delivered the opinion of the court:
Defendant, Edgar Christiansen, was indicted by a Cook County grand jury for the armed robbery of Lawrence Berry and the murders of Laura Steinke and Mousa Musleh (Mousa). Defendant was charged with the following offenses in connection with the Berry incident: armed robbery (Ill. Rev. Stat. 1981, ch. 38, par. 18 — 2); unlawful restraint (Ill. Rev. Stat. 1981, ch. 38, par. 10— 3); theft (Ill. Rev. Stat. 1981, ch. 38, par. 16 — 1(a)(1)); theft exceeding $300 (Ill. Rev. Stat. 1981, ch. 38, pars. 16 — 1(a)(1), (e)(3)); armed violence predicated on armed robbery, armed violence predicated on unlawful restraint and armed violence predicated on residential burglary (Ill. Rev. Stat. 1981, ch. 38, par. 33A — 2). Defendant was charged as follows in connection with the deaths of Steinke and Mousa: intentional murder, knowing murder, and felony murder based on armed robbery (Ill. Rev. Stat. 1981, ch. 38, pars. 9 — 1(a)(1), (a)(2), (a)(3), respectively); armed robbery (Ill. Rev. Stat. 1981, ch. 38, par. 18 — 2); armed violence premised on knowing murder, *103armed violence premised on felony murder, and armed violence premised on armed robbery (Ill. Rev. Stat. 1981, ch. 38, par. 33A — 2). Also in connection with the shooting death of Mousa, the defendant was charged with unlawful restraint (Ill. Rev. Stat. 1981, ch. 38, par. 10 — 3) and armed violence predicated on unlawful restraint (Ill. Rev. Stat. 1981, ch. 38, par. 33A — 2). Because three other persons were present at the time Mousa was killed, defendant was charged with the following additional counts: unlawful restraint of Samih Alkossa, Chris Churney, and Issa Musleh (Issa), the victim’s brother (Ill. Rev. Stat. 1981, ch. 38, par. 10 — 3), and armed violence based on the unlawful restraint of Alkossa, Churney, and Issa (Ill. Rev. Stat. 1981, ch. 38, par. 33A — 2).
Defendant pleaded not guilty by reason of insanity and waived his right to a jury trial on the issue of his guilt or innocence. The indictments were consolidated for trial, at the conclusion of which the court found that the defendant was not insane or mentally ill at the time these offenses were committed, thereby precluding a finding of not guilty by reason of insanity or guilty but mentally ill. The court then made the following findings. With respect to the armed robbery of Berry, the court found the defendant guilty as follows: guilty of armed robbery; guilty of unlawful restraint which was merged into the conviction for armed robbery. Defendant was found guilty on both counts of theft. The court found the defendant guilty of two counts of armed violence predicated respectively on armed robbery and unlawful restraint, merging these convictions with the prior conviction for armed robbery. The court found the defendant not guilty of armed violence predicated on residential burglary. With respect to the shooting death of Steinke, the court found the defendant guilty of intentional, knowing, and felony murder. The court also found the defendant guilty of armed robbery. There was a finding *104of guilty on two counts of armed violence premised on knowing murder and felony murder which were merged into the convictions for murder. The court further found the defendant guilty of armed violence based on armed robbery, merging this conviction with the conviction for armed robbery.
The court also found as follows with regard to the shooting death of Mousa: guilty of intentional, knowing, and felony murder; guilty of armed robbery; guilty of unlawful restraint, which was merged into the conviction for armed robbery; guilty on two counts of armed violence based on knowing murder and felony murder, which were merged into the convictions for murder; guilty of armed violence based on armed robbery, which was merged with the conviction for armed robbery. The court made no finding on the charge of armed violence, based on unlawful restraint. The court further found the defendant guilty of the unlawful restraint of Alkossa, Churney, and Issa, as well as guilty of armed violence based on the unlawful, restraint of Alkossa, Churney, and Issa.
The State indicated its decision to seek the death penalty for the murder convictions pursuant to section 9— 1(d) of the Criminal Code of 1961 (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(d)). The court accepted defendant’s waiver of the sentencing jury (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(d)(3)) and proceeded with the death penalty hearing. At the conclusion of the hearing, the court found that defendant was born March 27, 1937, and found beyond a reasonable doubt that he was 18 years of age or older at the time of the murders. The court also found beyond a reasonable doubt the existence of two statutory aggravating factors: the defendant had been convicted of two murders under the Illinois murder provision (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(b)(3)) and the defendant actually killed the two victims in the *105course of two separate felonies, armed robbery (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(b)(6)). The court then proceeded to a hearing in aggravation and mitigation (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(c)). At the conclusion of the hearing, the court found that there were “no mitigating factors sufficient to preclude the imposition of the sentence of death” (Ill. Rev. Stat. 1981, ch. 38, par. 9— 1(h)). The court, therefore, sentenced the defendant to death.
The court proceeded to impose sentence on the remaining convictions as follows: for the armed robbery of Berry, defendant was sentenced to 30 years’ imprisonment and three years’ mandatory supervised release. In addition, defendant was sentenced to two concurrent terms of five years’ imprisonment on the two convictions for theft. With respect to the Steinke incident, defendant was sentenced to 30 years’ imprisonment plus three years mandatory supervised release for armed robbery, to run concurrently with the sentence for the armed robbery of Berry. As to the Mousa incident, defendant again was sentenced to a concurrent term of 30 years’ imprisonment plus three years mandatory supervised release. On the convictions for unlawful restraint and armed violence based on the unlawful restraint of Alkossa, Churney, and Issa, defendant was sentenced to 30 years’ imprisonment plus three years supervised mandatory release, to run concurrently to the prior sentences for the armed robberies of Berry, Steinke, and Mousa. Because the death penalty was imposed, the cause comes before this court for direct review as provided by the Illinois Constitution of 1970 (Ill. Const. 1970, art. VI, sec. 4(b)) and Supreme Court Rule 603 (87 Ill. 2d R. 603).
We summarize the facts relative to each indictment as follows. With regard to the armed robbery of Berry, it was stipulated that, if Berry were to testify, he would state that he returned to his apartment on the afternoon *106of April 20, 1981, and found the defendant inside; that defendant was armed with a handgun; that defendant took $51 in cash and some gold chains from him; that he also took a .357 Smith and Wesson magnum and a box of .38-caliber bullets, a stereo, and a blue suitcase. Further, it was stipulated that Berry and the defendant each drank a beer while the defendant was deciding what to do with Berry; that defendant directed Berry to tie his own feet; that he then tied Berry’s hands together and tied them to a radiator. By further stipulation, Berry would have testified that defendant stated he would call the police to release Berry and that Berry was to tell the police that he was robbed by a black male. Additionally, it was stipulated that the defendant had his face covered during the robbery; that Berry viewed a lineup on April 23 and made an identification of the defendant after he requested that the defendant say “what am I going to do with you.” The parties also stipulated that a consent search of defendant’s apartment produced a stereo, a blue suitcase, and a box of .38-caliber bullets.
The parties also stipulated to the facts surrounding the shooting death of Steinke, an employee of a store called The Alley. Pursuant to the stipulation, Fernando Carballo would state, if called to testify, that he picked the defendant out of a lineup and identified him as the person he saw leaving The Alley on April 21, 1982. It was stipulated that the body of Steinke was found on April 21; that Steinke had been shot twice in the head; that these wounds were the cause of death. Additionally, it was stipulated that Sergeant Smith, firearms expert for the city of Chicago police department, if called to testify, would state that on April 22 he performed tests establishing that the bullets which killed Steinke were fired from the .357 Smith and Wesson magnum .38-cali-ber handgun stolen from Berry and recovered from the defendant at the time of his arrest. By further stipula*107tion, it was established that approximately $200 was missing from the cash register of The Alley, as well as some posters and lighters. Finally, it was stipulated that two posters and two lighters, identified as being property of The Alley, were uncovered during a consent search of defendant’s apartment on April 23.
Live testimony during the State’s case in chief established the facts surrounding the shooting death of Mousa. First to testify was Issa, the victim’s brother. He stated that the defendant entered his grocery store at closing time, 8 p.m., on April 22, 1982, took a grocery cart, placed a briefcase in the cart, and then proceeded to pick up various items which were also placed in the cart. Issa said that he approached the defendant and asked him to hurry so that he could close the store. He was within three feet of the defendant and testified that he could not smell the odor of alcohol. Issa then testified that, while, defendant was standing at the checkout counter, he called to Issa. Issa said that he responded to defendant’s call by approaching the counter. As he neared the defendant, Issa saw him pull a handgun from his briefcase, cock it, and point it at him. Issa noticed that defendant was wearing gloves. Continuing, he testified that defendant told him to move behind the counter and stand beside Mousa, the victim, and another employee, Alkossa. According to Issa, defendant demanded money which the victim handed over to the defendant. At this time, another employee, Churney, approached the checkout counter. Issa heard the defendant tell her to lie down on the floor, which she did. According to Issa, the defendant then instructed him, Alkossa, and the victim to lie down. While the victim was complying with the order, Issa observed the defendant place his gun within a few inches of the victim’s forehead and pull the trigger. He testified that he, Alkossa, and Churney got up and fled after the shooting. While fleeing, he heard a shot *108fired in his direction. That bullet was recovered later, and it was stipulated that it was fired from the .357 Smith and Wesson magnum handgun stolen from Berry and found in the defendant’s possession when he was arrested later that evening.
Issa further testified that he viewed a lineup on April 23 and identified the defendant as the man who robbed his store and shot his brother, Mousa. He also made an in-court identification of the defendant as the man he picked from the lineup.
On cross-examination, Issa stated that a bottle of vodka and a six pack of beer were among the items defendant placed in his cart. He also acknowledged that he had no special expertise in recognizing the behavior of an alcoholic or a polydrug abuser.
The next witness for the State’s case in chief on the Mousa killing was Alkossa, an employee of the grocery store. Alkossa testified that defendant entered the store at closing time, took a cart, placed a briefcase in the cart, and then proceeded to push the cart up and down the aisles, picking up several items: Alkossa stated that he went to the checkout counter and waited, along with the victim, for the defendant to finish shopping. According to Alkossa, defendant wheeled his cart up to the checkout counter and placed several items, including a bottle of vodka and a six pack of beer, on the counter. Alkossa placed the items in a bag. He noticed that the defendant was wearing gloves.
Alkossa further testified that defendant asked the victim if he was the manager. He heard the victim answer in the negative and point towards his brother, Issa. Alkossa then testified that the defendant called to Issa, who responded by approaching the checkout counter. As Issa approached, Alkossa stated that he observed the defendant pull a gun. He said that the defendant. demanded money, which he. received from the victim and *109placed in the briefcase. According to Alkossa, defendant then ordered everyone to lie down on the floor. While lying on the floor, Alkossa stated that he saw the defendant place his gun a few inches from the victim’s forehead and fire. Alkossa said that he immediately jumped to his feet and started running. He further testified that, throughout the entire incident, defendant did not appear to be under the influence of alcohol.
Alkossa also testified that the police brought the defendant to the store about 15 minutes after the robbery and shooting. He identified the defendant as the perpetrator. Alkossa stated that the next day, April 23, he viewed a lineup and again identified the defendant as the person who robbed the store and shot Mousa. Alkossa also made an in-court identification of the defendant as the perpetrator.
On cross-examination, Alkossa acknowledged that he had never seen the defendant before the incident. He also acknowledged that he had never observed the defendant under the influence of alcohol or other drugs.
Another employee, Churney, also testified as part of the State’s case in chief. She testified that on April 22 she approached the checkout counter as she was leaving. She stated that the defendant pointed a gun at her and ordered her to the floor along with the victim, Issa and Alkossa. She testified that, during this time, she was within three feet of the defendant and that she did not smell the odor of alcohol on his breath. Continuing her testimony, Churney said that, while on the floor, she saw the defendant shoot the victim. Churney further testified that she viewed a lineup on April 23, the day after the robbery and shooting, and picked out the defendant as the perpetrator.
The parties then stipulated that the cause of death of the victim , was a single gunshot wound to the head. Further, it was stipulated that the bullet which killed the *110victim was fired from the .357 Smith and Wesson magnum handgun stolen from Berry and found in the defendant’s possession at the time of his arrest.
The State, continuing its case in chief, called the officer who arrested the defendant. He testified that he arrested the defendant at about 8:15 p.m. on April 22 in an alley not far from the grocery store. The officer testified that, at the time of the arrest, defendant was wearing gloves and carrying a briefcase. The officer further testified that, after stopping the defendant, he placed the briefcase on the hood of his squadrol and then performed a patdown search. He stated that, as he completed his search of the defendant’s legs and started to stand up, he observed the defendant’s hand reaching into the briefcase. He seized the briefcase, opened it, and found a .357 Smith and Wesson magnum. He further stated he found approximately $500 in defendant’s right front pocket. The officer also testified that he did not smell the odor of alcohol on the defendant’s breath. He stated that the defendant did not sway or stagger.
The State called Detective Stevens, the officer who questioned the defendant about three hours after his arrest. Stevens stated that he did not smell the odor of alcohol on defendant’s breath. Stevens also stated that the defendant appeared lucid. Stevens further testified that before being asked any questions, defendant said to him, “Do you understand that the American Medical Association recognizes alcoholism as a disease.”
Stevens testified that, in response to his questions, defendant stated that he was an alcoholic and experienced blackouts. According to Stevens, defendant stated •that he did not remember being in the grocery store. When Stevens asked him where he got the gun, defendant told him that he bought it from a black male for $35. According to Stevens, defendant claimed to have pur*111chased the gun in front of a bar around 1 a.m. on the morning of April 22.
Stevens then testified about the substance of a second interview with the defendant. Stevens stated that he told the defendant that he had been identified in each of three lineups as the person who robbed a grocery store and shot a clerk. Stevens said that he also told the defendant that his story about how he obtained the gun could not be corroborated. In addition, Stevens told the defendant that the gun had been linked to another shooting which occurred on April 21. According to Stevens, the defendant responded by saying that he had not told the truth and that he would do so now.
Stevens continued, testifying that the defendant told him that he stole the gun from a former employer; that-he robbed The Alley; that he took the clerk into a back room; that he cocked the gun in order to scare her; that she made a move towards the gun; that he “heard” the gun go off. Stevens stated that the defendant said he returned home after the shooting and began drinking. Defendant told Stevens that he fell asleep, woke up around 6 p.m. on April 22, got up, went to the grocery store and robbed it. According to Stevens, the defendant said that he cocked the gun in order to frighten the clerk and that the gun discharged accidentally.
After giving this oral statement, defendant was interviewed by Assistant State’s Attorney Kathleen Wamick. Warnick also testified as part of the State’s case in chief. She stated that she interviewed the defendant about both the Steinke killing and the Móusa killing. Warnick testified that the defendant told her he had been drinking throughout the period in question but, according to Wamick, defendant was able to remember what transpired in each incident.
Warnick’s testimony about the content of defendant’s oral statement substantially paralleled the testimony of *112Detective Stevens as to the nature of the defendant’s statement. After receiving defendant’s oral statement, Warnick testified that she asked him whether or not he wanted to give a written statement. According to Warnick, defendant declined to do so. The State then rested its case.
The evidence presented by the defendant did not dispute the essential facts of the offenses charged but focused instead on his mental state at the time. Defendant did not testify in this regard. However, defendant did call Dr. Anthony Gaspero, a licensed clinical psychologist, who was qualified as an expert witness.
Dr. Gaspero testified that he interviewed the defendant in February 1983 and administered several psychological tests. Concerning the results of his examination, Gaspero testified that the defendant was a severe alcoholic with a 20- to 25-year history of alcohol abuse. He stated that, as a result of defendant’s alcoholism, defendant had lost most of his pancreas and was required to take insulin for the resulting diabetes. He also -testified that the defendant abused other drugs, particularly caffeine and the prescription drug Valium. Gaspero stated that, in his opinion, defendant also suffered from a severe depression which he stated was a feature of his personality and not a reaction , to specific traumatic life . events. Further, Gaspero indicated that he believed that the defendant also suffered from severe anxiety.
Gaspero testified that, in his opinion, the defendant was not responsible under the law for his behavior on April 20, 21, and 22. On the dates in question, the-defendant could neither “appreciate the criminality of his conduct [nor] *** conform his conduct to the requirements of law” (Ill. Rev. Stat. 1981, ch. 38, par. 6 — 2(a)). Specifically, he testified that on April 20, 21, and 22 the defendant was suffering from “[depression, anxiety, induced state of intoxication, substance use disorder, *113psychosexual disorder, and a history of chronic personality disorder, extreme physical deterioration, seizures, and blackouts.” Gaspero concluded that the defendant was “grossly impaired” and, as a result, was legally insane on the dates in question.
On cross-examination, Gaspero reaffirmed his opinion that defendant experienced alcohol-induced blackouts during April 20, 21, and 22. Under further questioning by the State, he acknowledged that the defendant could have acted purposefully during this time but maintained that, if the defendant was experiencing blackouts, he would not be able to remember such purposeful behavior.
The State, in rebuttal, called Dr. Michael Rabin, a licensed clinical psychologist, and Dr. Albert Stipes, a psychiatrist. Dr. Rabin testified that he interviewed the defendant pursuant to a court order asking for a determination of whether or not the defendant was insane at the time of the crimes and to what extent, if any, his mental state could be deemed a mitigating factor in the imposition of the death penalty.
Dr. Rabin testified that he did not find the defendant to be suffering from severe, clinical depression. Rabin testified that, based upon his examination of the defendant and his review of the police reports, he believed that the defendant was acting rationally and was legally sane during the period of April 20, 21, and 22.
Dr. Stipes testified as an expert who also evaluated the defendant pursuant to the court order mentioned above. Stipes indicated that he did not believe the defendant when he stated that he had not taken his insulin for three months. According to Stipes, failure to take insulin for that period of time would have been severely debilitating and could well induce a coma. However, Stipes testified that he did believe the defendant when he said that he could not remember what he was *114charged with. Stipes also gave his opinion that the defendant was legally sane on April 20, 21, and 22.
On cross-examination, Stipes agreed that defendant’s severe alcoholism and physical deterioration meant that the defendant was mentally ill as defined by Illinois law, in that he had a “substantial disorder of thought, mood, or behavior which afflicted [him] at the time of the commission of the offense[s], and which impaired [his] judgment ***” (Ill. Rev. Stat. 1981, ch. 38, par. 6-2(d)). Stipes also acknowledged that alcoholism is considered a mental disease or defect.
On redirect examination, Stipes reaffirmed his opinion that the defendant was legally sane at all times relevant to this case, despite the fact that the defendant suffers from a mental disease or defect. Also on redirect examination, Stipes stated that any mental impairment would depend upon the defendant’s degree of intoxication at the time of the offenses, as well as upon whether or not defendant had been taking his insulin and eating properly during the period in question.
The State and defendant then rested, and the court proceeded to hear closing arguments. Following argument, the court, as previously noted, found the defendant guilty of the murders of Steinke and Mousa. The matter thus proceeded to the death penalty hearing. After finding that the defendant was eligible for the death penalty, the court proceeded to take evidence in aggravation and mitigation.
The State introduced evidence of a significant, prior criminal history, as an additional aggravating factor. (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(c)(1).) In support, the State introduced the certified copy of defendant’s conviction for armed robbery in 1961. The State also introduced a certified copy of defendant’s conviction for theft in 1975. The defendant challenged the legality of using these convictions as aggravating factors, particularly *115taking issue with the 20-year-old conviction for armed robbery.
The defendant’s principal factor in mitigation was his mental illness, alcoholism, on the dates in question. Because of his alcoholism, defendant contended that the murders of Steinke and Mousa “[were] committed while [he] was under the influence of extreme mental or emotional disturbance” (Ill. Rev. Stat. 1981, ch. 38, par. 9— 1(c)(2)). In support of the presence of this statutory mitigating factor, defendant again called Dr. Gaspero, who testified substantially as he did during defendant’s trial on the issue of guilt or innocence.
The State rebutted Gaspero's testimony in mitigation by calling Dr. Rabin, who stated that he did not believe that the defendant was suffering from an extreme mental or emotional state or disturbance when the murders occurred.
The death penalty hearing proceeded to closing arguments, during which the defendant stressed his remorse. The State responded that defendant’s claimed remorse was a “phony exhibition” and a “bunch of bull crap.”
The death penalty hearing then concluded. After deliberation, the court announced its findings.
The court repeated its previous finding that two statutory aggravating factors were established by the State beyond a reasonable doubt: the. commission of two murders as defined by Illinois law and murder in the course of a felony, armed robbery (Ill. Rev. Stat. 1981, ch. 38, pars. 9 — 1(b)(3), (b)(6)). In addition, the court found that Steinke was “executed,” in that she was found face down in a “prone position with her hands behind her back as if waiting to be tied.” The court also found a “significant history of prior criminal activity” (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(c)(1)) based on the defendant’s prior convictions for armed robbery and theft. As to defendant’s principal factor in mitigation, the court *116found, after weighing all of the expert testimony, that, while the defendant was an alcoholic, he was not suffering from blackouts at the time of the offenses. The court specifically observed that the defendant gave oral statements describing the killings after being confronted by police with ballistics evidence and eyewitness identifications. The court found that the defendant was not suffering from “extreme mental or emotional disturbance” when he killed Steinke and Mousa. After considering all of the evidence in aggravation and mitigation and being unable to find any factors in mitigation sufficient to preclude imposition of the death penalty, the court sentenced the defendant to death (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(h)).
The defendant raises 13 issues on appeal, all of which are directed to his convictions for murder and his sentence of death. Two issues relate to his trial, on the issue of guilt or innocence. Six issues concern the conduct of defendant’s death penalty hearing. Five issues concern asserted constitutional deficiencies in the Illinois death penalty statute.
The defendant first contends that the trial court erred in finding him guilty rather than guilty but mentally ill. He argues that “[t]he evidence conclusively supports the conclusion that [he] was guilty but mentally ill within the meaning of the statute.” The mental illness asserted by the defendant is his alcoholism, which, he contends, caused him to experience blackouts while drinking during the period of April 20, 21, and 22, resulting in a loss of memory for the events occurring on those days.
The State counters by arguing that this issue is a factual one for the trial court to decide and that its decision should be affirmed unless “the determination is so improbable or unsatisfactory as to raise a reasonable doubt as to defendant’s sanity [or mental illness].” (People v. *117 Ward (1975), 61 Ill. 2d 559, 568.) The State contends that ample evidence was adduced at trial to support the court’s entry of a general finding of guilt and that the finding should stand. We agree.
Illinois law provides for the alternative finding of guilty but mentally ill where the defendant has asserted unsuccessfully the defense of insanity. The applicable provisions provide in pertinent part:
“A person who, at the time of the commission of a criminal offense, was not insane but was suffering from a mental illness, is not relieved of criminal responsibility for his conduct and may be found guilty but mentally ill.” Ill. Rev. Stat. 1981, ch. 38, par. 6 — 2(c).
“*** ‘[M]ental illness’ or ‘mentally ill’ means a substantial disorder of thought, mood, or behavior which afflicted a person at the time of the commission of the offense and which impaired that person’s judgment ***.” Ill. Rev. Stat. 1981, ch. 38, par. 6 — 2(d).
“When the defendant has asserted a defense of insanity, the court may find the defendant guilty but mentally ill if, after hearing all of the evidence, the court finds beyond a reasonable doubt that the defendant:
(1) is guilty of the offense charged; and
(2) was mentally ill at the time of the commission of the offense; and
(3) was not legally insane at the time of the commission of the offense.” Ill. Rev. Stat. 1981, ch. 38, par. 115 — 3(c).
“After a *** verdict of guilty but mentally ill ***, [t]he court may impose any sentence upon the defendant which could be imposed pursuant to law upon a defendant who had been convicted of the same offense without a finding of mental illness.” Ill. Rev. Stat. 1981, ch. 38, par. 1005 — 2—6(a).
We believe that the facts of this case, when viewed in light of these provisions, support the general finding of guilt entered by the court. For example, the three eyewitnesses to the Mousa robbery and shooting testified *118that the defendant did not appear to be intoxicated. Two of the witnesses, Issa and Churney, testified that they were within three feet of the defendant and did not smell the odor of alcohol on his breath. The officer who arrested the defendant approximately 15 minutes after the Mousa shooting did not smell the odor of alcohol and did not observe the defendant sway or stagger. Further, when the defendant was initially questioned after his arrest, he stated that he had been drinking and could not remember anything because the drinking caused him to experience blackouts. After being confronted with evidence linking the gun in his possession when arrested to two killings; with the fact that the police could not confirm his story about buying the gun from a black male in front of a tavern on April 22; and with the fact that three witnesses identified him as the person who robbed and shot Mousa, the defendant gave an oral statement recounting, with no apparent difficulty, the events of April 20, 21, and 22. His statement included a detailed account of the robbery and shooting of both Steinke and Mousa. Finally, even though defendant’s expert testified that he was legally insane when these crimes were committed, that testimony was disputed by the State’s experts who testified that the defendant was not insane and who also expressed some doubt that he was mentally ill during the period at issue. We also note that defendant covered his face during the Berry robbery and wore gloves during the robbery of the grocery store. When taken with other evidence, these facts suggest that the defendant was not suffering from alcohol-induced blackouts on April 20, 21, and 22 but, instead, was acting in accordance with preconceived plans.
A finding of guilty by the trier of fact will not be disturbed on appeal absent facts in the record which raise a reasonable doubt as to défendant’s sanity or, in the instant case, defendant’s mental illness at the time he *119committed the offenses. (People v. Gacy (1984), 103 Ill. 2d 1, 68-69, cert. denied (1985), 470 U.S. 1037, 84 L. Ed. 2d 799, 105 S. Ct. 1410; People v. Silagy (1984), 101 Ill. 2d 147, 168-69, cert. denied (1984), 469 U.S. 873, 83 L. Ed. 2d 156, 105 S. Ct. 227.) The record does not raise a reasonable doubt as to defendant’s mental illness at the time of these crimes. Consequently, a finding of guilty but mentally ill was neither warranted by the facts nor authorized by statute.
We note in passing that the defendant’s insistent contention that the proper verdict in this case was guilty but mentally ill is significant only insofar as it bears on imposition of the death penalty. Defendant concedes as much in his reply brief to this court by acknowledging that the death penalty can be imposed where a defendant is found guilty of murder but mentally ill. (Ill. Rev. Stat. 1981, ch. 38, par. 1005 — 2—6(a).) He argues, however, that a finding of guilty but mentally ill is critical to the sentencer’s decision as to whether or not to impose the death penalty. While this may be true, this argument clearly goes to the propriety of defendant’s death sentence rather than to the issue of his guilt or innocence. Indeed, the defendant renews this argument below in connection with his attack on his sentence of death. Therefore, it is sufficient at this point, that we find the evidence of defendant’s guilt adduced at trial amply supports the court’s general finding of guilt, and we affirm that finding.
Defendant next contends that he was denied a fair trial in violation of due process when Assistant State's Attorney Warnick testified during the State’s case in chief that the defendant, when asked if he wished to reduce his oral statement to writing, responded that he did not wish to do so. Defendant argues that this testimony was an impermissible comment on his right to remain silent and, thus, warrants a new trial.
*120Resolution of this issue turns upon whether or not the defendant, in fact, exercised his fifth amendment right to remain silent. If the defendant invoked this right, any comment at trial upon his subsequent silence constitutes a clear violation of his rights under the fifth amendment. (Wainwright v. Greenfield (1986), 474 U.S. 284, 292-95, 88 L. Ed. 2d 623, 629-32, 106 S. Ct. 634, 638-40; cf. Doyle v. Ohio (1976), 426 U.S. 610, 617-19, 49 L. Ed. 2d 91, 97-98, 96 S. Ct. 2240, 2244-45.) On the other hand, if the defendant did not invoke his right to silence, any comment relating to defendant’s decision not to give a written statement would not violate his right to remain silent.
We have reviewed the record thoroughly on this issue and conclude that the defendant did not exercise his right to remain silent. Detective Stevens gave unrebutted testimony as part of the State’s case that the defendant gave two oral statements subsequent to his arrest, after being apprised of his Miranda rights, and after his waiver of those rights. The record also indicates that the defendant gave a later oral statement to Assistant State’s Attorney Warnick, after again receiving and waiving his Miranda rights. This later oral statement to Warnick substantially paralleled the second oral statement given to Detective Stevens. It is clear therefore that the defendant did not choose to exercise his right to remain silent.
Where, as here, a defendant does not remain silent, after being apprised of his right to do so, and makes not just one but several oral statements, he has relinquished his rights under the fifth amendment. (People v. Adams (1985), 109 Ill. 2d 102, 119-20, cert. denied (1986), 475 U.S. 1088, 89 L. Ed. 2d 730, 106 S. Ct. 1476.) Defendant therefore cannot claim that testimony indicating that he was unwilling to memorialize one of his several oral statements violated his right to remain silent.
*121Having considered both arguments advanced by the defendant in support of his claim that he did not receive a fair trial on the issue of his guilt or innocence and having concluded that they are without merit, we turn to a consideration of the issues defendant raises regarding the conduct of his death penalty hearing.
Defendant first challenges the validity of his sentence of death on grounds that the court refused to consider his alcoholism as a statutory mitigating factor in that, as a consequence of his alcoholism, “the murder[s] [were] committed while the defendant was under the influence of extreme mental or emotional disturbance” (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(c)(2)). The State responds that the court did consider defendant’s alcoholism as a possible statutory mitigating factor but found that it was not sufficient to preclude the imposition of the death penalty (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(h)). In essence, the defendant argues that his alcoholism was not considered in mitigation, while the State argues that it was considered but rejected as being insufficient. Our review of the record of defendant’s sentencing hearing persuades us that the State is correct.
There was conflicting expert testimony at trial and during the sentencing hearing as to whether or not defendant was impaired at the time of these offenses by alcohol-induced blackouts and, if so, whether or not these blackouts constituted an extreme mental or emotional disturbance. There was also testimony at trial from the three eyewitnesses to the Mousa shooting that the defendant did not smell of alcohol and did not appear to be intoxicated. Further, the officer who arrested the defendant approximately 15 minutes after the Mousa incident also testified that the defendant did not smell of alcohol and did not appear impaired. Throughout the sentencing hearing, the court repeatedly stated that it would weigh all factors presented in aggravation and *122mitigation. In fact, during the hearing in aggravation and mitigation, the court indicated on at least three separate occasions that it would receive and weigh the evidence of defendant’s alcoholism. Furthermore, the court expressly distinguished the role of defendant’s alcoholism from the role of alcoholism in those cases in which this court found it to be a mitigating factor sufficient to reduce a sentence of death to imprisonment. (People v. Gleckler (1980), 82 Ill. 2d 145; People v. Walcher (1969), 42 Ill. 2d 159.) In so doing, the court expressly noted that, in both Gleckler and Walcher, the evidence established that the alcoholic defendant had been drinking and probably was intoxicated at the time of the killing; that the alcoholic defendant did not act alone in the perpetration of the offense; and, finally, that the alcoholic defendant was charged with only one killing. The court then observed that, in the instant case, there was sufficient evidence that the defendant was not intoxicated at the time of the offenses; that the defendant was the- sole perpetrator of the offenses charged; and that the defendant committed numerous offenses, including two murders, over the course of several days.
We believe that the record clearly refutes defendant’s contention that the court refused to consider his alcoholism as a possible mitigating factor. Here, the record indicates that the court examined the evidence in support of defendant’s claim that his alcoholism should be deemed a mitigating factor sufficient to preclude imposition of death and, after careful review, found that it was not sufficient.
The rule that this court will “not lightly overturn the findings of the trial court, particularly when they are amply supported by the record,” applies to findings made during the aggravation and mitigation phase of the death penalty hearing. (People v. Brownell (1980), 79 Ill. 2d 508, 539-40, cert. dismissed (1980), 449 U.S. 811, 66 *123L. Ed. 2d 14, 101 S. Ct. 59; see also People v. Owens (1984), 102 Ill. 2d 145, 159, cert. denied (1984), 469 U.S. 361, 83 L. Ed. 2d 297, 105 S. Ct. 361.) We believe that the record amply supports the finding of the court and can discern no reason to disturb it.
The defendant next argues that the court erred in finding in aggravation that the defendant had a “significant history of prior criminal activity” (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(c)(1)), where that finding was based in substantial part on a conviction for two armed robberies which was entered 22 years before the defendant’s conviction in the instant case. Defendant points to the 10-year limit on the admissibility of other crimes for purposes of impeachment. (People v. Warmack (1980), 83 Ill. 2d 112, 123-24; People v. Montgomery (1971), 47 Ill. 2d 510.) He asks that we apply the same 10-year limit to the aggravation and mitigation phase of the death penalty proceeding and bar the admission, for purposes of aggravation, of evidence of criminal convictions where more than 10 years have elapsed since the date of conviction or the release from confinement.
The State argues that the rules governing the admissibility of evidence on the issue of guilt or innocence do not control the admissibility of evidence during the aggravation and mitigation phase of a death penalty proceeding. According to the State, evidence is admissible in aggravation and mitigation if it is relevant and reliable and defendant’s conviction for two armed robberies is relevant and reliable and, hence, admissible regardless of when the conviction occurred. The State also notes that a court’s determination as to the relevance and reliability of evidence is within its sound discretion and should not be disturbed absent an abuse of that discretion.
The State recites the correct rules governing the admission of evidence during the aggravation and mitiga*124tion phase of the death penalty proceeding. (People v. Perez (1985), 108 Ill. 2d 70, 88, cert. denied (1986), 474 U.S. 1110, 88 L. Ed. 2d 931, 106 S. Ct. 898; People v. Brisbon (1985), 106 Ill. 2d 342, 364-65, cert. denied (1985), 474 U.S. 908, 88 L. Ed. 2d 241, 106 S. Ct. 276; People v. Eddmonds (1984), 101 Ill. 2d 44, 65, cert. denied (1984), 469 U.S. 894, 83 L. Ed. 2d 207, 105 S. Ct. 271.) Applying these rules to the instant case, we believe that the court correctly found defendant’s conviction for two armed robberies reliable. The State introduced a certified copy of defendant’s conviction, and there is no question raised as to its authenticity.
We also believe that the conviction for these two armed robberies was relevant. Among the offenses for which defendant was found guilty in the instant case were two armed robberies. When these two armed robberies are considered along with the two armed robberies occurring in 1961, the court could conclude that defendant’s adult life was characterized by a pattern of criminal behavior suggesting, in the words of the court, that his “potential for rehabilitation or restoration to useful citizenship is poor, very poor.”
The court applied the correct rule in deciding whether or not to admit the prior armed-robbery conviction. On this record, we conclude that the court did not abuse its discretion in ruling the prior conviction admissible.
Defendant also contends that he was denied a fair sentencing hearing when the prosecutor referred to his remorse as a “phony exhibition” and a “bunch of bull crap” and where the prosecutor stated that Dr. Stipes, an expert psychiatric witness for the State, testified that he “wouldn’t believe the words that come out of [defendant’s] mouth.”
The State responds that these statements were proper. With respect to the prosecutor’s remarks suggesting that defendant was feigning remorse, the State *125argues that these were invited by the defendant. As to the prosecutor’s characterization of Stipes’ testimony, the State maintains that it was a fair characterization. Alternatively, the State maintains that these remarks, if error, were harmless in that they were not prejudicial to the defendant.
We have reviewed the record on this issue and conclude that the statements complained of did not deprive the defendant of a fair sentencing hearing. During argument at the close of the hearing in aggravation and mitigation, defense counsel repeatedly referred to defendant’s remorse. Therefore, we agree with the State that the prosecutor’s comments, to which defendant objects, were invited. Invited remarks which are not prejudicial do not constitute error. (People v. Mack (1984), 105 Ill. 2d 103, 126-27; People v. Garcia (1983), 97 Ill. 2d 58, 87-88, cert. denied (1984), 467 U.S. 1260, 82 L. Ed. 2d 856, 104 S. Ct. 3555.) Aside from the general rule that counsel are given considerable latitude in closing argument, there is nothing in this record to suggest that the court was misled or was influenced improperly by the prosecutor’s remarks concerning defendant’s allegedly feigned remorse.
We conclude, however, that the prosecutor’s suggestion again during closing argument, that Dr. Stipes’ testimony indicated that he did not “believe the words that come out of [defendant’s] mouth,” was an overstatement, since Stipes clearly testified that he disbelieved the defendant only with regard to his statement that he had not taken his insulin in three months. Despite the prosecutor’s overstatement, we find no indication that the court gave it any weight at all in its decision to impose the death penalty. Absent a showing to the contrary, we believe that a court, sitting alone, considers only properly admitted evidence in making its determinations. (People v. Eddmonds (1984), 101 Ill. 2d 44, 65-66; *126 People v. Gilbert (1977), 68 Ill. 2d 252, 258-59.) In the instant case, we conclude that the court imposed the death penalty on the basis of evidence properly adduced in aggravation and mitigation and not on the basis of the remarks of the prosecutor in closing argument.
Defendant further contends that the court found that both victims had been “executed,” particularly detailing the reasons why the Steinke killing was an “execution,” and that this was an improper nonstatutory factor to consider in aggravation. Defendant argues that the court failed to consider his explanation that each shooting was accidental. Relying on People v. Jordan (1954), 4 Ill. 2d 155, the defendant argues that the finder of fact cannot disregard a defendant’s version of what occurred unless it is “improbable, *** uncorroborated, *** or contradicted in its material parts.” According to the defendant, the court erred in not believing his explanation and, instead, applying its own characterization to what occurred.
The State maintains that the trial court’s characterization of the shootings of Steinke and Mousa was an accurate description of what in fact happened. The State also argues that Jordan is not controlling since, in Jordan, there were no witnesses to the killing and this, court found that the defendant’s statement at the time of the incident and his testimony at trial were consistent and constituted a credible account of how the victim died. According to the State, only on such facts does Jordan require that the trier of fact accept a defendant’s version of events. Here, the State notes that there were three eyewitnesses to the Mousa shooting, none of whom testified that the shooting appeared to be an accident as the defendant claims.
We agree with the State that Jordan is not dispositive. Unlike Jordan, there are conflicting stories, at least as to Mousa’s death, which give rise to an inference that *127defendant’s account of the Steinke shooting, to which there were no witnesses, is improbable.
This issue must be resolved by an examination of the record. Steinke was shot twice in the side of the head. She was found lying on the floor with her hands, untied, behind her back. With respect to the shooting of Mousa, three eyewitnesses testified that the defendant placed his weapon within a few inches of Mousa’s forehead and fired.
This evidence directly undermines the defendant’s assertion that, in the Steinke incident, “he heard the gun discharge” after the victim appeared to make a slight move toward the gun. As to the Mousa shooting, the evidence flatly contradicts the defendant’s claim that the gun discharged accidentally when he turned back toward the victim after having looked out the store’s front window.
We also note that, in imposing the death penalty, the court described the shootings as purposeful and intentional. The record supports this characterization. We believe that the court used the term “execution” to underscore the intentional nature of defendant’s acts and that, because there was sufficient evidence to support a finding that the defendant acted intentionally, use of the term “execution,” under the facts of this case, was not error.
Defendant further contends that he was denied a fair sentencing hearing because the court denied him an opportunity to make a statement before imposing sentence on the murder convictions. He maintains that the right to make such a statement is “part of our concept of ordered liberty [so] as to constitute part of the due process guarantee.” Defendant also argues that he has been denied equal protection of the laws since defendants in noncapital cases are afforded, this opportunity while *128defendants in capital cases are denied the opportunity. Ill. Rev. Stat. 1981, ch. 38, par. 1005 — 4—1(a)(5).
The State, relying on Hill v. United States (1962), 368 U.S. 424, 428, 7 L. Ed. 2d 417, 421, 82 S. Ct. 468, 471, responds that allocution, or the opportunity to speak before imposition of sentence, is not a fundamental right encompassed by the concept of due process. Therefore, due process is not implicated when allocution is denied. As to the equal protection challenge, the State asks that we reaffirm our prior holding that the statutory denial to capital defendants of the opportunity to speak prior to imposition of sentence does not violate the guarantee of equal protection.
We agree with the State that Hill is dispositive of defendant’s due process challenge to the statutory prohibition. In Hill, the Supreme Court stated that “[t]he failure of a trial court to ask a defendant *** whether hhas anything to say before sentence is imposed *** is not a fundamental defect which inherently results in a complete miscarriage of justice, nor an omission inconsistent with the rudimentary demands of fair procedure.” Hill v. United States (1962), 368 U.S. 424, 428, 7 L. Ed. 2d 417, 421, 82 S. Ct. 468, 471.
Our decisions are in accord. (People v. Stewart (1984), 105 Ill. 2d 22, 74-75, cert. denied (1985), 471 U.S. 1131, 86 L. Ed. 2d 283, 105 S. Ct. 2666; People v. Gaines (1981), 88 Ill. 2d 342, 375, cert. denied (1982), 456 U.S. 1001, 73 L. Ed. 2d 1295, 102 S. Ct. 2285.) While defendant asserts that allocution is a right embodied within the concept of due process, he cites no case in support of this assertion nor offers any new argument. He asks only that we reconsider our prior holdings. We decline- to do so.
Similarly, we are not persuaded that the statutory prohibition of allocution applicable only tó capital defendants violates the guarantee of equal protection. This *129court has held that “the normal deference to legislative classifications should not be departed from unless the classification either impinge[s] on some right deemed fundamental or [is] directed against a ‘suspect class.’ ” (People v. Gaines (1981), 88 Ill. 2d 342, 380.) As this court has held, allocution is not a fundamental right; therefore, on that point, its denial does not raise an equal protection issue. And, obviously, the capital-non-capital classification established by the statute does not categorize persons on the basis of arbitrary characteristics such as race, sex, or national origin. In the absence of an invidious classification, our deference to the legislature presumes that a statutory classification is rational and, absent a showing of irrationality, the scheme will be upheld. The defendant has made no showing that the statutory classification at issue is irrational, and we decline to so hold.
Defendant’s final challenge to his sentencing hearing is merely a recapitulation of his previous challenges. Basically, he contends that the death penalty was an inappropriate sentence in his case because he was emotionally and mentally disturbed due to his depression, anxiety, and stress at the time of the murders; that he was an alcoholic; that he was addicted to other drugs; that he was in poor and deteriorating health; that he had a deprived childhood; that he was remorseful; and that he was a likely candidate for rehabilitation.
We have reviewed and rejected these contentions in our consideration of defendant’s earlier allegations of error as to imposition of the death penalty. Our resolution controls this issue. On this record, the evidence plainly supports the imposition of the death penalty and that sentence is affirmed.
We now turn to the challenges defendant raises to the constitutionality of Illinois’ death penalty statute. Defendant’s initial contention is that the statute is un*130constitutional because it places the burden on the capital defendant to prove that there is at least one mitigating factor sufficient to preclude the imposition of death. This court has considered and rejected this precise argument on a number of occasions. (See, e.g., People v. Montgomery (1986), 112 Ill. 2d 517, 534; People v. Morgan (1986), 112 Ill. 2d 111, 147-48; People v. Del Vecchio (1985), 105. Ill. 2d 414, 446, cert. denied (1985), 474 U.S. 883, 88 L. Ed. 2d 173, 106 S. Ct. 204.) We decline to reconsider these holdings.
Defendant next asserts, in the absence of argument or supporting authority, that the death penalty statute is unconstitutional because it vests a standardless discretion in the State’s Attorney to seek the death penalty. (Ill. Rev. Stat. 1981, ch. 38, par. 9 — 1(d).) Once again, we observe that this issue has been resolved against the defendant’s position on many occasions. See, e.g., People v. Brisbon (1985), 106 Ill. 2d 342, 362; People v. Stewart (1984), 104 Ill. 2d 463, 498-99, cert. denied (1985), 471 U.S. 1120, 86 L. Ed. 2d 267, 105 S. Ct. 2368; People ex rel. Carey v. Cousins (1979), 77 Ill. 2d 531, 535-39, cert. denied (1980), 445 U.S. 953, 63 L. Ed. 2d 788, 100 S. Ct. 1603.
Defendant’s third contention is that the death penalty statute is unconstitutional because it does not require a separate determination that death is the appropriate punishment in addition to a finding that there is no mitigating factor sufficient to preclude imposition of the death penalty. The defendant asks us to reconsider our prior holdings which he acknowledges have resolved this question against him. (See, e.g., People v. Morgan (1986), 112 Ill. 2d 111, 146-47; People v. Walker (1985), 109 Ill. 2d 484, 508-09; People v. Del Vecchio (1985), 105 Ill. 2d 414, 445-46.) In support of his request for reconsideration, defendant offers decisions from foreign jurisdictions. We decline to overrule the consistent holdings of *131this court on the basis of such decisions, which, of course, are not binding upon this court.
Defendant next asserts, again without supporting argument or authority, that the death penalty statute is unconstitutional because it does not provide for sufficient appellate review. He asks that we reconsider past decisions of this court which have concluded that a fair determination of whether or not to impose the death penalty is assured through the system of appellate review provided for by the Illinois Constitution of 1970 (Ill. Const. 1970, art. VI, sec. 4(b)), by the rules of this court, and by this court’s cases interpreting the death penalty statute. (See, e.g., People v. Neal (1985), 111 Ill. 2d 180, 202-03, cert. denied (1986), 476 U.S. 1165, 90 L. Ed. 2d 733, 106 S. Ct. 2292; People v. Wright (1985), 111 Ill. 2d 128, 161; People v. Perez (1985), 108 Ill. 2d 70, 96-97; People v. Kubat (1983), 94 Ill. 2d 437, 502-05, cert. denied (1983), 464 U.S. 865, 78 L. Ed. 2d 174, 104 S. Ct. 199.) We decline defendant’s invitation to reconsider the past holdings of this court on this question.
Defendant’s final constitutional challenge is that the death penalty statute fails to require that all aggravating factors relied upon by the sentencer are relevant and constitutionally permissible. As with defendant’s other challenges, this issue has been considered and decided adversely to his position on a number of occasions. (See, e.g., People v. Neal (1985), 111 Ill. 2d 180, 202-03; People v. Wright (1985), 111 Ill. 2d 128, 161; People v. Perez (1985), 108 Ill. 2d 70, 97.) Defendant offers no argument which would persuade us to reevaluate prior decisions on this issue, and we reaffirm those decisions.
For the reasons stated herein, we affirm the judgment of the circuit court of Cook County. The clerk of this court is directed to enter an order setting Wednesday, May 20, 1987, as the date on which the sentence of death entered by the circuit court is to be implemented. *132The 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, ch. 38, par. 119 — 5). A certified copy of the mandate of this court shall be transmitted by the clerk of this court to the Director of Corrections, to the warden of the Stateville Correctional Center, and to the warden of the institution wherein the defendant is confined.
Judgment affirmed.