delivered the opinion of the court:
Following a jury trial in the circuit court of Cook County, the defendant, Andrew Maxwell, was convicted of murder and attempted armed robbery. The defendant waived his right to a jury for purposes of a capital sentencing hearing, and the trial judge sentenced the defendant to death for the murder conviction. The judge imposed a 15-year prison term for the attempted armed robbery conviction. The defendant’s death sentence has been stayed pending direct review by this court. (See Ill. Const. 1970, art. VI, §4(b); 134 Ill. 2d Rules 603, 609(a).) *121For the reasons explained below, we affirm the judgment of the circuit court.
The offenses involved here occurred in Chicago on October 26, 1986. Harold Anderson testified at trial that sometime after 9 o’clock that evening he and Adrian Bracy were walking in the 8300 block of South Indiana Street when they were approached by three men, whom Anderson identified as the defendant, Jerry Thompson, and Gregory Howard. According to Anderson, the defendant pointed a gun at Bracy and announced a stickup. In response, Bracy threw a beer bottle he was carrying at the defendant. As Anderson retreated, he saw the defendant shoot Bracy. Anderson ran behind a house, and he later heard a second shot fired. Anderson returned to the scene of the shooting several moments later and found Bracy lying on the ground. A nearby resident testified that he heard two gunshots around 9:30 p.m. The witness looked out his window and saw two figures, followed by a third, running across his yard. He did not see the individuals’ faces. Police who were summoned to the neighborhood found Bracy’s wallet several feet from his body; the wallet contained identification but no money. An autopsy later established that Bracy died as a result of multiple gunshot wounds.
Over a defense objection, the State presented evidence of a series of three offenses committed by the defendant, Jerry Thompson, and Gregory Howard in Chicago during the evening of November 3, 1986. Terrance L. Wilson, who lived in the 10400 block of South Troy in Chicago, returned to his home around 8:50 that evening. Wilson testified that three men entered the garage as he parked his car. One of the men drew a gun and demanded Wilson’s car keys. Another man searched Wilson’s pockets and removed $90. The three men, whom Wilson identified as the defendant, Jerry Thomp*122son, and Gregory Howard, then got in the car and drove off.
Jose Flores, who lived in the 10600 block of Avenue B, left work at 10:45 p.m. on November 3, 1986. Flores testified that he was cut off by a black Monte Carlo containing three men while he was driving home. When Flores parked his car, he noticed the same Monte Carlo nearby. As Flores got out of his car, he was approached by three men, whom he identified as the defendant, Jerry Thompson, and Gregory Howard. The defendant pointed a gun at Flores and threatened to shoot him. Flores ran inside his house.
Dmitar Marich, who lived in the 10900 block of Avenue A in Chicago, returned home from work around 11 p.m. on November 3, 1986. Marich testified that he parked his car in the garage and got out of the vehicle. A man, whom Marich identified as the defendant, then put a gun to Marich’s head and took $20 from his shirt pocket. Two other men, whom Marich was not able to identify, were standing nearby. The three then ran off.
Patrolling officers spotted Wilson’s black Monte Carlo around 11:30 the evening of November 3. After a chase, the car crashed into a garage and three men jumped out. The officers captured one of the car's occupants, Jerry Thompson, but the other two escaped. Another officer on patrol saw the defendant several hours later. The officer pursued the defendant on foot and eventually apprehended him; the defendant’s .22-caliber revolver was subsequently found in a backyard along that same course. Bullet fragments removed from Bracy during the autopsy were shown to be consistent with test firings from the handgun abandoned by the defendant during the chase. Other evidence established that the defendant had stolen the gun during a burglary committed in September 1985, more than a year before the offenses charged here. Fingerprints positively identified as the *123defendant’s and Jerry Thompson’s had been found at the scene of the 1985 burglary.
Following his arrest for the string of offenses committed November 3, the defendant became a suspect in the murder and attempted armed robbery of Adrian Bracy. In a lineup conducted November 12, Harold Anderson identified the defendant and the two other offenders. That same day, the defendant gave law enforcement officers oral and signed statements admitting his involvement in the present offenses, and these confessions were introduced into evidence at trial. In his initial statement, the defendant admitted his participation in the crimes but denied that he was the one who had fired the gun. Later, when told, correctly, that he had been identified as the gunman, the defendant admitted to police officers that he had shot Bracy.
In his statements, the defendant said that he, Jerry Thompson, and Gregory Howard were driving around during the evening of October 26 looking for someone to rob; the defendant said that he was armed with a .22-cal-iber revolver. When they saw two people walking in the vicinity of 83rd and Wabash, they parked their car nearby and approached the intended victims on foot. The defendant announced the stickup to the victims. Bracy started swinging a bottle, and the second man backed away and ran off. Bracy threw the bottle at the defendant, missing him. According to the defendant, Bracy then reached into his pocket, as if to retrieve something. The defendant fired a total of three shots at Bracy. After the third shot was fired, Bracy stumbled and fell to the ground. Thompson and Howard searched Bracy’s pockets, but they did not find any money. The defendant, Thompson, and Howard then fled from the scene.
The defendant did not testify at trial. The only witness called, by the defense was Sady Holmes, who provided evidence of an alibi. Holmes, who was the mother *124of the defendant’s girlfriend, testified that during the evening of October 26, 1986, the defendant was at her home watching television with her daughter between 9 and 10 o’clock, the time of the offenses charged here.
Following the close of evidence, the jury found the defendant guilty of murder and attempted armed robbery. The matter then proceeded to a capital sentencing hearing. At the first stage of the bifurcated proceeding, the parties stipulated that the defendant was 19 years old in October 1986 and therefore had attained a death-eligible age at the time of his commission of the present offenses (see Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(b)). At the conclusion of the first stage of the hearing, the trial judge found the defendant eligible for the death penalty on the single ground urged by the State, commission of murder in the course of a specified felony, attempted armed robbery (111. Rev. Stat. 1985, ch. 38, par. 9— 1(b)(6)).
During the second stage of the sentencing hearing, the State presented further evidence of the defendant’s criminal history, in addition to the information that had already been introduced at trial. Mote Whiting, 69 years old, testified that he was accosted by the defendant and Jerry Thompson on January 1, 1984. The defendant struck Whiting on the head, knocking him to the ground. The defendant and Thompson then took Whiting’s wallet and fled. The defendant was convicted of robbery for that offense. ,
Stanley Brookins testified that early in the morning on November 1, 1986, he walked past the defendant and another man at the entrance to an alley. The defendant displayed a handgun and threatened to shoot Brookins; Brookins dared the defendant to fire the gun. Brookins then heard several shots but walked on. Sometime later, Brookins noticed that he was bleeding and discovered then that he had been struck by the defendant’s shots. *125Brookins was required to undergo two separate periods of hospitalization for treatment of the injuries he sustained as a result of the shooting.
At the sentencing hearing, the defendant presented mitigating testimony from eight witnesses. The defendant’s mother, Shirley Maxwell, testified that the defendant attended school regularly, though he did not graduate from high school. Mrs. Maxwell also stated that the defendant had been shot on two occasions because he refused to join a street gang. The defendant’s two sisters, Martha Brown and Monalisa Maxwell, described their brother as helpful and courteous. Martha stated that the defendant would often escort her to and from the housing project in which she lived. Monalisa stated that the defendant would baby-sit with her child and would repair broken things around the house.
The defendant’s girlfriend, Mary Holmes, testified that the defendant helped support their eight-month-old daughter. Mary also stated that the defendant would help people with their groceries and perform other errands. The defendant’s cousin, Michael Jones, who had lived with the Maxwell family in 1985, testified that the defendant helped him with his homework and taught him about cars during that period. Favorable testimony in mitigation was also provided by Ramona McIntosh, Judy Frazier, and Beatrice Griffin, who were neighbors and friends of the defendant’s family. These three witnesses stated that the defendant would often assist them with errands.
At the conclusion of the hearing, the trial judge sentenced the defendant to death for the murder of Adrian Bracy. The judge also sentenced the defendant to a 15-year prison term on his conviction for attempted armed robbery. Before this court, the defendant makes a number of challenges to the proceedings below, and we shall consider these arguments in turn.
*126I
A
The defendant raises three arguments with respect to the guilt-innocence phase of the proceedings. The defendant first contends that the trial judge erred in denying his motion to suppress the confessions he made to authorities on November 12, 1986. The defendant argues that the statements were taken in violation of the principles expressed in Edwards v. Arizona (1981), 451 U.S. 477, 68 L. Ed. 2d 378, 101 S. Ct. 1880, and Arizona v. Roberson (1988), 486 U.S. 675, 100 L. Ed. 2d 704, 108 S. Ct. 2093, which may bar police-initiated interrogation once an accused has asserted his right to counsel. The defendant maintains that he invoked his right to counsel on November 5, 1986, when, at a preliminary hearing on unrelated charges, he accepted the appointment of the public defender to represent him in those prosecutions. As we explain below, the Supreme Court recently rejected the same theory in McNeil v. Wisconsin (1991), 501 U.S. 171, 115 L. Ed. 2d 158, 111 S. Ct. 2204, decided after this case was argued orally, and we find McNeil to be controlling.
Prior to trial, the defendant moved to quash his arrest and suppress his statements, raising -several separate grounds in support of the motion. Before this court, however, the defendant renews only one contention, the McNeil issue, and we shall therefore limit our discussion accordingly. The relevant evidence presented at the defendant’s suppression hearing may be stated briefly. The defendant .was taken into custody on November 4, 1986, when he was arrested in connection with the series of offenses committed the previous evening. A preliminary hearing on those charges was conducted on November 5, 1986. During the hearing, the judge appointed the *127public defender to represent the defendant in those cases. The matter was continued, and the defendant was then remitted to the custody of the Cook County jail. A week later, on November 12, the defendant was transported from the county jail to Area Two police headquarters. There, the defendant was placed in a lineup and was questioned in connection with the present offenses. In several sessions of questioning, the defendant waived his rights under Miranda v. Arizona (1966), 384 U.S. 436, 16 L. Ed. 2d 694, 86 S. Ct. 1602, and gave law enforcement authorities statements confessing his involvement in the offenses. The public defender who had previously been appointed to represent the defendant on the unrelated charges was not present during these interrogations and apparently was not notified that they were occurring.
At the conclusion of the suppression hearing, the defendant argued that he invoked his right to counsel under Miranda with respect to the present offenses by accepting the appointment of the public defender to represent him in the unrelated prosecution. The defendant thus believed that the later interrogations were infirm. The trial judge rejected the defendant’s theory. The court ruled that the appointment of counsel to represent the defendant on the unrelated charges could not also operate as an invocation of his separate right to counsel under Miranda with respect to questioning on the present offenses. In so ruling, the trial judge expressly declined to follow the contrary decision of the court of appeals in United States ex rel. Espinoza v. Fairman (7th Cir. 1987), 813 F.2d 117. Before this court, the defendant renews his argument that his acceptance of appointed counsel at the November 5 preliminary hearing constituted an assertion of his right to counsel for purposes of the present crimes and therefore precluded *128law enforcement officers from interrogating him on the offenses charged here.
In McNeil v. Wisconsin (1991), 501 U.S. 171, 115 L. Ed. 2d 158, 111 S. Ct. 2204, the Supreme Court held that a defendant’s acceptance of the appointment of counsel to represent him in connection with one offense did not operate as an invocation of the defendant’s separaté right to counsel under Miranda with respect to questioning on other, unrelated offenses. The defendant in that case was taken into custody and charged with an armed robbery occurring in West Allis, Wisconsin. A public defender represented the defendant at his initial appearance on that charge. While that charge was pending, the defendant was questioned by officers with respect to a murder, attempted murder, and armed burglary committed in Caledonia, Wisconsin. The defendant later waived his Miranda rights and made statements confessing his involvement in the Caledonia offenses. The defendant was subsequently charged with and convicted of the Caledonia charges; his statements were introduced into evidence at trial.
Before the Supreme Court, the defendant contended that his confessions to the Caledonia offenses should have been suppressed, arguing that his prior acceptance of counsel to represent him on the West Allis charge operated as well as an assertion of his right to counsel with respect to Miranda. The Court rejected this argument, distinguishing between the two separate rights to counsel being asserted by the defendant. The Court explained that the sixth amendment right to counsel is “offense specific,” and is applicable only to the charge or charges with respect to which counsel has appeared on behalf of the accused. Thus, a defendant’s invocation of his sixth amendment right to counsel will bar further police-initiated interrogation with respect to the charged offense (Michigan v. Jackson (1986), 475 U.S. 625, 89 L. *129Ed. 2d 631, 106 S. Ct. 1404) but will not bar police-initiated questioning with respect to other, unrelated offenses. The Court noted, in contrast, that under Edwards v. Arizona (1981), 451 U.S. 477, 68 L. Ed. 2d 378, 101 S. Ct. 1880, and Arizona v. Roberson (1988), 486 U.S. 675, 100 L. Ed. 2d 704, 108 S. Ct. 2093, the assertion by an accused during custodial interrogation of his Miranda right to counsel will preclude further police-initiated questioning, even on unrelated offenses, unless counsel is present. (McNeil, 501 U.S. at 175-77, 115 L. Ed. 2d at 166-68, 111 S. Ct. at 2207-08.) Applying these principles to McNeil’s case, the Court concluded that the defendant’s statements, made in the wake of valid Miranda waivers, were admissible at the ensuing trial, notwithstanding the defendant’s earlier assertion of his offense-specific sixth amendment right to counsel on the unrelated charge.
The McNeil rationale is applicable here. The defendant’s acceptance of the appointment of counsel at the preliminary hearing on the unrelated offenses occurring November 3 did not also operate as an invocation of his separate right to counsel, under Miranda, for purposes of questioning on the present offenses. The sixth amendment right to counsel, invoked by the defendant at the preliminary hearing when he accepted the appointment of counsel, was “offense specific”; it did not also operate prospectively as an assertion of the separate Miranda right to counsel in future questioning on different charges, such as those at issue here. We must, therefore, give effect to the defendant’s waiver of his Miranda rights, made prior to his interrogations on the present offenses. The trial judge correctly declined to suppress the defendant’s statements on this ground.
B
The defendant next contends that the trial judge com*130mitted reversible error in permitting the State to present evidence of the series of three offenses committed by him, Jerry Thompson, and Gregory Howard on November 3, 1986. The defendant acknowledges that those three offenses share among themselves a number of common characteristics, but he argues that the three offenses were not sufficiently similar to the crimes charged here to be admissible in the present prosecution.
Testimony relating other crimes committed by the accused may be introduced at trial if the evidence is offered for a purpose other than to establish the defendant’s propensity to commit crime and if the probative value of the evidence outweighs its risk of unfair prejudice. (People v. Kokoraleis (1989), 132 Ill. 2d 235, 256; People v. McKibbins (1983), 96 Ill. 2d 176, 182.) A ruling allowing the introduction of evidence of other offenses committed by an accused will be upheld on appeal unless it represents an abuse of discretion. People v. Phillips (1989), 127 Ill. 2d 499, 522.
Applying these principles to the case at bar, we conclude that the trial judge did not abuse his discretion in admitting evidence of the offenses committed by the defendant, Thompson, and Howárd on November 3. The trial judge found the challenged testimony to be relevant because he believed that the information tended to show, in the present case, the defendant’s identity as one of the offenders and the defendant’s intent in accosting Bracy and Anderson. The record demonstrates sufficient similarities between that series of crimes and the offenses charged here to sustain the introduction of that evidence on the issue of identity. As we have stated, the three offenses occurred over the course of several hours during the evening of November 3, 1986. In each instance, the defendant was accompanied by the same two acquaintances, Jerry Thompson and Gregory Howard. The three would approach persons who were outdoors. *131One of them would then display a weapon to the intended victim in an apparent attempt at robbery; two of the three complaining witnesses in the November 3 offenses — Dmitar Marich and Jose Flores — specifically identified the defendant as the gunman.
Evidence of a defendant’s other crimes need not satisfy a test of “exact, rigorous identity” with the charged offense to be admissible as proof on the issue of identification (People v. Phillips (1989), 127 Ill. 2d 499, 520-21), for “some dissimilarity will always exist between independent crimes” (People v. Taylor (1984), 101 Ill. 2d 508, 521). Here, the defendant committed the present offenses while accompanied by the same two other persons, Gregory Howard and Jerry Thompson, who assisted him in the series of crimes he committed a week later, on November 3, 1986. This evidence was relevant, because it tended to show the defendant’s identity as an offender in the present case.
The evidence of the offenses committed by the defendant on November 3 was also relevant to the question of the defendant’s intent in approaching Anderson and Bracy. As this evidence demonstrated, Terrance Wilson and Dmitar Marich were both robbed; Jose Flores was able to elude the defendant and his companions. The evidence of the two other robberies tended to show that the defendant’s purpose in accosting the victims here was to commit robbery.
For these reasons, the evidence of the defendant’s involvement in the other offenses was relevant in the present prosecution. Moreover, we cannot say that the probative value of the evidence was outweighed by the risk of unfair prejudice to the defendant. We note that the jurors received an instruction on the limited purposes for which the testimony had been introduced; the jurors were told to consider this evidence only as proof of the defendant’s “identification, intent, motive, and de*132sign.” (See Illinois Pattern Jury Instructions, Criminal, No. 3.14 (2d ed. 1981).) In closing argument, the prosecutor strictly hewed to those restrictions, reminding the jurors of the limited purposes for which the evidence was received. As we have stated, the admissibility of such evidence is a question reserved to the sound discretion of the trial judge. (People v. Phillips (1989), 127 Ill. 2d 499, 522.) In the circumstances presented, we find no abuse of discretion.
C
The defendant’s final argument concerning the trial proceedings concerns the instructions submitted to the jury on the charge of murder. The defendant contends that the trial judge committed reversible error when, over a defense objection, he instructed the jury on felony murder, a theory that had not been alleged in the indictment. The defendant believes that the failure of the indictment to specifically allege his commission of murder under a felony murder theory precluded the trial judge from later submitting to the jury an instruction setting forth this additional theory.
In the form of the statute applicable in the present case, section 9 — 1(a) of the Criminal Code of 1961 defines the offense of murder in the following terms:
“A person who kills an individual without lawful justification commits murder if, in performing the acts which cause the death:
(1) He either 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
(2) He knows that such acts create a strong probability of death or great bodily harm to that individual or another; or
(3) He is attempting or committing a forcible felony other than voluntary manslaughter.” 111. Rev. Stat. 1985, ch. 38, par. 9 — 1(a).
*133Count I of the five-count indictment returned against the defendant charged him with murder under section 9 — 1(a)(1), alleging that he intentionally and knowingly shot and killed Adrian Bracy. Count II charged the defendant with murder under section 9 — 1(a)(2), alleging that he shot at Bracy, knowing that those acts created a strong probability of death or great bodily harm. A third count charged the defendant with the offense of attempted armed robbery. The two remaining counts charged the defendant with armed violence; those counts were nol-prossed before trial and are not at issue here. The indictment did not charge the defendant with murder under a felony murder theory, as provided in section 9 — 1(a)(3) of the Criminal Code.
Prior to the selection of a jury, the prosecutor stated that he would later seek to have the jury instructed on felony murder. Defense counsel objected to the request; the judge stated that instructions setting forth this additional theory would be given if the evidence so warranted. At the close of evidence, and over a renewed defense objection, the trial judge submitted to the jury instructions on the felony murder theory, in addition to the two theories of murder charged in the indictment. The jury returned general verdicts finding the defendant guilty of murder and attempted armed robbery. Because the murder verdict was a general one, it did not specify the particular theory or theories on which the jury’s determination of guilt for that offense rested.
Before this court, the defendant argues that the trial judge committed reversible error by instructing the jury on a theory of murder not specifically alleged in the indictment. The defendant claims that the use of the felony murder instruction denied him his right to due process under the Federal and State Constitutions (U.S. Const., amend. XIV; 111. Const. 1970, art. I, §2), de*134prived him of his right under the Illinois Constitution to be informed of the charges against him (111. Const. 1970, art. I, §§7, 8), and violated the pleading requirements found in section 111 — 3 of the Code of Criminal Procedure of 1963 (111. Rev. Stat. 1985, ch. 38, par. 111 — 3).
This court considered a similar argument in People v. Allen (1974), 56 Ill. 2d 536. The defendant in that case was indicted for murder under sections 9 — 1(a)(1) and 9— 1(a)(2) of the Criminal Code of 1961 (111. Rev. Stat. 1967, ch. 38, pars. 9 — 1(a)(1), (a)(2)); as in this case, the indictment did not specifically allege a felony murder theory, as provided by section 9 — 1(a)(3) (111. Rev. Stat. 1967, ch. 38, par. 9 — 1(a)(3)). The court rejected the defendant’s argument that the failure to allege a felony murder count in the indictment precluded the trial judge from later instructing the jury on that particular theory. The court explained:
“Under section 9 — 1 there is but one crime of murder, not three separate and distinct offenses as the defendant’s argument assumes. Each of subparagraphs (1), (2) and (3) under section 9 — 1(a) describes the mental state or the conduct of the defendant which must accompany the acts which cause the death. If the defendant were charged with murder under subparagraph (a)(1) and acquitted, he could not again be charged and tried for the murder of the same individual under subparagraph (a)(2) or (a)(3). Thus, there is no possibility that the defendant in this case could have been twice put in jeopardy. Also, the provision of our statute covering the effect of a former prosecution (111. Rev. Stat. 1967, ch. 38, par. 3 — 4) prohibits a subsequent prosecution of the defendant under such circumstances.
The record does not show that the defendant was in any way misled by the indictment in the preparation of his defense. He obviously was aware of the felony-murder theory of the State from the opening statement through the instructions to the jury. He never objected thereto nor did he allege surprise or ask for a continuance for the *135purpose of preparing a defense to this charge. The conference on instructions reveals that the defendant was not surprised by the felony-murder theory. Objections to the felony-murder instructions were not made on the basis of this contention. It was therefore not error for the court to instruct the jury under section 9 — 1(a)(3).” (Allen, 56 Ill. 2d at 543.)
In support of its holding, the court cited its decision in People v. Rosochacki (1969), 41 Ill. 2d 483, 491-92, which had rejected a similar argument by a defendant charged with murder under section 9 — 1(a)(1) of the Criminal Code but convicted under sections 9 — 1(a)(2) and 9— 1(a)(3) instead. See also People v. Laramore (1987), 163 Ill. App. 3d 783, 789-92.
The defendant contends that Allen is distinguishable because counsel in the present case, unlike counsel in Allen, specifically objected at trial to inclusion of this additional theory of guilt in the jury instructions. According to the defendant, the appropriate standard on review is that found in People v. Lutz (1978), 73 Ill. 2d 204, which requires strict compliance with the pleading requirements of section 111 — 3 of the Code of Criminal Procedure of 1963 (111. Rev. Stat. 1985, ch. 38, par. 111 — 3) if an accused has made a timely objection to the charging instrument. Section 111 — 3 provides that a charging instrument must specify the name of the offense, cite the statutory provision allegedly violated, “[s]et[ ] forth the nature and elements of the offense charged,” specify the date and county of the occurrence, and identify the accused. (111. Rev. Stat. 1985, ch. 38, par. 111 — 3.) In Lutz, the court held that an indictment charging the defendant with aggravated battery was fatally deficient under section 111 — 3 because both counts in the indictment failed to allege an essential element of the offense charged. There, the defendant had raised the same objections in a post-trial motion in arrest of judg*136ment, and the court concluded that strict compliance with the requirements of section 111 — 3 was therefore necessary, even in the absence of prejudice to the accused. Lutz, 73 Ill. 2d at 209-10.
In contrast, when the sufficiency of a charging instrument is challenged under section 111 — 3 for the first time on appeal, the instrument will be upheld “if it apprised the accused of the precise offense charged with sufficient specificity to prepare his defense and allow pleading a resulting conviction as a bar to future prosecution arising out of the same conduct. [Citations.]” (People v. Pujoue (1975), 61 Ill. 2d 335, 339.) The defendant contends that it was this less searching test that was applied in Allen, because in that case there was no timely objection to the variance between the allegations of the indictment and the subsequent trial evidence and jury instructions. We do not agree.
Although Allen noted the defendant’s failure to object to the variance, the court in that case viewed the absence of an objection not as determining the selection of the appropriate standard of review, but rather as supplying evidence that the defendant did not incur prejudice as a result of the variance. We note the existence of language in People v. Johnson (1976), 65 Ill. 2d 332, involving a charge of prostitution, that may be construed to support the defendant’s argument. In that case, after describing the Pujoue test, the court stated, “Much the same standard has been applied to cases where it is alleged for the first time on appeal that there was a variance between the pleading and the proof at trial. It has been held that a variance, to require reversal, must be material and of such character as to mislead the accused in making his defense or expose him to double jeopardy. [Citations.]” (Johnson, 65 Ill. 2d at 337.) The Johnson court’s intimation that a different standard might apply when an accused challenges a variance in the trial court *137was dictum. The defendant in Johnson had not challenged the variance prior to appeal, and the court therefore was not called upon to determine whether a different test would govern in that instance.
We do not consider that the provisions of section 111 — 3, prescribing what information a valid charge must contain, are implicated in the present case. Illinois law recognizes only a single offense of murder, which may be committed in a variety of ways. Just as the method of committing murder is not integral to the offense and therefore need not be specified in the charging instrument (see People v. Coleman (1971), 49 Ill. 2d 565, 571 (allowing formal amendments to indictment adding alternative allegations of methods and means by which murder was committed)), so, too, under Allen and Rosochacki, the precise statutory theory of the offense of murder is not a matter that must be specifically alleged.
We thus conclude that the appropriate standard for review in the present case is that expressed in Allen, which requires consideration of whether the variance between the murder charge and the proof and jury instructions has caused the defendant prejudice in his preparation for trial, and whether the variance may expose him to the risk of double jeopardy.
The defendant does not allege that he was denied the opportunity to adequately prepare for and defend against this additional theory of guilt. Indeed, on the present record, that contention would surely fail. The indictment returned by the grand jury charged the defendant with attempted armed robbery of the murder victim, among other offenses. The defense thus knew at the outset of the case that the State’s theory of guilt included the defendant’s commission of a separate felony against the murder victim; the defendant’s inculpatory statements, which were made available to the defense in discovery, clearly indicated that the attempt occurred dur*138ing the murder. Prior to selection of the jury, the prosecution provided notice to the defendant of its intent to seek to have the jury instructed on a felony murder theory, in addition to the other murder theories alleged in the indictment. Defense counsel objected at that time, but solely on the ground that the failure of the indictment to specifically allege the commission of felony murder barred the use of that theory at trial. Counsel did not also contend that use of that additional theory would in any way impair her ability to defend the case. During trial, the defendant made no claim of surprise to any of the evidence presented by the prosecution.
At the conclusion of the trial, the judge instructed the jury on felony murder over the defendant’s objection. As the judge determined, the evidence introduced by the State fully warranted the submission of an instruction on that theory; the defendant’s commission of the attempted armed robbery during the murder was shown by his own statements to authorities as well as by the testimony of eyewitness Harold Anderson. At the instructions conference, defense counsel again claimed only that use of the jury instruction was prohibited because the indictment failed to expressly allege this additional theory.
As these circumstances demonstrate, the defendant incurred no prejudice as a result of the State’s use of the felony murder theory of guilt. Before trial, the defense was apprised of the State’s intended use of the theory and, throughout the proceedings, had full opportunity to defend against it. Moreover, there is no threat that the defendant may twice be put in jeopardy for the present offenses. The indictment and record of proceedings in the present case are adequate protection against any risk of multiple punishments or multiple prosecutions for the murder. (Allen, 56 Ill. 2d at 543.) Although it would have been better if the State had alleged each theory of *139murder .in the charging instrument, we do not believe that the failure to do so in the present case precluded the submission of the felony murder theory to the jury.
These same considerations answer as well the defendant’s remaining contentions that the jury instructions used in the present case denied him due process under the Federal and State Constitutions and violated his State constitutional right to be apprised of the charges against him (U.S. Const., amend. XIV; 111. Const. 1970, art. I, §§2, 7, 8). The record clearly establishes that the defendant in the present case was provided with timely notice of the State’s felony murder theory and had an opportunity to defend against it, and thus the due process concerns he now raises were satisfied (see Jackson v. Virginia (1979), 443 U.S. 307, 314, 61 L. Ed. 2d 560, 570, 99 S. Ct. 2781, 2786). Accordingly, the defendant cannot be heard to argue that his murder conviction rests on a ground not presented below. (Cf. Presnell v. Georgia (1978), 439 U.S. 14, 58 L. Ed. 2d 207, 99 S. Ct. 235 (reviewing court improperly upheld death sentence on ground not presented to sentencing jury); Cole v. Arkansas (1948), 333 U.S. 196, 92 L. Ed. 644, 68 S. Ct. 514 (reviewing court improperly affirmed convictions on basis of offense on which jury had not been instructed).) As the State notes, the validity of amendments to charging instruments in State prosecutions is primarily a question of State law (see Watson v. Jago (6th Cir. 1977), 558 F.2d 330, 337), and we have found no invalid amendment here (see Blake v. Morford (6th Cir. 1977), 563 F.2d 248 (trader Tennessee law, defendant roperly convicted of felony murder though indictment alleged only premeditated murder theory; habeas relief therefore denied)).
The defendant correctly observes that the Illinois Constitution, as well as the Code of Criminal Procedure, forbids his conviction on an offense for which he has not *140been charged. (See People v. Schmidt (1988), 126 Ill. 2d 179, 183-85.) As we have stated, however, in section 9— 1 of the Criminal Code Illinois recognizes but one offense of murder, which, we have found, was adequately alleged in the indictment. We conclude, for the reasons set forth, that the indictment sufficiently charged the defendant with the offense of murder.
II
A
The defendant also raises several arguments concerning the sentencing hearing conducted in the present case. The defendant first contends that his waiver of a jury for purposes of the sentencing hearing was invalid because it vfras based on the erroneous advice of his attorney. The defendant made the waiver before trial, following the judge’s ruling permitting the State to introduce evidence of the defendant’s involvement in other offenses. The defendant asserts that counsel recommended waiver of the sentencing jury because she believed, incorrectly, that evidence of his participation in those offenses would be inadmissible at the sentencing hearing. The defendant now maintains that this advice was incompetent and that his jury waiver therefore is infirm because of counsel’s misapprehension of the law.
Prior to trial, the judge ruled that evidence of the burglary committed by the defendant and Jerry Thompson in September 1985, and evidence of the series of offenses committed by the defendant, Thompson, and Gregory Howard on November 3, 1986, would be admissible at trial. At the time of the present trial, the defendant had not yet been tried and convicted for those crimes. In the wake of the ruling, defense counsel made the following representations:
*141“[The defendant is] going to waive jury for death penalty phase at this time. And the reason for that is that we got boxed in by the introduction of these robberies. Here’s — we have a jury. They are going to hear about all these robberies. They are not allowed to hear unconvicted charges in an aggravation hearing; they are going to hear about all of this. If we took the jury or if this particular jury was going to hear the case, they would hear all about the robberies, and the State would not be allowed by Illinois case law to introduce them in an aggravation hearing, and yet they heard about them anyway, they are going to be so inflamed, they are going to say this man is so awful, and the fact he takes cocaine and is a drug addict.”
The trial judge then prepared to accept the defendant’s waiver. Counsel stated again her reasons for advising the defendant to waive a jury for purposes of sentencing:
“[DEFENSE COUNSEL]: Yes, your Honor,, on behalf of Mr. Maxwell we would be requesting that the jury not be Witherspooned. The reason for that is after we — well, there are several reasons for it. Number one is we’d prefer to have the Court decide the issue of death penalty.
THE COURT: Well, that is as much as I think you have to state at this point.
[DEFENSE COUNSEL]: Your Honor, in addition to that the jury hearing about Witherspoon will make them more inclined to find him guilty of murder if they are aware that this business — this issue of the death penalty is in the case at all, Judge, for one thing.
For another thing the State’s Attorney has indicated that they are going to introduce robberies and a burglary in addition to trying this man for murder. And that these — he’s not convicted of the robberies. He’s not convicted in the burglary, and those would be inadmissible in an aggravation hearing, but the jury is going to hear about it anyway. So for those reasons we would ask — Mr. Maxwell has decided to ask the Court to hear the issue of *142the death penalty and will waive his jury to the death penalty at this time, Judge.”
The trial judge then proceeded to admonish the defendant concerning his waiver of a jury for purposes of the capital sentencing hearing, and the defendant signed a form memorializing his action. Later, at the outset of the sentencing hearing, the defendant stated in response to the court’s questions that he wished to persist in his waiver of a sentencing jury.
The defendant argues that counsel was ineffective and his jury waiver therefore invalid. To prevail on a claim of ineffective assistance of counsel, an accused must show that counsel’s actions were professionally unreasonable and that he suffered prejudice as a result. (Strickland v. Washington (1984), 466 U.S. 668, 80 L. Ed. 2d 674, 104 S. Ct. 2052; see People v. Albanese (1984), 104 Ill. 2d 504, 526-27 (adopting Strickland standard).) The conduct challenged here pertains to the defendant’s waiver of his statutory right to submit the capital sentencing determination to a jury. (See Ill. Rev. Stat. 1985, ch. 38, par. 9 — 1(d); People v. Ruiz (1989), 132 Ill. 2d 1, 20; People v. Erickson (1987), 117 Ill. 2d 271, 289.) A capital defendant’s waiver of a sentencing jury must be knowing and intelligent. (Albanese, 104 Ill. 2d at 534-36.) Under the first prong of the Strickland test, we must determine whether counsel’s advice to the defendant “fell below an objective standard of reasonableness.” (Strickland, 466 U.S. at 688, 80 L. Ed. 2d at 693, 104 S. Ct. at 2064.) With respect to the second prong of the Strickland test, the parties agree that the appropriate inquiry in this case is whether there exists a reasonable likelihood that the defendant would not have waived his jury right in the absence of the alleged error. See Hill v. Lockhart (1985), 474 U.S. 52, 58-59, 88 L. Ed. 2d 203, 210, 106 S. Ct. 366, 370 (adapting Strickland test to claimed ineffective assistance involving *143guilty plea); People v. Huante (1991), 143 Ill. 2d 61, 69 (same).
Defense counsel was incorrect in her belief that evidence of the defendant’s involvement in offenses for which he had not yet been convicted could not be introduced at the sentencing hearing, for such evidence is admissible (People v. Collins (1985), 106 Ill. 2d 237, 282; People v. Ruiz (1982), 94 Ill. 2d 245, 267-68; People v. La Pointe (1981), 88 Ill. 2d 482, 498). Notwithstanding counsel’s error, we conclude, on the record before us, that counsel did not render ineffective assistance in advising the defendant to waive a jury, and that the defendant’s jury waiver therefore is not invalid on this ground.
As an examination of defense counsel’s remarks makes clear, counsel offered three distinct reasons in support of her decision to advise the defendant to waive a jury for the sentencing hearing. First, counsel apparently believed that the judge was more likely to be lenient than a jury; counsel stated that she and her client preferred that the judge make the sentencing determination. Second, counsel wanted to preclude death-qualification of the jury for .purposes of the guilt phase of the proceedings. (See Daley v. Hett (1986), 113 Ill. 2d 75.) Third, counsel did not want the sentencing decision to be made by a jury if its members had been exposed to, or, in counsel’s words, had been “inflamed” by, evidence of the defendant’s other offenses. For these reasons, then, counsel recommended that the defendant waive a jury for the death penalty hearing.
“A convicted defendant making a claim of ineffective assistance must identify the acts or omissions of counsel that are alleged not to have been the result of reasonable professional judgment.” (Strickland, 466 U.S. at 690, 80 L. Ed. 2d at 695, 104 S. Ct. at 2066.) Any one of the three grounds mentioned by counsel constitutes a *144valid reason for choosing to waive a sentencing jury. In the circumstances of this case, counsel’s mistaken belief concerning the admissibility of the other-crimes evidence did not result in an act or omission reflecting unreasonable professional judgment. This conclusion holds true even if the defendant is correct in his argument that counsel’s recommendation was motivated solely by the third reason given — avoiding a sentencing jury that was aware of the defendant’s record of criminal conduct— and that the two others mentioned by counsel were consequences, and not causes, of her recommendation. As matters unfolded here, defense counsel’s mistaken views regarding the admissibility at the sentencing hearing of the other-crimes evidence could not have prompted her to advise the defendant to waive a sentencing jury. The judge’s decision to admit this evidence at trial ensured that the jurors would learn of the information. Counsel’s ensuing recommendation that the defendant waive a jury for the sentencing phase was entirely consistent with counsel’s strategy to avoid submitting the sentencing determination to jurors who were aware of the defendant’s criminal record.
A different question would be presented if, after the judge ruled that the other-crimes evidence would be admissible at trial, counsel had then advised the defendant to waive a jury for the guilt phase but not the sentencing phase, believing that the evidence could not be introduced at sentencing. A different question would also be presented if the judge had excluded the evidence at trial and defense counsel, acting on her belief that the evidence would be inadmissible at the sentencing hearing as well, had then advised the defendant to submit the sentencing decision to a jury. In those instances, the defendant’s waiver or nonwaiver of a jury would be tied to counsel’s erroneous belief that the other-crimes evidence could not be introduced at the sentencing hearing. In the *145present case, however, the judge’s pretrial ruling effectively spared defense counsel from opting for a jury at sentencing on the basis of her mistaken belief and then learning, too late, of her error.
Counsel’s erroneous view that the other-crimes evidence would not be admissible at the sentencing hearing was therefore irrelevant under the circumstances here. Counsel achieved her strategic goal of not having the sentencing determination made by a jury if its members were aware of the defendant’s lengthy criminal record. In this case, her misapprehension regarding the admissibility of this evidence could have had no bearing on that strategy. We thus conclude that the defendant has failed to identify an act or omission of counsel that was the result of counsel’s allegedly unreasonable judgment.
Our conclusion that the defendant has failed to show that counsel acted in a professionally unreasonable manner is, of course, dispositive of the present argument, for a defendant pressing a claim of ineffective assistance cannot prevail unless he establishes both parts of the Strickland test. (See People v. Huante (1991), 143 Ill. 2d 61, 72.) Assuming, however, that counsel’s mistaken belief resulted in a professionally unreasonable act or omission, we next consider whether the defendant sustained prejudice as a consequence.
To establish the prejudice prong of the Strickland test, the defendant argues that he waived a sentencing jury in reliance on defense counsel’s erroneous belief that the other-crimes evidence would not be admissible at the sentencing hearing. As our preceding discussion demonstrates, however, that contention cannot be true. It is clear in this case that defense counsel would have offered the same recommendation if she had known that the evidence of the defendant’s other crimes would later be admissible at the sentencing hearing. As we have stated, one reason for counsel’s recommendation to the *146defendant that he forgo a jury for sentencing was to avoid submitting the sentencing determination to jurors who were aware of the defendant’s extensive criminal record. Recognition that the jurors would eventually acquire this information at the sentencing hearing could only have confirmed counsel in her assessment that a jury waiver was necessary to effectuate her strategy. Here, counsel achieved her avowed goal of not having the sentencing determination submitted to a jury if its members were aware of the defendant’s criminal history.
B
The defendant next contends that the trial judge, in imposing the death sentence, improperly refused to consider the mitigating evidence introduced in the defendant’s behalf during the second stage of the capital sentencing hearing. This evidence consisted of testimony from eight family members and friends of the defendant, who described him in favorable terms. As proof of the trial judge’s failure to consider this information, the defendant cites the judge’s comments at the sentencing hearing that he did not “see” any mitigating circumstances in the present case. As we explain below, we believe that the record demonstrates that the judge did not ignore the testimony in mitigation, but rather gave full consideration to the evidence presented by the parties.
At the conclusion of the sentencing hearing, the trial judge sentenced the defendant to death for the murder of Adrian Bracy. The judge prefaced his comments by noting the presentation at the sentencing hearing of “matters in aggravation, matters in mitigation, lengthy arguments by both Counsel.” The judge next recounted the offenses charged here as well as the other crimes shown to have been committed by the defendant. Addressing the defendant, the trial judge then stated:
*147“You are clearly at least as this Court views the facts as I’ve heard, unable to conform your conduct to the norms of society. I mean you aren’t even close, not even close. There is no question that you are a danger and a threat to the public. You have indicated that by your conduct. Therefore the only question now before me is what’s the penalty going to be. What’s the penalty going to be. And I have reviewed all of the facts that have been presented to me, both the testimony, the pre-sentence investigation, I have reviewed time and time again the statute which indicates what I am to consider and it gives me guidelines and we are at the second stage now. We have gone past the first stage. There is no question that you are, that certain factors exist making you eligible, if I can use that term, for the death penalty. And now we’ve reached the fact [sic] where we consider aggravating and mitigating factors and it is for me to determine whether there are any mitigating factors. And God forgive me[,] Mr. Maxwell, I don’t see any mitigating factors. I don’t see a single mitigating factor, and for that reason[,] sir, I am dutybound to impose the ultimate penalty, and I hereby sentence you to death. That will be the order.”
Focusing on the trial judge’s twin statements that he did not “see any mitigating factors” and did not “see a single mitigating factor,” the defendant argues that the judge improperly ignored the mitigating evidence introduced in the defendant’s behalf at the sentencing hearing.
The defendant correctly observes that the sentencing authority in a capital case, whether judge or jury, may not refuse to consider, or be forbidden to consider, relevant evidence in mitigation. (Hitchcock v. Dugger (1987), 481 U.S. 393, 398-99, 95 L. Ed. 2d 347, 353, 107 S. Ct. 1821, 1824; Skipper v. South Carolina (1986), 476 U.S. 1, 4-5, 90 L. Ed. 2d 1, 6-7, 106 S. Ct. 1669, 1671; Eddings v. Oklahoma (1982), 455 U.S. 104, 110-12, 71 L. Ed. 2d 1, 8-9, 102 S. Ct. 869, 874-75; Lockett v. Ohio (1978), 438 U.S. 586, 604-05, 57 L. Ed. 2d 973, 990, 98 *148S. Ct. 2954, 2964-65 (plurality opinion).) This does not mean, however, that the judge or jury is required to credit a defendant’s mitigating evidence. Though not free to disregard evidence in mitigation, the sentencer “may determine the weight to be given relevant mitigating evidence.” (Eddings, 455 U.S. at 114-15, 71 L. Ed. 2d at 11, 102 S. Ct. at 877.) A review of the remarks made by the trial judge in the present case demonstrates that he acted in accordance with these precepts.
The trial judge began his remarks by referring generally to the parties’ evidence in aggravation and mitigation, reflecting his awareness that the defendant’s evidence was mitigating. The judge next stated that he had examined “all of the facts that have been presented to me, both the testimony, the pre-sentence investigation.” The judge also stated that he had repeatedly reviewed the death penalty statute. In a bench proceeding, section 9 — 1(h) directs the sentencing judge to “consider any aggravating and mitigating factors as indicated in subsection (c)” (111. Rev. Stat. 1985, ch. 38, par. 9 — 1(h)); subsection (c) expressly states that mitigation is not limited to the circumstances specified in that provision (111. Rev. Stat. 1985, ch. 38, par. 9 — 1(c) (“Mitigating factors may include but need not be limited to The following: [listing five specific mitigating circumstances]”)). Before pronouncing sentence, the judge noted that he was at the stage in the proceedings “where we consider aggravating and mitigating factors” and that he was required to determine “whether there are any mitigating factors.”
The trial judge’s remarks plainly refute the defendant’s claim that the judge refused to consider, or failed to consider, the mitigating testimony introduced in the defendant’s behalf at the sentencing hearing. Consideration of the defendant’s mitigating evidence did not obligate the trial judge to impose a sentence other than death. (People v. Phillips (1989), 127 Ill. 2d 499, 535.) *149When the judge’s remarks are viewed in context, as they must be (see People v. Jones (1988), 123 Ill. 2d 387, 421 (rejecting argument that sentencing judge failed to consider certain favorable evidence)), those comments demonstrate that the judge considered the defendant’s mitigating evidence but found that it was not sufficient to preclude imposition of the death penalty. Accordingly, the judge sentenced the defendant to death. 111. Rev. Stat. 1985, ch. 38, par. 9 — 1(h).
C
In his final series of arguments, the defendant challenges the facial validity of the death penalty statute (111. Rev. Stat. 1985, ch. 38, par. 9 — 1), contending that various aspects of the statutory scheme violate the eighth and fourteenth amendments (U.S. Const., amends. VIII, XIV). The same arguments have been rejected on other occasions, however, and the defendant fails to offer any persuasive ground that would warrant our reconsideration of those holdings.
The death penalty statute does not unconstitutionally cast on the defendant the burden of establishing that a sentence other than death should be imposed in his case (Silagy v. Peters (7th Cir. 1990), 905 F.2d 986, 998-99; People v. Orange (1988), 121 Ill. 2d 364, 390; People v. Caballero (1984), 102 Ill. 2d 23, 49), nor is the statute invalid for failing to impose on the State a burden of persuasion at the second stage of the sentencing hearing (People v. Jones (1988), 123 Ill. 2d 387, 426; People v. Eddmonds (1984), 101 Ill. 2d 44, 68; People v. Free (1983), 94 Ill. 2d 378, 421). The statute is not invalid for failing to require the sentencing authority to make a separate, additional finding that death is the appropriate penalty in the case. (People v. Whitehead (1987), 116 Ill. 2d 425, 462-63; People v. Guest (1986), 115 Ill. 2d 72, 112; People v. Morgan (1986), 112 Ill. 2d 111, 147.) Nor *150is the statute invalid for affording the prosecutor discretion in determining whether to seek the death penalty in a particular case. Silagy, 905 F.2d at 993-94; People v. Lewis (1981), 88 Ill. 2d 129, 146; People ex rel. Carey v. Cousins (1979), 77 Ill. 2d 531, 534-43.
In addition, the death penalty statute is not invalid for failing to require the prosecution to provide an accused with pretrial notice of its intent to seek the death penalty (People v. Silagy (1984), 101 Ill. 2d 147, 161-62; People v. Gaines (1981), 88 Ill. 2d 342, 369), or with notice of the aggravating evidence to be introduced at the sentencing hearing (People v. King (1986), 109 Ill. 2d 514, 547; People v. Albanese (1984), 104 Ill. 2d 504, 540; Gaines, 88 Ill. 2d at 369). Nor is the statute invalid for failing to provide each sentencing jury with information regarding the precise range of sentences available in the case. (People v. Phillips (1989), 127 Ill. 2d 499, 543; People v. Stewart (1984), 104 Ill. 2d 463, 495.) Comparative proportionality review is not required by the Federal Constitution (Pulley v. Harris (1984), 465 U.S. 37, 79 L. Ed. 2d 29, 104 S. Ct. 871), and the Illinois death penalty statute is not invalid for failing to provide such review (King, 109 Ill. 2d at 551; Stewart, 104 Ill. 2d at 499; People v. Kubat (1983), 94 Ill. 2d 437, 502-04; People v. Brownell (1980), 79 Ill. 2d 508, 541-44). In view of the decisional law upholding these aspects of the death penalty statute, we must reject the defendant’s further argument that the cumulative operation of these features invites the arbitrary and capricious imposition of the sentence. People v. Kokoraleis (1989), 132 Ill. 2d 235, 292-93; Phillips, 127 Ill. 2d at 542-43.
* * *
For the reasons stated, the defendant’s convictions and sentences are affirmed. The clerk of this court is directed to enter an order setting Tuesday, May 12, 1992, *151as the date on which the sentence of death, entered in the circuit court of Cook County, is to be carried out. The defendant shall be executed in the manner provided by section 119 — 5 of the Code of Criminal Procedure of 1963 (111. Rev. Stat. 1989, ch. 38, par. 119 — 5). The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, to the warden of Stateville Correctional Center, and to the warden of the institution where the defendant is now confined.
Judgment affirmed.
JUSTICES HEIPLE and FREEMAN took no part in the consideration or decision of this case.