
665 N.E.2d 1290 (1996)
172 Ill.2d 1
The PEOPLE of the State of Illinois, Appellee,
v.
Anton BROWN, Appellant.
No. 74532.
Supreme Court of Illinois.
March 28, 1996.
Rehearing Denied June 3, 1996.
As Modified on Denial of Rehearing June 3, 1996.
*1296 David J. Bradford, Locke E. Bowman and Kathleen M. Banar, Chicago, for appellant.
Roland W. Burris, Attorney General, Springfield, and Jack O'Malley, State's Attorney, Chicage (Arleen C. Anderson, Assistant Attorney General, Chicago, and Renee G. Goldfarb and Linda Woloshin, Assistant State's Attorneys, of counsel), for the People.
Justice MILLER delivered the opinion of the court:
Following a jury trial in the circuit court of Cook County, defendant, Anton Brown, was convicted of three counts of first degree murder. At a separate sentencing hearing, the same jury found defendant eligible for the death penalty and further determined that there were no mitigating circumstances sufficient to preclude imposition of that sentence. Accordingly, the trial judge sentenced defendant to death. Defendant's death sentence has been automatically stayed pending direct review by this court. Ill. Const.1970, art. VI, § 4(b); 134 Ill.2d Rs. 603, 609(a). In this appeal, defendant raises numerous errors in various proceedings below as grounds for reversal in this court. For the reasons that follow, we affirm defendant's convictions and sentences.

I. BACKGROUND
On September 10, 1990, defendant was charged by indictment in the circuit court of Cook County with six counts of first degree murder. Ill.Rev.Stat.1989, ch. 38, pars. 9-1(a)(1), (a)(2). The indictments were based on the September 2 and 3, 1990, murders of Aretha C. Phillips and her two children, Monique Belton, who was two years old at the time of death, and John Belton, Jr., who was three years old at the time of death.
The evidence at trial established that Gloria Wallace, Aretha's mother, attempted to call Aretha on September 4, 1990, on her beeper. However, another woman, whom Wallace did not recognize, answered the beeper. Wallace then called the police. She told the police that her daughter's apartment windows were open, but that she could not contact her daughter. Wallace asked the police to go to Aretha's apartment to look for her daughter. The police subsequently met Wallace at Aretha's apartment. On arriving at the apartment, Wallace found a note, which she testified she gave to the police, on the door of the apartment. The note was from Aretha's baby-sitter and stated that the baby-sitter was supposed to baby-sit for Aretha, but that Aretha did not show up. The police then knocked on the door, but there was no answer. Having no key of her own, Wallace begged the police to enter the apartment. The police refused, stating that they had no authority to enter or to allow her to enter. After Wallace told the police that she was fearful for her daughter's life because she had not seen or heard from her daughter for a couple of days and it was unusual for the apartment windows to be open, the police called the fire department for assistance.
Ronnie Herring, a Chicago fireman, received a call to assist police. When he arrived at the location, he was met by several police officers and the "mother of the girl they were looking for." He was told to enter the apartment and look around to see if anything was irregular. Herring placed a ladder up to a partially opened window on the second floor and climbed through the window. He found himself in a bedroom with two beds. He saw nothing unusual in either of the two bedrooms in the apartment. Herring then searched the rest of the apartment, and after finding nothing unusual, he asked the police if they wanted him to let them into the apartment. The police answered no, but asked Herring to look around again. After finding nothing unusual, Herring left the apartment the same way he had entered.
Later that same day, Wallace filed a missing person's report on Aretha and the two children. After filing the report, she also went over to the store where defendant, who lived with Aretha, worked to see if defendant *1297 had seen Aretha. Defendant's boss told Wallace that defendant had left, saying that he "was going to see his girlfriend." Defendant's boss gave Wallace defendant's employment application, and Wallace proceeded to go to the address defendant gave on the application. A woman at the address told Wallace that she did not know defendant. Wallace also made various other attempts to find Aretha, including attempting to speak with defendant's aunt, calling Aretha's friends and relatives, and looking in the alleys and dumpsters for her.
The following day Wallace and her husband returned to Aretha's apartment. Wallace's husband climbed into Aretha's apartment through an open window and then unlocked the front door to let Wallace in. Wallace went into Aretha's bedroom and saw a pile of clothes on the floor surrounded by flies. She attempted to pick up the clothes, but could not because there was something under them. She also testified that she saw blood under the clothes. Wallace then left the apartment and flagged down a police car. She told the police officer that she thought her daughter was dead and that she could not find her grandchildren. Wallace and the police officer returned to the apartment. Shortly thereafter, several other police officers arrived at the scene.
After Officer Robert Johnson arrived at the apartment, he proceeded directly to the rear bedroom. In the bedroom, he saw a bundle of clothes. He subsequently looked under the clothes and saw a small portion of a woman's partially deteriorated face. Johnson then left the bedroom, secured the area, and called his supervisor, the crime lab, and detectives.
Detectives James O'Leary and James Redmond were assigned to the case. They went to the apartment and were met by Wallace and her husband. O'Leary then spoke with Johnson and proceeded to the rear bedroom of the apartment. O'Leary was directed to a pile of clothing on the floor. He observed the right arm of Aretha extending out from under the clothes. O'Leary then removed the top cover from the body and observed multiple stab wounds to the body. He covered the body and then went into the other bedroom. Meanwhile Johnson had entered the other bedroom and saw something wrapped in a shower curtain under one of the beds. He poked at the mass with a stick. He felt the bundle again after flipping the mattress over. Johnson then left the bedroom and notified the detectives. O'Leary proceeded to enter the bedroom and stick his hand into the shower curtain. He felt a shoulder and an arm and, after probing further, felt another shoulder and arm. O'Leary testified that he knew then that there were two children in the shower curtain.
After the crime lab and medical examiner had finished processing the bedroom where Aretha's body had been found, the detectives unwrapped the body. Aretha was dressed in a white nightgown. There was blood on the sheets and blanket, and there was a pillow with blood on it over her head. The detectives then proceeded to uncover the children. The two bodies were intertwined, and each child was only wearing white underwear. The bodies were beginning to decompose and, therefore, the detectives were unable to detect any notable injuries. The detectives then proceeded to examine the rest of the apartment. O'Leary testified that there was no damage to the locking device on the front door, but that part of the privacy lock on Aretha's bedroom door had been broken.
O'Leary then had a conversation with Wallace. O'Leary asked Wallace if anyone else lived in the apartment with Aretha and the children. Wallace gave O'Leary defendant's name and description. Wallace also told the detective where defendant might be found. Wallace testified that the police asked her if she had any idea who might have murdered the victims, and she gave them defendant's name and description. O'Leary also asked if there was anything in the apartment that might identify defendant or help the police find defendant. Wallace told O'Leary about a photo album that she had seen the week before. After looking through the album, Wallace told the detective that defendant's photograph was gone, pointing to a blank spot in the album where a photograph had apparently been removed. After the apartment *1298 had been processed, the detective asked Wallace if anything was missing from the apartment. Wallace stated that several pieces of property were missing, including Aretha's car, beeper, television, microwave, and stereo.
Detectives subsequently began their attempts to locate defendant. That evening, defendant was brought to the police station by his uncle, Officer Charles Maratre. Defendant was taken into custody and, after several interviews with police, confessed to the three murders. Testimony regarding the circumstances surrounding defendant's confession was substantially the same as that presented at the suppression hearing. Defendant's confession was read into the record.
Defendant stated that he had lived with Aretha at the apartment where her body was found on and off since June 1990. Defendant asserted that on September 2, 1990, he worked at Farmer's Market until 5 p.m. Before leaving work, he borrowed $50 from his boss. After he left work, he bought some wine and cocaine with the money he had borrowed from his boss. He then went directly to Aretha's apartment. Aretha and the children arrived at the apartment around 7 p.m.
After dinner, defendant asked Aretha to dress the children so they could go out. Defendant wanted to visit a friend to borrow some money. Aretha dressed the children, and they all went out. Defendant first tried to borrow some money from a friend of his mother. When he was unsuccessful, defendant went to visit his aunt. Defendant's aunt gave him $5. At this point, Aretha and the children were in the car. Later, Aretha walked up to defendant and told him that she wanted to go home. Defendant and Aretha began to argue, and they eventually left after defendant's aunt told defendant to go home. Rather than go home, however, defendant went to visit his uncle at his store, but missed him because the store was closed. Defendant then drove home, stopping on the way to purchase $5 worth of gas. Defendant, Aretha, and the children returned home at approximately 9:15 or 9:30 that night.
After returning to the apartment, Aretha undressed the children and put them to bed. The children were wearing only their underwear. Aretha then went into her bedroom and put on a nightgown. Defendant later entered Aretha's bedroom, where an argument regarding drugs and money ensued between the two. Following the argument, Aretha rolled over like she was going to sleep.
Defendant proceeded to go into the kitchen and grab a knife. He then returned to the bedroom and sat on the edge of the bed. Aretha rolled over, and defendant stabbed her with the knife. Aretha screamed, and defendant stabbed her again. Aretha then began to cry, and defendant stabbed her again. Defendant stated that he did not know how many times he stabbed her, but thought that he stabbed her at least once in the neck.
Defendant next rinsed off the knife in the kitchen, placed the knife in a sock, put the sock in a garbage bag, and then threw the bag into a garbage chute outside. After disposing of the knife, defendant sat on the couch to think. He then returned to the bedroom and saw that Aretha was still breathing. Defendant placed a pillow over Aretha's face and held it there for a long time.
After placing the pillow over Aretha's face, defendant left the apartment. He proceeded to sell Aretha's beeper for $30 to someone downstairs. He also sold Aretha's television to another person for about $40. Defendant stated that he made these people go up to the apartment to get the television. Defendant then returned to the apartment and took the keys to Aretha's car. He locked the door to Aretha's bedroom before he left. Defendant next rented Aretha's car to somebody in exchange for some cocaine. Defendant then returned to the apartment and sat on the couch to think about what to do about the children. Defendant stated that he decided to leave the children in the apartment.
Defendant asserted that he went into the children's bedroom and saw that they were still sleeping. He then filled the bathtub with water. Defendant returned to the bedroom *1299 and picked up John. He carried the child into the bathroom, placed him in the bathtub, and "held him under the water for a long time." Defendant then repeated the process with Monique, carrying her into the bathroom and holding her under the water "for a long time." After Monique stopped breathing, defendant ripped the shower curtain down and wrapped the two children in it. He then placed the bodies under their bed.
Defendant next kicked in the door to Aretha's bedroom and wrapped Aretha's body in a quilt. He then moved the body to the floor and piled clothing on top of it. Defendant stated he hid the bodies because he was scared and did not want anyone to find them. At this point, it was daylight, and defendant began to get himself ready for work. Defendant then went to work. At the conclusion of his statement, defendant wrote "and regrets it all."
Defendant's aunt, Belinda Maratre, essentially corroborated the statements in defendant's confession regarding the defendant seeking to borrow money from her on the evening of September 2, 1990. The testimony of Corey Bender and Gary Parson also corroborated defendant's statements that he sold various pieces of Aretha's property.
At approximately 1 a.m. on September 3, 1990, Parson and Bernard Mitchell were in the breezeway under Aretha's apartment building when defendant asked Mitchell if he was interested in buying a beeper. Mitchell purchased the beeper for $20. Shortly thereafter, Bender joined Parson and Mitchell in the breezeway. Defendant later approached the men again, this time inquiring if any of them wanted to buy a television. Bender responded that he was interested and asked where the television was. Defendant told Bender that it was at his house and took Bender and Mitchell up to the second floor of the apartment building. Defendant used a key to get into the apartment. Bender asked where the television was, and defendant answered that it was in the back bedroom. Defendant would not allow Bender to go with him to get the television. When Bender asked if he could use the bathroom, defendant told him no and then began closing all the doors in the apartment. When defendant returned with the television, Bender gave him $30 for it. Bender further testified that after he gave defendant the money, defendant asked how he could get rid of three bodies.
Bender and Mitchell then left with the television and returned to the breezeway. A short time later, defendant returned to the breezeway and asked if anyone was interested in a car. Parsons indicated that he was and asked defendant if he could bring the car around to the parking lot so he could look at it. After defendant brought the car around, Parsons got in and looked at the car. Parsons then asked defendant for the title. When defendant could not find the title, Parsons told defendant that he did not want the car. Parsons testified that defendant then drove off.
Bender further testified that when he learned about the murders, he called police. The police eventually picked him up and took him to his apartment to get the television. On September 18, 1990, both Bender and Parsons viewed lineups and identified defendant.
A forensic pathologist testified that he concluded that the cause of death of Aretha was multiple stab wounds, but that he could not rule out suffocation as a possible cause of death or joint cause of death. There were a total of nine stab wounds on the body. The stab wounds were located on the face, head, neck, chest, back, arm, and hands of the body. All wounds were consistent with having been inflicted with a knife. The pathologist further testified that he concluded that the children died as a result of strangulation, but that he could not rule out drowning as an additional cause of death. The pathologist estimated that the time of death was between four to six days prior to his examination. He admitted that a more precise estimate could not be given because the bodies were seriously decomposed.
The theory of the defense was that Wallace was responsible for the murders. The defense introduced evidence that an order of protection had been entered against Wallace. The order of protection restricted Wallace's access to Aretha and the children. Evidence *1300 was also presented that Aretha had made out a police report on April 20, 1990, alleging that Wallace had assaulted her. Moreover, Wallace testified that she had wanted Aretha to get defendant out of the apartment and away from the children. Wallace had told Aretha that defendant was no good because he was on drugs and was abusing Aretha. Wallace also testified that she told Aretha that she would keep trying until she got defendant out of Aretha's life. Wallace further testified, however, that on Mother's Day, Aretha had given her a card apologizing for taking her to court and embarrassing her. After that, Wallace stated, she saw Aretha almost every day, and when she did not see her, she would call Aretha on her beeper.
The defense also elicited testimony from various police officers that blood and other samples collected from Aretha's apartment were not tested to determine if they matched the defendant's blood and hair. Moreover, the only fingerprint lifted from the apartment did not match defendant's fingerprints.
Based on the evidence presented, the jury found defendant guilty of three counts of first degree murder. The same jury found defendant eligible for the death penalty. At the conclusion of the second stage of the sentencing hearing, the jury found that there were no mitigating factors sufficient to preclude imposition of the death penalty. The judge accordingly sentenced defendant to death for the three murders.
Defendant raises numerous allegations of errors in this appeal. In the discussion that follows, we will generally consider these issues in the sequence in which they occurred in the proceedings below.

II. DISCUSSION

A. Suppression Hearing
Defendant contends that he did not receive effective assistance of counsel at a pretrial hearing to suppress defendant's confession. Defendant alleges that trial counsel was ineffective because counsel (1) failed to call a drug expert to explain the impact of drug addiction and cocaine withdrawal on defendant's ability to understand the voluntariness of his confession, and (2) failed to question a number of prosecution witnesses regarding defendant's physical appearance and mental state at the time defendant was taken into custody. Defendant alleges that had counsel presented such evidence, his confession would have been suppressed.
We first summarize the evidence at the suppression hearing. According to the State's testimony, that defendant came to the police station on September 5, 1990, at about 9 p.m. At that time, he was placed in an interview room. Defendant was advised of his Miranda warnings and was questioned by O'Leary for approximately 20 minutes. Defendant was then placed in lock-up.
At approximately 10:20 a.m. the following day, defendant was placed in an interview room. After being placed in the interview room, defendant was again informed of his Miranda warnings. O'Leary and Redmond then proceeded to question defendant. The interview was terminated 20 minutes later when defendant denied committing the murders.
At about 1 p.m., Detective Robert McGuire met with defendant. Defendant was given his Miranda warnings and asked whether he wished to speak to McGuire. Defendant agreed. McGuire testified that during the course of the interview defendant asked if there were any pictures of the crime scene and if he could see them. McGuire retrieved the photos and gave them to defendant. After being given the photos, defendant was given a Coke and a cigarette. Defendant then told McGuire that he wanted to confess. McGuire called O'Leary and Redmond into the room, and defendant subsequently explained how he had killed the victims. O'Leary and Redmond both denied ever telling defendant that his life was not "worth a nickel." They also testified that defendant never mentioned that he was undergoing cocaine withdrawal, nor did they observe any signs of withdrawal or physical trauma.
After defendant finished his statement, the Cook County State's Attorney's office was called. About 4 that afternoon, Assistant State's Attorneys John Mahoney and Michael Gerhardstein met with defendant. Present at this meeting were the two assistant State's *1301 Attorneys, defendant, and McGuire. Mahoney began the questioning by asking defendant how he was feeling and then advised defendant of his Miranda warnings. Defendant was asked whether he understood these rights. Defendant indicated that he did and that he would speak to them about the murders. The interview lasted about an hour.
Around 7:30 p.m., defendant reviewed a written version of his statement. He made corrections to the statement and then signed it. Defendant also signed the backs of photographs taken by the police of the victims' bodies to indicate where defendant had left the bodies. Defendant was then photographed. At the suppression hearing, Mahoney testified that defendant never asked for an attorney, nor was a statement ever made that his life was not worth a nickel. Mahoney further stated that there was nothing unusual about defendant's physical appearance that would indicate he was undergoing cocaine withdrawal.
Testimony was further elicited that detectives involved in defendant's case received awards from the Chicago police department commending them for their work in defendant's case. The award was signed by the commander of the Area One Violent Crimes, Detective Division, Frederick B. Miller, and stated, in part, that after "persistent interrogation" defendant began to make incriminating statements and, after applying "skillful psychological technique," defendant confessed. Miller testified that Sergeant John Ridges submitted the application for the award for his signature, and he therefore could not describe the "skillful psychological skills" that the award referred to or what was meant by the terms "persistent interrogation." Redmond, who received one of the awards, also testified that he did not know the basis of the opinion that "skillful psychological techniques" had been used, nor did he believe that such techniques had been used.
Ridges testified that he recommended that the detectives should receive the award because of the exceptional job they had done in investigating the case that culminated in defendant's confession. Ridges explained that the phrase "skillful psychological techniques" was probably a poor choice of words, but that he tried to summarize a series of events that resulted in defendant's confession. He stated that the reference to "persistent interrogation" was obtained from reports indicating that defendant had been questioned two or three times.
In support of the motion to suppress, defendant's uncle, Charles Maratre, testified that he brought defendant to the police station after being told by defendant's mother that the police wanted to question defendant about the murders. Maratre picked defendant up to take him to the police station at approximately 4:30 p.m. Maratre described defendant as being tired and intoxicated. On cross-examination, Maratre said that he told defendant why he was being taken to the police station and that defendant understood what he was saying. Maratre also stated that defendant asked him questions on the ride over to the station and that the questions made sense. He further testified that defendant was able to get into his car unassisted and was able to walk up the stairs at the police station by himself.
Defendant also testified at the suppression hearing to a version of events different than those the police testified to. Defendant stated that on September 5, 1990, he was at a friend's house getting "high" on cocaine, marijuana and beer. He recalled having about three or four 40-ounce containers of beer and testified that he had "over a hundred dollars worth" or one gram of cocaine. He did not remember how much marijuana he had smoked. While at his friend's house, he called his mother and was told that the police wanted to question him. After speaking with his mother, defendant testified that he continued to get high.
Defendant further asserted that once at the station, Redmond told him, "Look, we know you did it. Her mother told us you did it, so why don't [you] tell us to make it easier on yourself because if you go back on the street, [your] life wouldn't be worth a nickel." He also stated that he was not given his Miranda warnings and that he did ask for an attorney. Defendant testified that when he asked for an attorney Redmond asked whether defendant could afford one. Defendant testified that he then asked to speak *1302 with his mother because he could not afford an attorney. Redmond responded that nothing could be done for defendant now. After that exchange, Redmond began asking defendant questions about the murders saying things like "I won't rest until you tell the truth about what happened" and that "[Aretha and the children] would forgive you if [you] told the truth about the incident."
Defendant further testified that about an hour after that conversation ended, Redmond returned and did not give defendant any Miranda warnings. At this time, Redmond had photos of the victims' bodies and essentially told him the same things as before. Defendant also stated that when he was returned to lock-up, he overheard Redmond tell a guard not to permit defendant to have a phone call. Defendant further testified that when he spoke with McGuire he was not given his Miranda rights and that he was sick to his stomach, light-headed, cold and confused. He further claimed that he did not remember speaking with the assistant State's Attorneys. On cross-examination, defendant testified that he understood the conversation he had with his mother and that he further understood why his uncle was taking him to the police station. He also stated that the signature on the confession looked like his signature, but he did not remember signing it.
In rebuttal, both Redmond and McGuire testified that defendant was given his Miranda warnings and denied that defendant ever asked for an attorney. They further denied making any of the statements defendant attributed to them. Moreover, both Redmond and McGuire asserted that defendant did not appear to beill, nor did defendant complain of being ill. Based on the evidence presented at the suppression hearing, the trial judge denied defendant's motion to suppress.
In Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the United States Supreme Court established a two-prong test for considering ineffective-assistance claims. See also People v. Albanese, 104 Ill.2d 504, 525-26, 85 Ill.Dec. 441, 473 N.E.2d 1246 (1984). To succeed on an ineffective-assistance claim, a defendant must establish that counsel's performance was deficient and that the deficient performance was prejudicial to the defense. Strickland, 466 U.S. at 687,104 S.Ct. at 2064, 80 L.Ed.2d at 693. To establish prejudice, a defendant "must show that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." Strickland, 466 U.S. at 694, 104 S.Ct. at 2068, 80 L.Ed.2d at 698. A reviewing court "need not determine whether counsel's performance was deficient before examining the prejudice suffered by the defendant as a result of the alleged deficiencies." Strickland, 466 U.S. at 697, 104 S.Ct. at 2069, 80 L.Ed.2d at 699.
Assuming that trial counsel was deficient for failing to call a drug expert to testify and for failing to question the prosecution's witnesses about defendant's state at the time he was arrested, we do not believe that defendant was prejudiced as a consequence of these alleged deficiencies in counsel's representation. The State's evidence at the suppression hearing consisted primarily of testimony from detectives and an assistant State's Attorney who had questioned defendant while in custody. All the witnesses testified that defendant did not show symptoms of undergoing cocaine withdrawal, nor did defendant ever mention that he was ill. Moreover, defendant's own testimony, as well as his uncle's, showed that defendant was lucid and understood why he was being taken to the police station for questioning. The State further presented evidence that defendant was given his Miranda warnings on various occasions and that defendant expressed his desire to speak with the police and an assistant State's Attorney. The trial judge found the State's witnesses to be more credible and denied the motion to suppress. The evidence that defendant made his statement's "freely, voluntarily and without compulsion or inducement of any sort" was compelling. People v. Clark, 114 Ill.2d 450, 457, 103 Ill.Dec. 102, 501 N.E.2d 123 (1986). Since the State had already made clear that defendant did not show signs of cocaine withdrawal, we do not believe that there is a reasonable probability that the motion to suppress would have been granted had defense *1303 counsel called an expert or questioned the prosecution's witnesses about defendant's physical state. "A reasonable probability is a probability sufficient to undermine confidence in the outcome." Strickland, 466 U.S. at 694, 104 S.Ct. at 2068, 80 L.Ed.2d at 698. Our confidence in the outcome of the suppression hearing has not been undermined.

B. Voir Dire

Defendant next raises several challenges to the selection of the jury in his case. Defendant argues that he is entitled to a new sentencing hearing because the trial judge failed to follow the mandate of Morgan v. Illinois, 504 U.S. 719, 112 S.Ct. 2222, 119 L.Ed.2d 492 (1992), in life-qualifying prospective jurors. In Morgan, the Supreme Court held that it was a violation of due process for a trial judge in a capital case to refuse to ask potential jurors during voir dire whether they would automatically impose the death penalty if defendant should be convicted. Morgan, 504 U.S. at 734-39, 112 S.Ct. at 2232-35, 119 L.Ed.2d at 506-09. Defendant claims that the trial judge violated the mandates of Morgan by refusing to ask the following question offered by him: "If you sign a guilty verdict convicting Anton Brown of first degree murder of a two-year old child, a three-year-old child and their mother, would you be able to consider reasons not to impose the death penalty, or would you automatically impose the death penalty?"
Although the trial judge refused to ask the question submitted by defendant, the trial judge did ask the following question to all prospective jurors:
"Does anybody who is on the jury have any philosophical, religious, conscientious scruples or convictions that would require them automatically to impose the death penalty if there were a guilty verdict? Do you understand the question? I am just asking the reverse. Is there anybody who would find they would automatically impose the death penalty?
* * * * * *
I am asking you to tell us whether or not you have such strong convictions that you could not ever vote for the death penalty or that you would always vote for the death penalty. We are looking for the extremes.
It is probable that most of the people here are in the middle, and they might think there are cases where the death penalty is appropriate and they might think there are cases where the death penalty is not appropriate. These questions are aimed at finding the people who would never vote for the death penalty under all circumstances or only vote for the death penalty if there is a conviction of murder rather than some other sentence. * * * So that's the question. Is there anybody that could always vote for the death penalty under all circumstances?"
We find that the trial judge in this case fully complied with Morgan. Morgan held only that a defendant is entitled to have potential jurors questioned as to whether they would automatically vote to impose the death penalty upon a finding of guilt, without regard to the aggravating or mitigating circumstances present in the case. See People v. Hope, 168 Ill.2d 1, 29, 212 Ill.Dec. 909, 658 N.E.2d 391 (1995). The trial judge here asked all the potential jurors whether they would automatically vote to impose death if they should convict defendant of murder. The question submitted by defendant, inquiring how the venire members would act given the particular aggravating circumstances of the victims' murders in the present case, is clearly not required by Morgan. Hope, 168 Ill.2d at 29, 212 Ill.Dec. 909, 658 N.E.2d 391. To the contrary, Morgan specifically directed its holding toward discovering jurors for whom "the presence or absence of either aggravating or mitigating circumstances is entirely irrelevant." Morgan, 504 U.S. at 729, 112 S.Ct. at 2229, 119 L.Ed.2d at 502-03. Conducting an inquiry into whether a potential juror would vote to impose the death penalty, given a particular set of circumstances, is thus not required by Morgan. Hope, 168 Ill.2d at 30, 212 Ill.Dec. 909, 658 N.E.2d 391.
Further, we note that the questions propounded by the trial judge were sufficient to cull from prospective jurors their view on the death penalty so that defendant could intelligently *1304 exercise his challenges for cause of prospective jurors who would unwaveringly impose the death penalty after a finding of guilt. The judge's questions were not generalized questions of fairness and impartiality, but rather were specific questions aimed at determining a prospective juror's view on imposing the death penalty. Thus, we find that the trial judge's voir dire was sufficient to satisfy defendant's right under Morgan to make inquiry. Accordingly, we reject defendant's argument that his right to have the jury "life-qualified" was denied by the denial of his proffered question.
The defendant next argues that the trial judge erred in dismissing for cause prospective juror Mildred Gore. Defendant argues that the trial court erred in dismissing Gore without conducting a specific inquiry as to whether she could set aside her scruples against the death penalty and follow her oath.
At the beginning of voir dire, the trial judge asked the venire members whether any of them had religious or moral scruples that would prevent them from imposing the death penalty. Gore was one of the four venire members who said that they did. The following is an excerpt from the voir dire examination of Gore:
"[Judge Neville]: Is your opinion such that no matter what the facts were, no matter what the facts in the case were or no matter what the background of the defendant was, that under no circumstances would you ever consider signing a verdict directing the Court to sentence the defendant to death?
[Prospective Juror Thompson]: I don't feel I could make that decision.
[Judge Neville]: So is your answer you would always vote no no matter what the facts were, no matter what the background was?
[Prospective Juror Thompson]: Yes.
[Judge Neville]: Ms. Gore, what about you?
[Prospective Juror Gore]: The same."
During a subsequent individual voir dire examination of Thompson, Thompson indicated that she did not know whether she could vote to impose the death penalty. She further stated that she could not say that under no circumstances would she consider the death penalty. Defendant argues that because Thompson changed her answer after individual voir dire, Gore was improperly excused without having the same opportunity.
A venire member who expresses only general objections to the death penalty may not be excused for cause. People v. Mahaffey, 128 Ill.2d 388, 416, 132 Ill.Dec. 366, 539 N.E.2d 1172 (1989). A venire member's views regarding the death penalty will however warrant exclusion for cause where they will "`prevent or substantially impair the performance of his duties as a juror in accordance with his instructions and his oath.'" Wainwright v. Witt, 469 U.S. 412, 424, 105 S.Ct. 844, 852, 83 L.Ed.2d 841, 851-52 (1985), quoting Adams v. Texas, 448 U.S. 38, 45, 100 S.Ct. 2521, 2526, 65 L.Ed.2d 581, 589 (1980). A trial judge is granted wide discretion in ruling on a motion to excuse a potential juror for cause based upon the juror's voir dire. Hope, 168 Ill.2d at 31, 212 Ill.Dec. 909, 658 N.E.2d 391; People v. Seuffer, 144 Ill.2d 482, 502, 163 Ill.Dec. 805, 582 N.E.2d 71 (1991).
The trial judge in the present case found that Gore's response to the question reflected Thompson's response that she would never vote for the death penalty under any circumstance. The judge found Gore's response to the question posed to be succinct and unequivocal, reflecting a disqualifying attitude toward the death penalty or its imposition. Consequently, the judge concluded that further inquiry was unnecessary. To the contrary, however, the judge found Thompson's first response that she did not feel that she could make a decision to impose the death penalty to be equivocal. Therefore, the trial judge allowed further inquiry into her view toward the death penalty.
From our review of the record, we conclude that the trial judge did not abuse his discretion in excusing Gore for cause without additional inquiry into her view on the death penalty. As the trial judge noted, Gore's response was succinct and unequivocal. Given the trial judge's superior position in determining the meaning of a juror's remarks, we *1305 cannot say that the judge erred in excusing Gore for cause. Hope, 168 Ill.2d at 31, 212 Ill.Dec. 909, 658 N.E.2d 391; People v. Steidl, 142 Ill.2d 204, 244, 154 Ill.Dec. 616, 568 N.E.2d 837 (1991); Mahaffey, 128 Ill.2d at 416-17, 132 Ill.Dec. 366, 539 N.E.2d 1172.
Defendant also contends that he is entitled to a new trial because the trial court prohibited him from making a prima facie case of racial discrimination under Batson v. Kentucky, 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69 (1986), prior to swearing in the jury and in failing to give proper consideration to his claim.
When defense counsel initially raised a Batson challenge, the judge stated that he thought the allegation was insulting. He further told defense counsel that he would have to make his record at another time. Defense counsel responded that he had to make a record, and the trial judge said that he was going to let him make a record all through the trial. After the jury had been selected and the trial began, the trial judge then allowed defense counsel to make a complete Batson challenge to the selection of the jury on the record. Without having the State respond to the allegations, the trial judge found that there was no Batson violation.
Although we agree with defendant that it is better that challenges to the composition of the jury be resolved prior to the swearing in of the jury, we do not believe that defendant was prejudiced by not resolving the issue until after the jury was sworn because there was clearly no violation of Batson in this case. Under Batson, a defendant must first establish a prima facie case of purposeful discrimination in jury selection by showing that (1) defendant belongs to a racial group capable of being singled out for differential treatment; (2) the State removed members of defendant's race from the venire by using peremptory challenges; and (3) these facts "`and any other relevant circumstances raise an inference'" of purposeful racial discrimination. People v. Jackson, 145 Ill.2d 43, 99, 163 Ill.Dec. 859, 582 N.E.2d 125 (1991), quoting People v. Hope, 137 Ill.2d 430, 452, 148 Ill.Dec. 252, 560 N.E.2d 849 (1990). Examples of possible "relevant circumstance" include (1) a pattern of strikes against black venire members; (2) disproportionate use of strikes against such members; (3) whether the excluded blacks were a heterogenous group sharing race as their only common character; (4) the level of black representation in the venire as compared to the jury; (5) prosecutorial questions and statements during voir dire and while exercising challenges; and (6) the races of defendant and victim or of defendant and witnesses. Jackson, 145 Ill.2d at 99, 163 Ill.Dec. 859, 582 N.E.2d 125; People v. Garrett, 139 Ill.2d 189, 203, 151 Ill.Dec. 329, 564 N.E.2d 784 (1990).
Since Batson, the Supreme Court has held that a defendant may object to the race-based exclusion of jurors whether or not the defendant and the excluded venire members share the same race. Powers v. Ohio, 499 U.S. 400, 111 S.Ct. 1364, 113 L.Ed.2d 411 (1991). Therefore, the only question that remains is whether, considering "all relevant circumstances," defendant has established a prima facie case of discrimination. People v. Edwards, 144 Ill.2d 108, 151-53, 161 Ill.Dec. 788, 579 N.E.2d 336 (1991). A trial court's determination that a defendant has failed to establish a prima facie case of discrimination will not be overturned unless it is against the manifest weight of the evidence. Mahaffey, 128 Ill.2d at 413, 132 Ill.Dec. 366, 539 N.E.2d 1172.
Considering the circumstances in this case, we conclude that the trial court's finding that defendant failed to establish a prima facie case of discrimination was not against the manifest weight of the evidence. At the conclusion of the jury selection, the State had used three challenges. The excluded venire members did not share race as their only common characteristic for being excused. One of the black venire members was a disgruntled former police officer, and another had relatives who were criminal defense attorneys that worked in the building. As to the other venire member the State excused, we note that defendant sought to exclude this prospective juror first. Further, five of the jurors sitting in defendant's case were black. Moreover, defendant and the three victims were of the same race. The *1306 record also does not reflect any statements or questions by the State illustrating a motivation to exclude black jurors on the basis of their race. Because none of the relevant circumstances for establishing purposeful discrimination are evident in the record, we conclude that the trial judge gave thoughtful consideration to defendant's claim and properly determined that defendant failed to make a prima facie showing of purposeful racial discrimination.

C. Guilt Phase
Defendant next argues that he was denied effective assistance at trial because trial counsel (1) failed to present any evidence of defendant's drug addiction or drug usage, (2) failed to introduce into evidence that certain detectives received awards as the result of their investigation of defendant's case or failed to effectively cross-examine the detectives regarding these awards, and (3) failed to present any evidence regarding defendant's physical and mental state at the time he signed his confession.
As previously noted, claims of ineffective assistance of counsel are examined under the two-prong test established in Strickland. See also Albanese, 104 Ill.2d at 527, 85 Ill. Dec. 441, 473 N.E.2d 1246. Under Strickland, a defendant must show both a deficiency in counsel's performance and that there is a reasonable probability that, but for counsel's errors, the result of the proceeding would have been different. Strickland, 466 U.S. at 694, 104 S.Ct. at 2068, 80 L.Ed.2d at 698; People v. Hampton, 149 Ill.2d 71, 108, 171 Ill.Dec. 439, 594 N.E.2d 291 (1992). A court may resolve the ineffective-assistance claim without determining whether counsel was actually deficient, if the court is able to conclude that no prejudice resulted from the complained of conduct. Strickland, 466 U.S. at 697, 104 S.Ct. at 2069, 80 L.Ed.2d at 699; People v. Flores, 153 Ill.2d 264, 283-84, 180 Ill.Dec. 1, 606 N.E.2d 1078 (1992).
In the present case, we find that even if trial counsel's performance was deficient as defendant alleges, such deficiencies would not have affected the outcome of the trial. Defendant gave a detailed confession to the murders, and his confession was corroborated by various other witnesses. Moreover, there was extensive evidence that defendant's confession was voluntarily given. We therefore cannot say that defense counsel's alleged deficiencies in failing to present evidence of defendant's drug usage, his physical state at the time he confessed, or evidence of the awards certain detectives received would have changed the outcome of defendant's trial. Witnesses testified that defendant did not appear to be under the effect of drugs or cocaine withdrawal at the time of his confession, and an innocent explanation was given for the words used on the award certificates. Further, evidence that defendant committed the murders was overwhelming. Accordingly, we reject defendant's claim of ineffective assistance of counsel.
Defendant next argues that the trial court erred in several of its evidentiary rulings. Specifically, defendant claims that the trial judge erred in limiting his cross-examination of Wallace with regard to the fact that she had previously used a false name and gave a false birth date to the police. Defendant further argues that the trial judge erred in refusing to reopen the cross-examination of Wallace to allow evidence that Wallace had been arrested for criminal trespass to a vehicle, that she used a false name and birth date at the time she was arrested for the trespass, and that she had previously been arrested for obstructing the police and for battering a police officer. Defendant also argues that the trial court erred in refusing to permit into evidence specific allegations Aretha made about her mother in seeking an order of protection. These allegations included that Wallace had allegedly abused and threatened to kill Aretha on several occasions. Moreover, defendant alleges that the trial court erred in allowing the prosecution to elicit testimony from Wallace regarding the contents of the note Wallace found at Aretha's apartment on September 4, 1990.
As previously noted, the evidence of guilt marshalled by the State against defendant was overwhelming. Not the least of it was defendant's statements to the police that he had committed the murders of the three victims. Among the other evidence of defendant's guilt was testimony from his aunt that *1307 corroborated defendant's statement that before killing the victims he attempted to borrow money from her. Defendant's confession was also corroborated by the testimony of two individuals that he had sold Aretha's property following the murders. Testimony from various police officers connected to the case and the pathologist also corroborated defendant's statements about how and when the murders had occurred. Because of the compelling evidence adduced against defendant at trial, we find that even if the trial judge erred in his evidentiary rulings, as defendant claims, the errors were harmless beyond a reasonable doubt. People v. Williams, 164 Ill.2d 1, 23, 206 Ill.Dec. 592, 645 N.E.2d 844 (1994).
Defendant also argues that the trial court erred in refusing to permit defendant to cross-examine Corey Bender about his parole status and the pending criminal charge against him. Defendant alleges that this information would have established Bender's bias or motive to testify falsely. Again, we find that based on the overwhelming evidence of defendant's guilt any error committed in the trial judge's ruling was harmless beyond a reasonable doubt.
Defendant next contends that the trial judge's hostility toward defense counsel and defendant denied him a fair trial. In support of his argument, defendant points to eight separate incidents which allegedly reflect the trial judge's hostility toward defense counsel and defendant.
It is well settled that the trial judge has a duty to refrain from conveying improper impressions to the jury. People v. Harris, 123 Ill.2d 113, 137, 122 Ill.Dec. 76, 526 N.E.2d 335 (1988). A hostile attitude toward defense may be prejudicial and erroneous. Harris, 123 Ill.2d at 137, 122 Ill.Dec. 76, 526 N.E.2d 335. However, for a trial judge's comments to constitute reversible error, defendant must demonstrate that the comments constituted a material factor in the conviction or were such that an effect on the jury verdict was the probable result. Harris, 123 Ill.2d at 137, 122 Ill.Dec. 76, 526 N.E.2d 335; see also People v. Heidorn, 114 Ill.App.3d 933, 937, 70 Ill.Dec. 439, 449 N.E.2d 568 (1983). In his argument, defendant points to a number of instances in the record allegedly reflecting the trial judge's hostility toward defense. Defendant does not, however, attempt to demonstrate how these alleged instances of hostility constituted a material factor in the outcome of his trial. We therefore reject defendant's argument.
Defendant next contends that the trial court erred in denying defendant's motion for a continuance before allowing Ezekial Ajoa, the supervisor where Aretha worked, to testify. Prior to jury selection, the State presented an amended answer to discovery. The amended answer provided the defense with the names of additional witness who would be called at trial, including Ajoa. Defendant objected to Ajoa's being called as a witness. The assistant State's Attorney informed the trial judge that Ajoa would testify that Aretha was scheduled to work on September 3, 1990, but that she did not show up for work. When defense counsel pointed out that there were no time records showing this, the assistant State's Attorney informed the trial judge that Ajoa would be testifying from memory. The assistant State's Attorney further informed the trial judge that the facts Ajoa would be testifying to were mentioned in the police reports and the only thing new was the name of the person who was going to provide that information. The defense later asked for a continuance in order to subpoena employment records from Aretha's place of employment. The motion was denied. Defendant now claims that it was error to deny the motion because he was not given a reasonable opportunity to determine whether records existed supporting Ajoe's "recollection" of Aretha's work schedule.
It is clear that the granting of a continuance for additional time to prepare for trial is a matter resting within the sound discretion of the trial court. People v. Lewis, 165 Ill.2d 305, 327, 209 Ill.Dec. 144, 651 N.E.2d 72 (1995). Where it appears that the refusal of additional time in some manner embarrassed the accused in the preparation of his defense and thereby prejudiced his rights, a resulting conviction will be reversed. Lewis, 165 Ill.2d at 327, 209 Ill.Dec. 144, 651 *1308 N.E.2d 72. Where, however, there is sufficient evidence to support a finding of guilt, the denial of a continuance will not constitute reversible error. Lewis, 165 Ill.2d at 327, 209 Ill.Dec. 144, 651 N.E.2d 72.
In the present case, we find that defendant was not prejudiced by the denial of his motion for continuance. As was previously stated, the fact that Aretha did not show up for work was contained in the police reports. Had defendant wanted to obtain Aretha's employment records to verify her absence, defendant could have done so before trial. We therefore do not find that the denial of defendant's motion for a continuance hampered the preparation of his defense. Moreover, defendant does not show how the continuance would have affected the outcome of the trial, nor do we believe that it did. We therefore reject defendant's argument.
Defendant further argues that the trial court erred by admitting into evidence autopsy photographs of the victims, photographs of the victims at the scene of the crimes, and photographs of Aretha's stab wounds. Defendant contends that the autopsy photos and the photos from the crime scene were not relevant and, therefore, there was no reason to admit them into evidence other than to inflame the jury. As to the photographs of the stab wounds, defendant alleges that these photos were cumulative of the medical examiner's testimony regarding the location and number of the wounds and therefore served only to inflame the prejudices of the jury.
The decision to admit photographs into evidence is left to the discretion of the trial judge, and the judge's decision will not be overturned absent an abuse of discretion. People v. Kitchen, 159 Ill.2d 1, 34, 201 Ill.Dec. 1, 636 N.E.2d 433 (1994); People v. Henderson, 142 Ill.2d 258, 319, 154 Ill.Dec. 785, 568 N.E.2d 1234 (1990); People v. Scott, 148 Ill.2d 479, 546, 171 Ill.Dec. 365, 594 N.E.2d 217 (1992); People v. Lucas, 132 Ill.2d 399, 439, 139 Ill.Dec. 447, 548 N.E.2d 1003 (1989). Among the valid reasons for admitting photographs of a decedent is to prove the nature and extent of injuries and the force needed to inflict them, the position, condition, and location of the body, and the manner and cause of death, to corroborate a defendant's confession, and to aid in understanding the testimony of a pathologist or other witness. Kitchen, 159 Ill.2d at 35, 201 Ill.Dec. 1, 636 N.E.2d 433; Henderson, 142 Ill.2d at 320, 154 Ill.Dec. 785, 568 N.E.2d 1234; see also People v. Owens, 65 Ill.2d 83, 90, 2 Ill.Dec. 298, 357 N.E.2d 465 (1976). Moreover, while such photographs may be cumulative of the testimony of a witness, they may also aid jurors in understanding this testimony. Henderson, 142 Ill.2d at 320, 154 Ill.Dec. 785, 568 N.E.2d 1234; Owens, 65 Ill.2d at 90, 2 Ill.Dec. 298, 357 N.E.2d 465. If photographs are relevant to prove facts at issue, they are admissible and can be shown to the jury unless their nature is so prejudicial and so likely to inflame the jurors' passions that their probativeness is outweighed. Kitchen, 159 Ill.2d at 35, 201 Ill.Dec. 1, 636 N.E.2d 433.
The challenged photos were not included in the record. Based on this state of the record, we are unable to say that the trial judge abused his discretion by admitting the photographs. Scott, 148 Ill.2d at 547, 171 Ill.Dec. 365, 594 N.E.2d 217. We also note that based on descriptions of the photos in the parties' briefs it would seem that each photo met at least one of the above criteria for admission. The photos apparently established the nature and extent of the injuries, they corroborated defendant's confession, and they aided the jury in understanding testimony regarding the causes of death.
Defendant also argues that the trial judge erred in permitting the State to display Aretha's nightgown on the torso of a mannequin. Defendant contends that the display of the nightgown in this manner served no other purpose than to inflame the jury. The record does not include a photo of the mannequin used. We are therefore unable to say that the trial judge abused his discretion by allowing the State to use a mannequin to display the nightgown.
Defendant next complains that certain comments made by the prosecution during rebuttal argument violated his constitutional rights. Defendant argues that these remarks were prejudicial and denied him a *1309 fair trial because they could only be interpreted by the jury as shifting the burden of proof to the defendant.
In rebuttal argument, the prosecutor stated:
"Make it Christmas for him and rationalize every piece of evidence, but the point remains why is it necessary for someone to have to explain away that amount of evidence? Not one or two things does he have to explain; but we just heard an hour of explanation as to each little thing that he has to explain. Why? Because each and every circumstance, each and every piece of evidence, it's not deflected. It goes right to Anton Brown and to nobody else.
* * * * * *
If there was anybody in the world that could describe the relationship between those two women [Aretha and Wallace], post-April as different than Gloria described it, you can be sure the defense would have had the people up on the stand."
We do not agree with the defendant that the jury would have understood the preceding comments as shifting the burden of proof to the defense. The prosecutor was simply making references to the evidence and/or defendant's arguments. Moreover, as the State correctly points out, the latter comment was in response to statements made by defense counsel in closing arguments:
"I believe the evidence in this case shows that [Wallace], if she didn't come right out and lie, she certainly exaggerated. She certainly stretched the truth in significant portions of her testimony.
But you think probably the most important piece or lack of evidence regarding Gloria is there's no support for her. There's nobody. They didn't bring out anybody or anything to show us that Gloria Wallace is a truthful person.
Where is anybody fromthat Gloria knows, that Aretha knows, that said yeah, Aretha and I were on good terms. The Order of Protection is old news. We patched our differences up. Nothing."
The prosecutor's comment regarding the absence of witnesses may therefore be construed as a response to defense counsel's own comments. Because the comments were invited, they cannot be relied upon as error on appeal. Mahaffey, 128 Ill.2d at 423-25, 132 Ill.Dec. 366, 539 N.E.2d 1172 (finding that the prosecutor's comment during rebuttal argument regarding defense counsel's failure to call a certain witness was invited by references in defense counsel's argument that the State failed to call the witness).
As a final contention that he is entitled to a new trial, defendant contends that the trial judge erred in refusing to allow the public defender to withdraw based on a conflict of interest. Defendant was initially represented by Assistant Public Defender Kathleen Pantel of the Murder Task Force. When it became clear that the State might call as a witness a man whom she represented, Pantel sought leave to withdraw as counsel. Her supervisor also sought leave to withdraw. The motion was granted, and Gerald Block, another assistance public defender, was appointed to represent defendant. Block eventually moved to withdraw as counsel, explaining that appointment of new counsel did not cure the conflict that necessitated the withdrawal of Pantel and her supervisor. He also alleged that his own expertise was not the equivalent of members of the Murder Task Force. On appeal, defendant essentially argues that because one public defender had a conflict of interest every public defender in the same office had a conflict of interest.
In People v. Robinson, 79 Ill.2d 147, 37 Ill.Dec. 267, 402 N.E.2d 157 (1979), this court held that, in determining whether a conflict of interest exists, individual attorneys who comprise the staff of the public defender, unlike members of a private law firm, are not members of an entity, "which should be subject to the rule that if one attorney is disqualified by reason of a conflict of interest then no other member of the entity may continue with the representation." Robinson, 79 Ill.2d at 159, 37 Ill.Dec. 267, 402 N.E.2d 157. The Robinson court stated that a case-by-case examination was necessary to determine whether any facts peculiar to the *1310 case preclude the representation of the individuals whose interests were allegedly in conflict. Here, the only relationship between counsel is the fact that they were both employed by the same public defender. No conflict is shown by the record and nothing indicates that counsel's representation of defendant was in any manner inhibited. Under the circumstances shown by the record, the court did not err in denying counsel's motion to withdraw. See also People v. Coates, 109 Ill.2d 431, 94 Ill.Dec. 421, 488 N.E.2d 247 (1985).

D. Sentencing
Having determined that no reversible error occurred during the guilt phase of defendant's trial, we now consider the alleged errors at the sentencing phase.

1. Eligibility Phase

Defendant contends that his death sentence must be vacated and his cause remanded for a new sentencing hearing because his death sentence was imposed based on the unconstitutionally vague aggravating factor of section 9-1(b)(7) of the Criminal Code of 1961 (Code) (Ill.Rev.Stat.1989, ch. 38, par. 9-1(b)(7)). This section provides that a person convicted of murder is eligible for the death penalty if "the murdered individual was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty." Ill.Rev.Stat. 1989, ch. 38, par. 9-1(b)(7). Defendant argues that the terms used in the statute to describe the conduct that will sustain a finding of eligibility"exceptionally brutal or heinous behavior indicative of wanton cruelty"are unconstitutionally vague because they fail to adequately channel the discretion of the sentencer without a limiting construction. See Maynard v. Cartwright, 486 U.S. 356, 108 S.Ct. 1853, 100 L.Ed.2d 372 (1988). Defendant argues that the trial judge should have instructed the jury that eligibility under section 9-1(b)(7) requires that the murder involve prolonged pain, torture, or premeditation. Because the jury did not have the benefit of such a "limiting instruction," defendant argues his death sentence must be vacated and his cause remanded for resentencing. See Lucas, 132 Ill.2d at 443-46, 139 Ill.Dec. 447, 548 N.E.2d 1003; People v. Tye, 141 Ill.2d 1, 31-32, 152 Ill.Dec. 249, 565 N.E.2d 931 (1990).
A defendant may not generally challenge an instruction on appeal unless he makes a contemporaneous objection and, if appropriate, tenders an alternative instruction at trial. People v. Rissley, 165 Ill.2d 364, 406, 209 Ill.Dec. 205, 651 N.E.2d 133 (1995); People v. Banks, 161 Ill.2d 119, 146, 204 Ill.Dec. 107, 641 N.E.2d 331 (1994). Although defendant objected to the proposed instruction, citing Lucas, defendant only argued that the facts surrounding the death of the two children did not constitute "exceptionally brutal or heinous behavior indicative of wanton cruelty" as that phrase was defined in Lucas. We note that defendant did not object on the ground that the instruction was unconstitutionally vague without a limiting instruction, nor did he submit an alternative instruction containing the limiting language. We therefore find any error waived. Rissley, 165 Ill.2d at 407, 209 Ill.Dec. 205, 651 N.E.2d 133.
We have, however, recognized a narrow exception to the waiver rule. Rissley, 165 Ill.2d at 407, 209 Ill.Dec. 205, 651 N.E.2d 133; People v. Easley, 148 Ill.2d 281, 336-38, 170 Ill.Dec. 356, 592 N.E.2d 1036 (1992); 134 Ill.2d R. 451(c). Plain errors affecting substantial rights may be considered by a reviewing court even if a defendant fails to properly preserve the issue. 134 Ill.2d R. 451(c). The plain error rule applies when the evidence is closely balanced or when the error is of such magnitude that it deprives the defendant of a fair trial. People v. Fields, 135 Ill.2d 18, 60, 142 Ill.Dec. 200, 552 N.E.2d 791 (1990); People v. Carlson, 79 Ill.2d 564, 576-77, 38 Ill.Dec. 809, 404 N.E.2d 233 (1980). We do not find the evidence in this case closely balanced, and thus examine whether the alleged error deprived defendant of a fair trial.
Further, we do not believe that failing to instruct the jury with the limiting language of Lucas would have deprived defendant of a fair trial because any error in that regard was harmless beyond a reasonable doubt. In Clemons v. Mississippi, 494 U.S. 738, 741, 110 S.Ct. 1441, 1444, 108 *1311 L.Ed.2d 725, 733 (1990), the Supreme Court held that the federal Constitution does not prevent a state reviewing court from upholding a death sentence that is based, in part, on an invalid or improperly defined aggravating circumstance either by reweighing the aggravating and mitigating evidence or on the grounds of harmless error. See also People v. Tenner, 157 Ill.2d 341, 387, 193 Ill.Dec. 105, 626 N.E.2d 138 (1993); People v. Pitsonbarger, 142 Ill.2d 353, 376-77, 154 Ill.Dec. 562, 568 N.E.2d 783 (1990). Here, we find that even had the jury been given the limiting instruction in Lucas, the jury would have reached the same result, and thus conclude that any alleged error was harmless beyond a reasonable doubt.
The evidence showed that after defendant murdered Aretha and sold some of her belongings, he sat on the couch in the apartment to think about what to do with the children. Defendant then methodically filled the bathtub with water. He subsequently carried John, who was asleep in his bed, into the bathroom and held his head under the water for a "long time." Defendant subsequently repeated the process with Monique. After that, defendant wrapped the children in a shower curtain and placed them under Monique's bed. Based on the evidence, we find that the murder of the two children comports with the established definition of the phrase "exceptionally brutal or heinous behavior indicative of wanton cruelty." See Banks, 161 Ill.2d at 146, 204 Ill.Dec. 107, 641 N.E.2d 331; People v. Fair, 159 Ill.2d 51, 80-82, 201 Ill.Dec. 23, 636 N.E.2d 455 (1994); Tye, 141 Ill.2d at 32, 152 Ill.Dec. 249, 565 N.E.2d 931. Thus, we find that any error that occurred in failing to instruct the jury on the limiting language in Lucas does not require a remand for resentencing.

2. Sentencing Phase

Defendant next contends that his first amendment right of freedom of association was violated by the introduction of evidence in the capital sentencing hearing that he was a member of a gang. Relying on Dawson v. Delaware, 503 U.S. 159, 112 S.Ct. 1093, 117 L.Ed.2d 309 (1992), defendant contends that his death sentence should be vacated and the cause remanded for a new sentencing hearing because the evidence of his gang affiliation was not relevant to any issue at sentencing.
In Dawson, the Court held that it was a violation of a person's first amendment right to freely associate when the State introduces evidence during a death penalty hearing regarding a defendant's gang affiliation, when it is irrelevant to proving any aggravating circumstances. Dawson, 503 U.S. at 166, 112 S.Ct. at 1098, 117 L.Ed.2d at 317-18; see also People v. Ward, 154 Ill.2d 272, 342, 181 Ill.Dec. 884, 609 N.E.2d 252 (1992) (first amendment violation occurs upon admission of evidence of gang affiliation that is "irrelevant to proving any aggravating circumstances"). However, evidence of gang affiliation is admissible during a capital sentencing hearing to show a defendant's behavior, violations, and discipline while in prison. Hope, 168 Ill.2d at 38-39, 212 Ill.Dec. 909, 658 N.E.2d 391; People v. Simms, 168 Ill.2d 176, 191-92, 213 Ill.Dec. 576, 659 N.E.2d 922 (1995); People v. Coleman, 158 Ill.2d 319, 357, 198 Ill.Dec. 813, 633 N.E.2d 654 (1994). Evidence of gang affiliation may also be admitted to rebut mitigating evidence offered by a defendant. Dawson, 503 U.S. at 167-68, 112 S.Ct. at 1098-99, 117 L.Ed.2d at 318-19 ("just as the defendant has the right to introduce any sort of relevant mitigating evidence, the State is entitled to rebut that evidence with proof of its own").
The trial judge denied defendant's motion in limine seeking to exclude any evidence of defendant's involvement in gangs. In the wake of that adverse ruling, defendant in mitigation elicited testimony from Redmond that he had never seen defendant involved in any gang activities. Defendant also presented testimony from Maratre that he had no knowledge of defendant's ever being involved with gangs. In rebuttal the State introduced a photograph of the defendant wearing a shirt with a gang symbol on it, and testimony from an expert on street gangs explaining the meaning of the symbol.
Contrary to the State's argument, we do not believe that defendant's own presentation of gang-related testimony waived any objection to the State's evidence or opened the *1312 door to its introduction. As defendant observes, his use of such testimony was in response to the trial court's adverse disposition of the defense motion in limine, and defense counsel apparently sought to blunt the impact of the State's planned introduction of this information. See People v. Williams, 161 Ill.2d 1, 34, 204 Ill.Dec. 72, 641 N.E.2d 296 (1994); People v. Spates, 77 Ill.2d 193, 198-200, 32 Ill.Dec. 333, 395 N.E.2d 563 (1979).
Nevertheless, we believe that any error in the trial judge's ruling on the motion in limine was harmless beyond a reasonable doubt. The circumstances surrounding the present offenses, as described earlier, were particularly aggravating. In addition, there was evidence of prior criminal activity by defendant. On this record, we believe that the admission of information concerning the defendant's gang involvement was harmless beyond a reasonable doubt. See People v. Ward, 154 Ill.2d 272, 344, 181 Ill.Dec. 884, 609 N.E.2d 252 (1992).
Defendant next contends that his constitutional rights were violated by the introduction of evidence regarding his criminal history through unreliable hearsay testimony. Specifically, defendant objects to the testimony of Officer Frederick Barrett that an alleged victim, Jerry Singleton, told Barrett that defendant handed a gun to another person and told this person to shoot Singleton. Defendant also objects to Barrett's testimony that he later found a gun in the vicinity where defendant and the other person were and that the bullets in the gun had "filed" tips. Moreover, defendant asserts that this hearsay also provided insufficient foundation for the admission into evidence of the gun and the "filed" bullets.
At a capital sentencing hearing, the rules of evidence are relaxed and evidence is admissible as long as it is both relevant and reliable. Simms, 168 Ill.2d at 190, 213 Ill.Dec. 576, 659 N.E.2d 922; People v. Edgeston, 157 Ill.2d 201, 236, 191 Ill.Dec. 84, 623 N.E.2d 329 (1993). The evaluation of a testimony's relevance and reliability lies within the sound discretion of the trial judge. Jackson, 145 Ill.2d at 115, 163 Ill.Dec. 859, 582 N.E.2d 125. The fact that the evidence presented contains hearsay does not make it per se objectionable, nor does it deny defendant his right to confront witnesses. People v. Young, 128 Ill.2d 1, 54, 131 Ill.Dec. 86, 538 N.E.2d 461 (1989).
Officer Barrett testified that he was assigned to investigate a report of shots being fired at a particular location. When he arrived at the location, Jerry Singleton informed Barrett that defendant, while walking with Maurice Brown, handed Maurice a gun, and directed him to shoot at Singleton. Maurice then fired two shots at Singleton. Officer Barrett toured the area where the shots were fired. Officer Barrett observed defendant and Maurice going into a game room and followed them. Officer Barrett found a gun with two empty chambers on the floor next to defendant and Maurice. The other chambers of the gun were loaded with live bullets with their tips filed off. Defendant was subsequently charged with unlawful use of a weapon and aggravated assault. Defendant failed to appear in court on the charges, and a bond forfeiture warrant was issued. It is not clear from the record what happened to defendant after the bond forfeiture warrant was issued.
After reviewing the evidence, we cannot say that the trial judge abused his discretion in determining that the evidence was both relevant and reliable to defendant's sentencing, thus admitting the testimony, gun, and bullets into evidence. Defendant's attack on the admissibility of the evidence is twofold. Defendant first challenges the admissibility of the evidence because he was unable to cross-examine Singleton. However, as we have stated, the fact that evidence contains hearsay does not make it per se objectionable. Defendant also challenges the admissibility of the evidence on the ground that it was unreliable. After Singleton made the statements regarding defendant to Barrett, Barrett observed defendant nearby, followed him, and subsequently found a gun with two empty chambers at defendant's feet. Given the circumstances of the testimony, we conclude that the testimony was reliable. See People v. Brisbon, 106 Ill.2d 342, 364-65, 88 Ill.Dec. 87, 478 N.E.2d 402 (1985). Further, *1313 such evidence was clearly relevant as an aggravating factor at the second stage of the sentencing hearing. Moreover, we note that once admitted it was up to the jury to determine the weight to be given to this evidence.
Defendant next argues that the trial judge unconstitutionally restricted his presentation of mitigating evidence. Specifically, defendant contends that the trial judge erred in refusing to permit defendant to present evidence of the Mother's Day cards he sent to his mother while in jail and letters submitted on his behalf by various members of his family and friends. Defendant also alleges that the trial judge cajoled defense counsel into not calling defendant's son as a witness.
As to the Mother's Day cards, defendant sent his mother two hand-drawn Mother's Day cards while he was in prison. The trial judge allowed one of the cards into evidence, but refused to allow the other one into evidence. The card that was not allowed into evidence contained various statements, including "I'm praying everyday that these people let me go. Maybe soon they will realize they're [sic] mistake." The major thrust of this card was that defendant was innocent. However, residual doubt about the defendant's guilt is not a mitigating circumstance which may be presented at a sentencing hearing because it is not a fact about the defendant's character or the circumstances of the crimes which may call for a penalty less than death. Therefore, the trial judge did not abuse his discretion in excluding such evidence. See Edgeston, 157 Ill.2d at 245, 191 Ill.Dec. 84, 623 N.E.2d 329; Fields, 135 Ill.2d at 66-68, 142 Ill.Dec. 200, 552 N.E.2d 791. We further note that the statements made in the card regarding defendant's innocence were self-serving. Moreover, any mitigating factors that could be drawn from this letter were cumulative of the mitigating evidence contained in the other card the trial judge allowed into evidence.
We also find that the trial judge did not err in refusing to admit the letters submitted by family members and friends. As the trial judge acknowledged, the content of these letters was cumulative of testimony already given. Accordingly, we find that defendant's right to present mitigating evidence was not violated by the trial judge's exclusion of this evidence.
With regard to calling defendant's son as a witness in mitigation, the trial judge stated that there was no problem with the jury knowing that defendant had a five-year-old son. The trial judge asserted, however, that the issue was whether the boy was qualified to testify because of his young age. The trial judge further explained that there were many ways that the jury could be informed that defendant had a son and what the relationship was with his son. The judge then cautioned the defense that if he chose to put the son on the stand, the defense would be restricted to the extent that the boy was not competent to testify. The defense then stated that it would attempt to elicit the information from the boy's mother. Based on the record as a whole, we cannot say that the trial judge restricted defendant from presenting testimony of his son. Rather, the trial judge was simply informing defendant of the problems he might encounter if he did put the son on the stand as opposed to obtaining the information from another witness.
Defendant further argues that the prosecution's closing argument violated his constitutional rights because it (1) unconstitutionally diminished the jury's sense of final responsibility; (2) created a misimpression that defendant's life could only be spared if he presented a mitigating factor that compensated for the harm caused by his crime; (3) unfairly commented on the defendant's silence; and (4) misstated the statutory sentencing standard to imply that death should always be imposed when more than two persons are killed. Defendant's citations to the prosecution's statements are generally incomplete. When viewed in the proper context, none of the comments made by the prosecution in closing arguments violated the defendant's constitutional rights. Rather, they were either proper responses to statements defense counsel made in closing argument or evidence adduced at the sentencing hearing. We therefore reject defendant's arguments.
*1314 For example, defendant argues that his cause must be remanded for a new sentencing hearing because certain statements in the prosecutor's argument diminished the jury's sense of responsibility. Defendant objects to the following statements:
"There's not enough mitigation. If you haven't heard that thing that pricks your ear and says, yeah, that's sufficient, then you have the duty to sign the verdict that says, there is no mitigation sufficient to preclude the imposition of the death penalty, and you're not killing him.
* * * * * *
What a copout. What a cowardly shifting of the responsibility. You didn't do anything here. He did. How reprehensible it is to put it on you.
* * * * * *
Having failed to put it on [Wallace], they now put it on you."
It is clear, however, that when the prosecutor's comments are read in context, he was merely making an assessment of the evidence presented at the sentencing hearing and was focusing on the jurors' duty to follow the law. The jurors were instructed that if they found sufficient mitigating circumstances to preclude imposition of the death penalty, then the death penalty could not be imposed. The prosecutor's comments did not seek "to minimize the jury's sense of responsibility for determining the appropriateness of death." Caldwell v. Mississippi, 472 U.S. 320, 341, 105 S.Ct. 2633, 2646, 86 L.Ed.2d 231, 247 (1985). To the contrary, a complete review of the prosecutor's comments reveals that he was careful to insure that the "jury recognize[d] the gravity of its task and proceed[ed] with the appropriate awareness of its `truly awesome responsibility.'" Caldwell, 472 U.S. at 341, 105 S.Ct. at 2646, 86 L.Ed.2d at 247; see also Mahaffey, 128 Ill.2d at 427-29, 132 Ill.Dec. 366, 539 N.E.2d 1172.
Defendant further complains that the pattern jury instructions fail to convey that the State has the burden of persuasion at the second stage of the sentencing hearing. Defendant specifically challenges the jury instructions that informed the jury that the court would sentence defendant to death if the jury found that there were "no mitigating factors sufficient to preclude imposition of a death sentence." We have previously addressed and rejected this argument, finding that the jury instructions do not misstate the law or deny a defendant a fair trial. See People v. Thomas, 137 Ill.2d 500, 539, 148 Ill.Dec. 751, 561 N.E.2d 57 (1990); Pitsonbarger, 142 Ill.2d at 409, 154 Ill.Dec. 562, 568 N.E.2d 783. We see no reason to depart from our previous rulings on this issue here.
Defendant next claims that the jury instructions used in his case required the jury to find that each of the three statutory mitigating factors listed was present to preclude imposition of the death penalty. The jury was instructed:
"Mitigating factors include:

First: The following if supported by the evidence:
1. The defendant has no significant history of prior criminal activity.
2. The murder was committed while the defendant was under the influence of an extreme mental or emotional disturbance, although not such as to constitute a defense to the prosecution.
* * * * * *
3. The defendant may be rehabilitated or restored to useful citizenship.

Second: Any other reason supported by the evidence why the defendant should not be sentenced to death." Illinois Pattern Jury Instructions, Criminal, No. 7C.06 (2d ed. Supp.1989) (hereinafter IPI Criminal 2d).
Defendant contends that a reasonable juror would interpret the above instruction as requiring that each of the three statutory mitigating factors be found in order to preclude a death sentence. Defendant did not raise a specific objection to the above instruction on this basis, and we therefore deem defendant's argument waived. See Rissley, 165 Ill.2d at 406, 209 Ill.Dec. 205, 651 N.E.2d 133; Banks, 161 Ill.2d at 146, 204 Ill.Dec. 107, 641 N.E.2d 331. We also do not believe that defendant's claim falls within the limited exception to the waiver rule, as the evidence *1315 against defendant was not closely balanced and defendant's argument results from a strained interpretation of the jury instruction. Rissley, 165 Ill.2d at 407, 209 Ill.Dec. 205, 651 N.E.2d 133; Easley, 148 Ill.2d at 336-38, 170 Ill.Dec. 356, 592 N.E.2d 1036; 134 Ill.2d R. 451(c).
Defendant further argues that the trial judge erred in refusing to hold an evidentiary hearing on the constitutionality of the pattern jury instructions used in his case and in refusing to use alternative instructions offered by him which were allegedly needed to remedy the constitutional infirmities of the pattern jury instructions. Defendant bases his argument on a study conducted by Professor Hans Zeisel and found persuasive by the district court in United States ex rel. Free v. Peters, 806 F.Supp. 705 (N.D.Ill. 1992), that found the pattern jury instructions used in Free confused and misled jurors in a manner requiring that the death sentence in Free be vacated.
We first note that defendant did not ask the trial judge here to conduct an evidentiary hearing on the instructions until three months after defendant was sentenced to death. After the trial judge denied the motion, defendant then submitted, as an offer of proof, a transcript of the evidentiary hearing conducted in Free. Since defendant did not seek an evidentiary hearing on the validity of the sentencing instructions until after he was sentenced to death, defendant's request was untimely, and the issues are thus waived.
Moreover, even if the issues were not waived, we find defendant's argument to be without merit. This court has on numerous occasions rejected the argument that the district court's decision in Free renders the pattern jury instructions unconstitutional, pointing out that the district court's ruling regarding Professor Zeisel's study was reversed on review in Free v. Peters, 12 F.3d 700 (7th Cir.1993). People v. Franklin, 167 Ill.2d 1, 29, 212 Ill.Dec. 153, 656 N.E.2d 750 (1995); People v. Taylor, 166 Ill.2d 414, 437, 211 Ill.Dec. 518, 655 N.E.2d 901 (1995); People v. Mahaffey, 165 Ill.2d 445, 471, 209 Ill.Dec. 246, 651 N.E.2d 174 (1995); People v. Holman, 164 Ill.2d 356, 379, 207 Ill.Dec. 467, 647 N.E.2d 960 (1995); People v. Williams, 161 Ill.2d 1, 59, 204 Ill.Dec. 72, 641 N.E.2d 296 (1994); People v. Thompkins, 161 Ill.2d 148, 198, 204 Ill.Dec. 147, 641 N.E.2d 371 (1994); People v. Banks, 161 Ill.2d 119, 147, 204 Ill.Dec. 107, 641 N.E.2d 331 (1994); People v. Kokoraleis, 159 Ill.2d 325, 333, 202 Ill.Dec. 279, 637 N.E.2d 1015 (1994); People v. Kitchen, 159 Ill.2d 1, 47, 201 Ill.Dec. 1, 636 N.E.2d 433 (1994). We continue to adhere to the view that the district court's decision in Free does not render the pattern jury instructions unconstitutional. In light of our continuing rejection of the district court's reasoning in Free, we find no error in the trial judge's denial of defendant's request for an evidentiary hearing or in refusing defendant's alternative instruction relating to this issue. Moreover, because the Zeisel study was conducted on the 1984 version of the IPI Criminal 2d jury instruction, whereas the defendant's case was tried under the 1987 version of the instructions, the Zeisel study has questionable relevance in this case. Further, the fact that defendant argues he would have offered additional evidence, other than transcripts from the Free hearing, to support his motion for an evidentiary hearing does not persuade us to reach a different result. The "additional evidence" defendant sought to present was the same witnesses called in the Free hearing.
Defendant has, however, been allowed to supplement the record on appeal with a summary of a study conducted by Professor Shari Diamond in December 1994. Professor Diamond's study concerned a jury's ability to understand the jury instructions used in Illinois death penalty hearings. The study was designed to address two of the primary objections to the Zeisel study, specifically that the Zeisel study did not provide a proper measure of juror comprehension because (1) it did not use a "control group" to determine whether jury instructions rewritten to improve clarity would improve performance on the comprehension measures, and (2) it did not account for juror deliberations. The result of the Diamond study confirmed the findings of the Zeisel study that the pattern jury instructions confuse jurors.
We note that no argument has been provided us regarding the Diamond study's effect *1316 on defendant's case. The only mention of the Diamond study was a simple statement of the study's existence and that defendant had supplemented the record with the study during rebuttal at oral argument before this court. We would therefore be justified in not commenting on the supplemental material. In any event, we are equally unpersuaded by the Diamond study that the instructions given in defendant's case were so confusing as to be constitutionally infirm. First, the instructions used at defendant's sentencing hearing were taken from the 1987 version of the Illinois Pattern Jury Instructions. It is unclear, however, from defendant's supplemental material what version of the IPI Professor Diamond studied. Therefore, the relevance of the Diamond study to defendant's case is questionable. Moreover, although the Diamond study claims to correct two deficiencies in the Zeisel study, there still remain more generalized problems with the research. Perhaps the most fundamental objection is the "lack of comparability between the test setting and the sentencing hearing." See Free, 12 F.3d at 705. There is no reason to suppose that actual jurors who have sat through trial and a sentencing hearing would respond to the sentencing instructions in the same way as the test subjects who simply listened to an audiotaped description of the evidence presented in the case and an audiotape of the instructions, as was done in the Diamond study. See Free, 12 F.3d at 705-06; Gacy v. Welborn, 994 F.2d 305, 311-14 (7th Cir.1993). Accordingly, we do not find that the Diamond study requires us to remand the cause for an evidentiary hearing.
As a final matter with regard to this issue, we must dispose of defendant's motion to supplement the record on appeal with certain materials that were inadvertently omitted. Specifically, defendant wishes to supplement the record with several proposed jury instructions that were refused and approximately 200 pages of transcript from the evidentiary hearing conducted by the federal district court in Free. No objection has been made to the motion, and the motion has been taken with the case. Defendant's motion to supplement the record is allowed.
Defendant also argues that the trial judge erred in refusing to specifically instruct the jury that defendant's age and drug use must be considered as mitigating factors. Defendant also contends that the trial judge erred in refusing to specifically instruct the jury that it may consider sympathy as a mitigating factor. This court has previously held that nonstatutory mitigating factors need not be specified in an instruction when the jury is instructed that it may consider any relevant mitigation. A mercy instruction need not be given for the same reason. See Jackson, 145 Ill.2d at 114, 163 Ill.Dec. 859, 582 N.E.2d 125; People v. Sanchez, 115 Ill.2d 238, 269-70, 104 Ill.Dec. 720, 503 N.E.2d 277 (1986). The jury here was instructed that it could consider any mitigating evidence supported by the record, and we therefore reject defendant's arguments.
Citing Mills v. Maryland, 486 U.S. 367, 108 S.Ct. 1860, 100 L.Ed.2d 384 (1988), defendant next argues that the trial judge erred in refusing an instruction which made it clear that jurors may consider a mitigating factor even if other jurors do not agree on it. In People v. Ramey, 152 Ill.2d 41, 77, 178 Ill.Dec. 19, 604 N.E.2d 275 (1992), this court rejected substantially the same argument, stating:
"Unlike the Maryland statute construed in Mills, the Illinois death penalty statute does not require the jury to reach unanimous agreement as to the existence of any mitigating factors before it can decide not to impose the death penalty. Rather, in Illinois, a sentencing jury is required to unanimously determine that mitigating factors sufficient to preclude the death penalty do not exist before that penalty can be imposed. In Illinois, unlike Maryland, the belief by one juror that any one mitigating factor sufficient to preclude the death penalty exists is sufficient to do so. As such, Illinois' death penalty procedure clearly provides for meaningful consideration of any and all mitigating factors." (Emphasis in original.)
While in Mills the instructions given to the jury could have been interpreted as requiring unanimous agreement that a mitigating factor or factors existed to preclude death, no *1317 such interpretation can be ascribed to the Illinois death penalty statute. Ramey, 152 Ill.2d at 77, 178 Ill.Dec. 19, 604 N.E.2d 275. We therefore reject defendant's argument.
Defendant further argues that regardless of whether the instructions were unconstitutional, this court should order a new sentencing hearing at which clear jury instructions are used. Because we have found that there was no error regarding the instructions used at sentencing, we find that there is no need to remand for a new sentencing hearing.
Defendant next contends that the trial judge's hostility toward defense counsel and defendant rendered the sentencing hearing fundamentally unfair, thus entitling defendant to a new sentencing hearing. In support of his argument, defendant points to 16 separate incidents which allegedly reflect the trial judge's hostility toward defense counsel and defendant. Defendant does not demonstrate how the alleged hostility affected the outcome of the trial, and we therefore conclude that any alleged hostility toward the defense was not prejudicial. Harris, 123 Ill.2d at 137, 122 Ill.Dec. 76, 526 N.E.2d 335; see also People v. Heidorn, 114 Ill.App.3d 933, 937, 70 Ill.Dec. 439, 449 N.E.2d 568 (1983).
Defendant also argues that his constitutional rights were violated when the trial judge engaged in an ex parte discussion with the prosecution. After opening statements in the second phase of the sentencing hearing, defense counsel told the trial judge that he had just been shown a large photo of defendant wearing a tee-shirt with the letters "GWA" printed on it. Defense counsel further informed the trial judge that the State had suggested that it was going to call an expert in gang activities to explain what the letters on the shirt meant. Defense counsel then explained his objections to the use of the expert and the photo regarding defendant's affiliation with a gang. The State elected not to introduce the evidence at that time. During the presentation of mitigating factors, defense counsel elicited testimony from witnesses that defendant was not involved in a gang. The State then sought to use the expert and the photo to rebut this evidence. When the defense counsel asked how the State was going to present this information, the trial judge responded that he had spoken with the State and they were going to present the evidence in conformity with what was argued earlier.
We note that defense counsel made no objection when he initially learned of the conversation between the trial judge and prosecution that the conversation constituted an improper ex parte communication. Having made no objection at trial, defendant has waived the issue and cannot now be heard to claim reversible error. People v. Enoch, 122 Ill.2d 176, 119 Ill.Dec. 265, 522 N.E.2d 1124 (1988); People v. Marigny, 51 Ill.2d 445, 451, 282 N.E.2d 734 (1972); People v. Buscher, 221 Ill.App.3d 143, 147-48, 163 Ill.Dec. 634, 581 N.E.2d 788 (1991).
Defendant further maintains that trial counsel provided ineffective assistance at sentencing by (1) failing to present significant mitigating evidence, (2) failing to explain to the jury the role of mitigating factors under the death penalty statute, and (3) waiving rebuttal argument. The "significant mitigating evidence" that defendant alludes to was various witnesses who were in court, but were not called to testify. Defendant does not explain what these witnesses would have testified to or how the failure to call them prejudiced him. We therefore reject defendant's ineffective-assistance claim on this point. Moreover, we also reject defendant's ineffective-assistance claim on the two other points. Even if defense counsel's performance was deficient by waiving rebuttal arguments and failing to explain the role of mitigating factors to the jury, we do not find that these alleged errors would have had an impact on the jury so that it would have found mitigating factors sufficient to preclude imposition of the death penalty.
Defendant next contends that his constitutional rights were violated by the trial judge's denial of his request for a right of allocutionthe right to address the jury at the second stage of the sentencing hearing by way of an unsworn statement. Defendant also argues that the guarantees of equal protection and due process are violated by the denial of allocution in capital cases, while *1318 allowing it in noncapital proceedings. See Ill.Rev.Stat.1991, ch. 38, par. 1005-4-1(a)(5).
This court has consistently rejected the argument that a defendant in a capital case has a right of allocution. Thus, it follows that defendant's constitutional rights could not have been violated by being denied the opportunity to make an unsworn statement before imposition of a sentence. Moreover, this court has previously considered and rejected defendant's other argument that the statutory prohibition of allocution to capital defendants violates the guarantees of due process and equal protection. We see no reason to depart from this court's prior rulings here. People v. Christiansen, 116 Ill.2d 96, 128-29, 107 Ill.Dec. 198, 506 N.E.2d 1253 (1987); People v. Szabo, 113 Ill.2d 83, 95, 100 Ill.Dec. 726, 497 N.E.2d 995 (1986); People v. Perez, 108 Ill.2d 70, 89, 90 Ill.Dec. 932, 483 N.E.2d 250 (1985); People v. Stewart, 105 Ill.2d 22, 74-75, 85 Ill.Dec. 241, 473 N.E.2d 840 (1984); People v. Williams, 97 Ill.2d 252, 303-04, 73 Ill.Dec. 360, 454 N.E.2d 220 (1983); People v. Gaines, 88 Ill.2d 342, 374-80, 58 Ill.Dec. 795, 430 N.E.2d 1046 (1981).
Defendant also argues that the numerous constitutional errors allegedly occurring at his trial prejudiced him during the sentencing proceedings. However, having found no errors at trial, we must reject defendant's contention that these alleged errors prejudiced him at sentencing.
As a final matter, defendant next raises a number of challenges to the constitutionality of the Illinois death penalty statute (Ill.Rev. Stat.1989, ch. 38, par. 9-1). As we explain below, this court has previously considered and rejected the same arguments in other cases, and defendant has not presented us with any reasons to reach a different result here.
Our cases have held that the death penalty statute does not unconstitutionally impose on the defendant a burden of establishing that a noncapital sentence should be imposed. People v. Mahaffey, 166 Ill.2d 1, 34, 209 Ill.Dec. 607, 651 N.E.2d 1055 (1995); People v. Harris, 164 Ill.2d 322, 351, 207 Ill.Dec. 400, 647 N.E.2d 893 (1994); Thompkins, 161 Ill.2d at 196-97, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Bean, 137 Ill.2d 65, 138-40, 147 Ill.Dec. 891, 560 N.E.2d 258 (1990); Fields, 135 Ill.2d at 76, 142 Ill.Dec. 200, 552 N.E.2d 791; People v. Orange, 121 Ill.2d 364, 390, 118 Ill.Dec. 1, 521 N.E.2d 69 (1988); People v. Caballero, 102 Ill.2d 23, 49, 79 Ill.Dec. 625, 464 N.E.2d 223 (1984). We have also held that the statute does not prevent the sentencer from giving meaningful consideration to mitigating evidence. Simms, 168 Ill.2d at 200, 213 Ill.Dec. 576, 659 N.E.2d 922; Thompkins, 161 Ill.2d at 196, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Page, 155 Ill.2d 232, 283, 185 Ill.Dec. 475, 614 N.E.2d 1160 (1993). Our case law has further established that the statute is not invalid for failing to require the prosecution to provide the accused with pretrial notice of its intent to seek the death penalty. Mahaffey, 166 Ill.2d at 33, 209 Ill.Dec. 607, 651 N.E.2d 1055; Harris, 164 Ill.2d at 351, 207 Ill.Dec. 400, 647 N.E.2d 893; Thompkins, 161 Ill.2d at 197, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Silagy, 101 Ill.2d 147, 161-62, 77 Ill.Dec. 792, 461 N.E.2d 415 (1984); Gaines, 88 Ill.2d at 369, 58 Ill.Dec. 795, 430 N.E.2d 1046. Moreover, we have held that the statute sufficiently minimizes against the risk of arbitrary or capriciously imposed death sentences. People v. Wiley, 165 Ill.2d 259, 302, 209 Ill.Dec. 261, 651 N.E.2d 189 (1995); Fair, 159 Ill.2d at 95, 201 Ill.Dec. 23, 636 N.E.2d 455; People v. Spreitzer, 123 Ill.2d 1, 44, 121 Ill.Dec. 224, 525 N.E.2d 30 (1988); People v. Ashford, 121 Ill.2d 55, 90, 117 Ill.Dec. 171, 520 N.E.2d 332 (1988).
Further, the statute is not unconstitutional because it vests a standardless discretion in the prosecutor to seek the death penalty. Young, 128 Ill.2d at 60, 131 Ill.Dec. 86, 538 N.E.2d 461; Christiansen, 116 Ill.2d at 130, 107 Ill.Dec. 198, 506 N.E.2d 1253; People v. Brisbon, 106 Ill.2d 342, 362, 88 Ill.Dec. 87, 478 N.E.2d 402 (1985). Nor does the discretion afforded by the statute to the prosecution in deciding whether to seek the death penalty in a particular case result in its arbitrary or capricious imposition. Mahaffey, 166 Ill.2d at 33, 209 Ill.Dec. 607, 651 N.E.2d 1055; Thompkins, 161 Ill.2d at 197, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Williams, 147 Ill.2d 173, 264-66, 167 Ill.Dec. 853, 588 N.E.2d 983 (1991); People v. Stewart, *1319 123 Ill.2d 368, 378-79, 123 Ill.Dec. 927, 528 N.E.2d 631 (1988); People ex rel. Carey v. Cousins, 77 Ill.2d 531, 539-42, 34 Ill.Dec. 137, 397 N.E.2d 809 (1979). The statute also does not violate separation of powers principles by vesting a judicial function in a nonjudicial officer. Thompkins, 161 Ill.2d at 197, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Franklin, 135 Ill.2d 78, 119-20, 142 Ill.Dec. 152, 552 N.E.2d 743 (1990); People v. Lewis, 88 Ill.2d 129, 146, 58 Ill.Dec. 895, 430 N.E.2d 1346 (1981).
This court has previously rejected the argument that a sentencer's consideration of nonstatutory aggravating factors during the second stage of a death penalty hearing results in the arbitrary imposition of a death sentence. Taylor, 166 Ill.2d at 439, 211 Ill. Dec. 518, 655 N.E.2d 901; Young, 128 Ill.2d at 59, 131 Ill.Dec. 86, 538 N.E.2d 461; Orange, 121 Ill.2d at 390-91, 118 Ill.Dec. 1, 521 N.E.2d 69; People v. Neal, 111 Ill.2d 180, 203, 95 Ill.Dec. 283, 489 N.E.2d 845 (1985). Moreover, this court has also rejected the contention that the statute has a discriminatory effect on minority defendants. Thompkins, 161 Ill.2d at 198, 204 Ill.Dec. 147, 641 N.E.2d 371; People v. Kokoraleis, 132 Ill.2d 235, 291, 138 Ill.Dec. 233, 547 N.E.2d 202 (1989); Orange, 121 Ill.2d at 392, 118 Ill.Dec. 1, 521 N.E.2d 69; see McCleskey v. Kemp, 481 U.S. 279, 107 S.Ct. 1756, 95 L.Ed.2d 262 (1987). We have further held that the statute does not place an unconscionable burden on the defendant to demonstrate why he should live, nor does it require a defendant to prove, after he has been found eligible for the death penalty, that the death penalty should not be imposed. People v. Strickland, 154 Ill.2d 489, 538-39, 182 Ill.Dec. 551, 609 N.E.2d 1366 (1992); People v. Mitchell, 152 Ill.2d 274, 345-46, 178 Ill.Dec. 354, 604 N.E.2d 877 (1992); People v. Hampton, 149 Ill.2d 71, 115-17, 171 Ill.Dec. 439, 594 N.E.2d 291 (1992); Pitsonbarger, 142 Ill.2d at 408, 154 Ill.Dec. 562, 568 N.E.2d 783.

III. CONCLUSION
For the reasons stated, the judgment of the circuit court of Cook County is affirmed. The clerk of this court is directed to enter an order setting Tuesday, September 10, 1996, as the date on which the sentence of death, entered by the circuit court of Cook County, is to be carried out. The defendant shall be executed in the manner provided by law (725 ILCS 5/119-5 (West 1992)). 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.
Affirmed.
