defendant to death, finding that no mitigating circumstances were sufficient to preclude imposition of that penalty.
The defendant first argues, in opposition to the sentence of death, that there was no evidence that the killing was intentional. In making this argument the defendant relies on his confession, in which he disclaimed any intent to shoot the victim and explained that the gun had discharged accidentally. The defendant argues that his version of events must be accepted as true, for it supplied the only account of what occurred in the store, and it was not inherently improbable or contradicted by other facts or circumstances in evidence. See People v. Jordan (1954), 4 Ill. 2d 155.
*541The defendant’s version of how the victim happened to be shot did not go uncontradicted. At trial, several persons testified to the position of the victim’s body immediately following the shooting. These witnesses — two women who were working in the store next door, and the first police officer to arrive on the scene — found the victim on his knees, with the upper part of his body slumped over; although an ambulance was called, it is not apparent from the testimony whether the victim was still alive at that point. This testimony tends to support the State’s theory that the defendant positioned the victim on his knees and then fired the gun, in the manner of an execution.
This theory is not undermined, as the defendant believes, by the testimony of the pathologist, Dr. Tae An, who performed the autopsy. Dr. An testified that he found no sign of stippling around the bullet hole at the back of the victim’s head. Dr. An explained that “stippling” is the deposit of gun powder left around a wound when a gun is fired at close range, within 20 inches of the body; according to Dr. An, the absence of stippling usually means that the gun was fired at a distance, though he said that powder from a firing at close range could be filtered out by hair or brushed off the body.
The defendant argues that the State’s theory of how the murder occurred is inconsistent with Dr. An’s testimony regarding the absence of stippling. But that testimony pertained to the range at which the gun was fired, rather than the intent with which it was fired. Moreover, the defendant’s own explanation is inconsistent with that, for he said that the accidental discharge of the gun was near the victim’s head.
The State observes too that the defendant admitted that he fired the gun and said that he did so once. This seems also to be inconsistent with the defendant’s statement that the gun went off accidentally.
*542The statutory aggravating circumstance relied on here as the basis on which the death penalty could be imposed is a narrow form of the felony-murder rule. (Ill. Rev. Stat. 1979, ch. 38, par. 9—1(b)(6).) It permits imposition of the death penalty if, during the course of one of several specified felonies, the victim is killed by the defendant or receives fatal injuries inflicted by the defendant or inflicted contemporaneously by an accomplice. Two alternative mental states are provided: that “the defendant killed the murdered individual intentionally or with the knowledge that the acts which caused the death created a strong probability of death or great bodily harm.” (Ill. Rev. Stat. 1979, ch. 38, par. 9— 1(b)(6)(b).) Accordingly, death sentences have been upheld in the absence of a finding of intent but when the evidence has been sufficient to support a finding of the alternative mental state, knowledge. (People v. Owens (1984), 102 Ill. 2d 88, 108 (victim died of cardiac arrest as a result of beatings administered by the defendant; evidence was sufficient to sustain finding that the defendant acted knowingly); see People v. Eddmonds (1984), 101 Ill. 2d 44, 62 (evidence that defendant pushed the face of a nine-year-old into pillow, causing him to smother, was sufficient to show that defendant acted intentionally or knowingly).) Here, a requisite mental state was established by the defendant’s own account — that he was pushing the victim while holding a loaded gun to his head. We believe that would be sufficient proof, under the circumstances here, that the defendant acted knowingly.
The defendant next argues that prejudice resulted in the sentencing hearing from the testimony of the victim’s high school classmate, Kenneth Wilson. This testimony was brought into the sentencing hearing by the parties’ general stipulation, made at the outset of the hearing, regarding the testimony of the witnesses pre*543sented at trial. The defendant argues here, as he did earlier in opposing his convictions, that the evidence was irrelevant and prejudicial.
The evidence was offered to dispel the implication that the victim took part in the alleged drug sales at the store, and, as we have said, defense counsel acquiesced in the presentation of the testimony. Moreover, any error caused by this was harmless. No specific reference was made to the information in the sentencing hearing. We see no reason here to believe that the information played a part in the trial judge’s decisions that the death penalty could be imposed and that it should be imposed.
Next, the defendant challenges the waiver that he made before trial of the right to a jury at the capital sentencing hearing. The defendant argues that under the Illinois death penalty statute the waiver was premature and could not be made when it was and, alternatively, that the waiver was not knowingly and intelligently made, regardless of its timing.
Before the selection of a jury began, the defendant asked the court to accept his waiver of the right to a determination of his sentence by a jury, upon his conviction and the State’s request for a capital sentencing hearing. Before accepting the waiver, the trial judge explained to the defendant the sequence of trial and sentencing in a capital case, his right to a jury at sentencing if the death penalty was sought, and the two-stage hearing that would occur then. The defendant said that he understood the process and that he realized that he was not waiving his right to a jury at trial. The defendant’s apparent reason for making the waiver when he did was to prevent the questioning of the prospective jurors who would determine his guilt or innocence about their attitudes toward capital punishment; the trial judge informed the parties that no questions on that subject would be asked during voir dire. The trial judge also told the defendant *544that the waiver could not be withdrawn after jury selection began. The defendant then presented a signed jury-waiver form to the court, and it was accepted.
The defendant first argues that his waiver was premature. He relies on section 9—1(d) of the Criminal Code of 1961 (Ill. Rev. Stat. 1979, ch. 38, par. 9—1(d)), which provides:
“Separate sentencing hearing. Where requested by. the State, the court shall conduct a separate sentencing proceeding to determine the existence of factors set forth in Subsection (b) and to consider any aggravating or mitigating factors as directed in Subsection (c). The proceeding shall be conducted:
1. before the jury that determined the defendant’s guilt; or
2. before a jury impanelled for the purpose of the proceeding if:
A. the defendant was convicted upon a plea of guilty; or
B. the defendant was convicted after a trial before the court sitting without a jury; or
C. the court for good cause shown discharges the jury that determined the defendant’s guilt; or
3. before the court alone if the defendant waives a jury for the separate proceeding.”
The defendant argues that, under that statute, his right to a jury’s determination of his sentence could not arise until the State requested a capital sentencing hearing; that request, in turn, could not be made until the defendant was convicted. The defendant concludes that his pretrial waiver of a jury for sentencing was premature, for at that time he simply did not have that right to waive. The defendant notes that the appellate court, by similar reasoning, has held that a trial judge does not err in refusing to accept, in advance of trial, a defendant’s waiver of the right to a jury at a capital sentencing hearing. (People v. Wolfbrandt (1984), 127 Ill. App. 3d 836.) *545In that case the defendant, charged with murder, chose to be tried by a jury, and the prospective jurors were examined on their attitudes toward capital punishment; apparently either the prosecutor later decided not to seek the death penalty or the sentencing authority did not impose it.
The defendant’s interpretation of the statute does not convince us that he is entitled to another sentencing hearing. We note that at no time in the circuit court did the defendant express any dissatisfaction with the early waiver or regret over that decision. Moreover, the waiver pertained only to the choice of a sentencing authority; it did not implicate the integrity of the sentencing decision or the manner by which it was reached. If error occurred, then, it was not the type about which the defendant, having invited, may now complain. (Cf. People v. Baynes (1981), 88 Ill. 2d 225 (reversible error occurred in use of polygraph evidence at trial, even though evidence was admitted by parties’ stipulation); People v. Youngbey (1980), 82 Ill. 2d 556 (new sentencing hearing required when trial judge imposed sentences without benefit of presentence investigation reports, even though reports were waived by defendants).) The procedure followed here was, at worst, untimely. The statutory deviations in the cases cited by the defendant are more fundamental, altering the basic scope and nature of those jurisdictions’ capital sentencing schemes. Cf. State v. Patterson (1982), 278 S.C. 319, 295 S.E.2d 264 (cause remanded for new trial where trial court permitted defendant to plead guilty on condition that he be sentenced by a jury; plea agreement violated statutory provision that a defendant who pleads guilty can be sentenced only by the court); State v. Finnell (1984), 101 N.M. 732, 688 P.2d 769 (by parties’ stipulation, death qualification of jury delayed until sentencing, with result that composition of sentencing jury was not identical to *546that of trial jury, in violation of statutory requirement that sentencing be conducted before original jury; cause remanded for resentencing).
The defendant also argues that his waiver of a jury for the sentencing hearing was not knowing and intelligent, for he was not advised in open court of the requirement that a jury’s decision imposing the death penalty be unanimous.
This court previously has declined to adopt a rule that would require an admonition regarding the unanimity requirement; waiver of a jury for sentencing has been upheld although that advice did not appear in the record. (People v. Madej (1985), 106 Ill. 2d 201, 220-21; People v. Albanese (1984), 104 Ill. 2d 504, 535-36.) We conclude here that defendant’s waiver was knowing and intelligent.
The defendant also argues that death is an inappropriate sentence here. We disagree. The trial judge carefully considered the evidence before him, and we cannot say that he abused his discretion in sentencing the defendant to death.
Finally, the defendant raises a number of constitutional challenges to the Illinois death penalty statute, premised mainly on the eighth amendment and the due process clause of the fourteenth amendment of the United States Constitution (U.S. Const., amends. VIII, XIV). For the most part, the same arguments previously have been considered and rejected by this court. The statute is not unconstitutional for failing to require the State to prove beyond a reasonable doubt the absence or nonexistence of mitigating circumstances sufficient to preclude imposition of the death penalty (People v. Eddmonds (1984), 101 Ill. 2d 44, 68; People v. Garcia (1983), 97 Ill. 2d 58, 80-82; People v. Free (1983), 94 Ill. 2d 378, 421; People v. Brownell (1980), 79 Ill. 2d 508, 531-34), nor does it place on the defendant, in violation of those *547constitutional guarantees, the risk of nonpersuasion on that matter (People v. Caballero (1984), 102 Ill. 2d 23, 49; see People v. Kubat (1983), 94 Ill. 2d 437, 504-05; People v. Brownell (1980), 79 Ill. 2d 508, 531-34). The discretion granted by the statute to the prosecutor in deciding whether to seek the death penalty in a particular case is not unconstitutional, nor does it violate the separation-of-powers provision of the Illinois Constitution (Ill. Const. 1970, art. II, sec. 1). (People v. Lewis (1981), 88 Ill. 2d 129, 146; People ex rel. Carey v. Cousins (1979), 77 Ill. 2d 531, 535-43.) The defendant also argues that the statute violates a variety of constitutional provisions by failing to require, and by actually precluding, notice to an accused in advance of trial of the State’s intention to seek the death penalty; specifically, the defendant argues that that violates both State and Federal rights to notice and due process (U.S. Const., amends. VI, XIV; Ill. Const. 1970, art. I, secs. 2, 8). We note that the defendant apparently had notice here of the State’s intention; as we have already discussed, the defendant waived, in advance of trial, the determination of his sentence by a jury. Thus, the defendant cannot complain now that he did not have actual notice. Apart from those considerations, however, this court previously has held that the lack of notice does not operate to deprive an accused of the effective assistance of counsel (People v. Gaines (1981), 88 Ill. 2d 342, 369; see People v. Silagy (1984), 101 Ill. 2d 147, 161-62), and we decline to reconsider the question here.
Next, the defendant argues that one of the mitigating circumstances set out in the statute, “no significant history of prior criminal activity” (Ill. Rev. Stat. 1979, ch. 38, par. 9—1(c)(1)), is standardless and vague. The defendant acknowledges that its constitutionality was upheld in People v. Lewis (1981), 88 Ill. 2d 129, 144-46, but asks that that decision be reconsidered. Moreover, *548the defendant makes the related argument that the opposite of that, a significant history of prior criminal activity, was used here as a nonstatutory aggravating circumstance and is similarly vague and standardless.
In support of these contentions the defendant relies on Arnold v. State (1976), 236 Ga. 534, 224 S.E.2d 386. In Arnold the sole statutory aggravating circumstance found by the sentencing jury as a basis for imposing the death penalty was the defendant’s “substantial history of serious assaultive criminal convictions.” The defendant there had two earlier convictions — assault with intent to murder, and armed robbery — and he argued that both “substantial history” and “serious assaultive criminal convictions” were vague. The Georgia Supreme Court held that the determination required by the adjective “substantial” was “highly subjective” and therefore unconstitutional (Arnold v. State (1976), 236 Ga. 534, 541, 224 S.E.2d 386, 392); the court did not consider the defendant’s additional argument that the latter phrase, “serious assaultive criminal convictions,” suffered from the same deficiency. Arnold was cited in Gregg v. Georgia (1976), 428 U.S. 153, 202, 49 L. Ed. 2d 859, 891, 96 S. Ct. 2909, 2939 (opinion of Stewart, J., joined by Powell and Stevens, JJ.), where the United States Supreme Court noted with approval the Georgia court’s evident concern “that the new sentencing procedures provide guidance to juries.”
The use of a mitigating circumstance similar to the one at issue here was approved by the Supreme Court in Proffitt v. Florida (1976), 428 U.S. 242, 257, 49 L. Ed. 2d 913, 925-26, 96 S. Ct. 2960, 2969; there the court rejected the argument that a mitigating circumstance in Florida’s death penalty statute, “The defendant has no significant history of prior criminal activity” (428 U.S. 242, 248-49 n.6, 49 L. Ed. 2d 913, 921 n.6, 96 S. Ct. 2960, 2965 n.6), was imprecise and could not be deter*549mined by a judge or jury.
It should be noted that, in Illinois, the defendant’s criminal record is not a statutory aggravating circumstance and therefore, under the Illinois statute, could not supply a basis for determining, in the first phase of the sentencing hearing, that the penalty of death may be imposed. The distinct function served by the statutory aggravating circumstances was explained in People v. Lewis (1981), 88 Ill. 2d 129, 145, where the court said:
“Aggravating factors serve as necessary prerequisites without which the death sentence cannot be imposed; they delineate the borderline between those cases in which death is a possible punishment and those in which it cannot be considered; because of their manifest importance, their scope must be somewhat more precisely marked than the suggestions of mitigating factors which the jury may weigh in cases where the death sentence is a possibility.”
Once the sentencing authority determines that death is a possible punishment, the Illinois death penalty statute permits, as it must, the sentencing authority to consider relevant mitigating circumstances, both statutory and nonstatutory, in determining whether the death sentence should be imposed (Ill. Rev. Stat. 1979, ch. 38, pars. 9—1(c), (g), (h); see Jurek v. Texas (1976), 428 U.S. 262, 271, 49 L. Ed. 2d 929, 938, 96 S. Ct. 2950, 2956 (opinion of Stevens, J., joined by Stewart and Powell, JJ.)). Relevant aggravating circumstances, both statutory and non-statutory, may also be considered in making this second determination. Ill. Rev. Stat. 1979, ch. 38, pars. 9—1(c), (g), (h).
That a defendant has or does not have a significant history of prior criminal activity is a relevant circumstance for a judge or jury to consider in making the second sentencing determination, whether the death penalty should be imposed. We do not believe that the statutory *550formulation of the mitigating circumstance, “The defendant has no significant history of prior criminal activity” (Ill. Rev. Stat. 1979, ch. 38, par. 9—1(c)(1)), or the opposite formulation suggested for a nonstatutory aggravating circumstance, “The defendant has a significant history of prior criminal activity,” is imprecise.
The defendant raises two objections pertaining to the scope and adequacy of our review of decisions imposing the death penalty. First, the defendant argues that the sentencing authority should be required to express its findings regarding mitigating circumstances set out in the death penalty statute (see Ill. Rev. Stat. 1979, ch. 38, par. 9—1(c)). The defendant asserts that specific findings on those matters would enhance the review of those cases in which the death penalty is imposed. To illustrate the possible importance of an express finding, the defendant points out that, in the second phase of the sentencing hearing held Here, both the State and defense counsel urged the trial judge to consider the defendant’s criminal record; the State argued that the record was significant, and defense counsel argued that it was insignificant. The trial judge did not expressly resolve the conflict; he found merely that there were no mitigating circumstances sufficient to preclude a sentence of death.
Although the requirement of an explanation or designation by the sentencing authority of certain reasons necessary for imposition of the death penalty has been noted with approval in decisions upholding the validity of death penalty statutes (see, e.g., Gregg v. Georgia (1976), 428 U.S. 153, 195, 206-07, 49 L. Ed. 2d 859, 886-87, 893, 96 S. Ct. 2909, 2935, 2940-41 (opinion of Stewart, J., joined by Powell and Stevens, JJ.); Proffitt v. Florida (1976), 428 U.S. 242, 251, 259-60, 49 L. Ed. 2d 913, 922, 927, 96 S. Ct. 2960, 2966, 2970 (opinion of Stewart, J., joined by Powell and Stevens, JJ.)), this court consistently has held that a statement of findings is not consti*551tutionally required in the second part of a sentencing hearing (People v. Stewart (1984), 104 Ill. 2d 463, 497; People v. Kubat (1983), 94 Ill. 2d 437, 504; People v. Gaines (1981), 88 Ill. 2d 342, 383; People v. Brownell (1980), 79 Ill. 2d 508, 541-44). Meaningful review can, and does, occur in its absence, and the trial judge’s failure here to say whether he found the defendant’s criminal record to be significant or insignificant is no impediment to that process.
Finally, the defendant argues that the Illinois death penalty statute lacks adequate provisions for the comparative review of death sentences. Specifically, the defendant points to the absence of an express procedure for this court’s consideration of those murder convictions in which death is not the sentence imposed; without information on those cases, the defendant argues, affirmance of his sentence here would violate the eighth amendment of the Federal Constitution (U.S. Const., amend. VIII). Comparative proportionality review is not required by the Federal Constitution, however (Pulley v. Harris (1984), 465 U.S. 37, 79 L. Ed. 2d 29, 104 S. Ct. 871), and this court has consistently held that the absence of the suggested procedure does not render the statute invalid (People v. Stewart (1984), 104 Ill. 2d 463, 499; People v. Kubat (1983), 94 Ill. 2d 437, 502-04; People v. Brownell (1980), 79 Ill. 2d 508, 541-44). The defendant has given us no reason here to reconsider those holdings, and we decline to do so.
Ill
The clerk of this court is directed to enter an order fixing Tuesday, May 13, 1986, as the date on which the sentence of death entered in the circuit court is to be carried out. The defendant shall be executed by lethal injection in the manner provided by section 119 — 5 of the Code of Criminal Procedure of 1963 (Ill. Rev. Stat. 1983, *552ch. 38, par. 119—5). A certified copy of the mandate in this case shall be furnished by the clerk of this court to the Director of Corrections, to the warden of the State-ville Correctional Center, and to the warden of the correctional center where the defendant currently is confined.
Judgment affirmed.