
737 N.E.2d 264 (2000)
193 Ill.2d 120
249 Ill.Dec. 874
The PEOPLE of the State of Illinois, Appellee,
v.
Patrick PAGE, Appellant.
Nos. 83921, 83922.
Supreme Court of Illinois.
August 10, 2000.
Rehearing Denied October 2, 2000.
*265 *266 *267 *268 John C. Greenlees and Terri L. Marroquin, of the Office of the State Appellate Defender, of Chicago, for appellant.
James Ryan, Attorney General, of Springfield, and Richard A. Devine, State's Attorney, of Chicago (William L. Browers, Assistant Attorney General, of Chicago, and Renee Goldfarb and Linda D. Woloshin, Assistant State's Attorneys, of counsel), for the People.
Justice BILANDIC delivered the opinion of the court:
Defendant, Patrick Page, was charged in the circuit court of Cook County with two separate murders and various other offenses. Defendant was first tried for the May 1987 murder of John Goodman. The jury found defendant guilty of murder, armed robbery, and home invasion. The jury then found that defendant was eligible for the death penalty (see Ill.Rev.Stat. 1985, ch. 38, pars. 9-1(b)(3), (b)(6)), and that there were no mitigating factors sufficient to preclude a sentence of death. The trial court therefore sentenced defendant to death for the murder conviction. The trial court imposed concurrent 60-year terms of imprisonment for defendant's remaining convictions. On direct appeal, this court affirmed defendant's convictions and sentences. People v. Page, 155 Ill.2d 232, 185 Ill.Dec. 475, 614 N.E.2d 1160 (1993) (Goodman case).
Defendant was next tried for the fall 1985 murder of Charles Howell. The jury found defendant guilty of murder and armed robbery. The jury also found that defendant was eligible for the death penalty (see Ill.Rev.Stat.1985, ch. 38, pars. 9-1(b)(3), (b)(6)), and that there were no mitigating factors sufficient to preclude a death sentence. The trial court sentenced defendant to death for the murder conviction and to an extended 60-year term of imprisonment for the armed robbery conviction. This court affirmed defendant's convictions and sentences on direct appeal. People v. Page, 156 Ill.2d 258, 189 Ill.Dec. 371, 620 N.E.2d 339 (1993) (Howell case).
Defendant filed a pro se post-conviction petition in the Goodman case. Appointed counsel filed a post-conviction petition in the Howell case. Appointed counsel later filed a supplemental post-conviction petition that consolidated the issues in both cases. The State filed a motion to dismiss the post-conviction petition in each case. Appointed counsel subsequently filed a consolidated amended post-conviction petition that superseded all prior post-conviction petitions but refers to exhibits attached to those earlier petitions. The State filed a motion to dismiss the consolidated amended post-conviction petition (post-conviction petition). After hearing arguments on the State's motion, the trial court dismissed defendant's post-conviction petition without an evidentiary hearing.
Defendant now appeals from the dismissal of his post-conviction petition. For the reasons set forth below, we affirm the trial court's dismissal of defendant's post-conviction petition.

BACKGROUND
The facts relating to defendant's trials are set forth in this court's opinions on direct appeal. Because an understanding of some of the trial evidence is necessary to evaluate defendant's arguments in this post-conviction proceeding, we present a summary of that evidence.
*269 Defendant has been convicted of three murders, the Goodman and Howell murders at issue in this case, as well as the murder of Dale Andrew Devine. On May 16, 1987, defendant was arrested by the Olympia Fields police department as part of the investigation into Goodman's murder. Over the next several days, defendant gave law enforcement authorities several statements admitting his involvement in the three murders. On two occasions during that time, defendant led Olympia Fields police officers on an unsuccessful search of the area in Wisconsin where defendant claimed that he buried Goodman's body.
On May 19, 1987, defendant gave a court-reported statement in which he confessed to the three murders. Defendant revealed that, during the fall of 1985, defendant, Kenneth Cheney, and Gerald Feinberg murdered Devine. Devine and Cheney became involved in a drug deal in which Devine apparently "ripped off" Cheney. Devine was residing with defendant at this time. Defendant contacted Feinberg and told him that Devine was at his house. Feinberg came to defendant's house, and defendant and Feinberg tied up Devine with an extension cord. Defendant then called Cheney and told him that Devine was at his house. Cheney came over and, using a hypodermic needle, injected Devine with barbiturates. Defendant took approximately $100 from Devine's pocket and gave it to Cheney.
Defendant, Feinberg, and Cheney then transported Devine to a wooded area near Wilmington, Illinois. Cheney asked Devine how he wanted to die, either by being stabbed with a knife or by being injected with a hypodermic needle. Devine indicated that he preferred the injection. Cheney attempted to inject an air bubble into Devine's bloodstream. When this did not kill Devine, Cheney slit Devine's throat with the knife. Cheney then directed defendant and Feinberg to stab Devine, which they did. After the murder, defendant, Cheney, and Feinberg drove to Cheney's home, where they drank alcohol and smoked marijuana. Two days later, defendant and Cheney returned to the murder scene, and Cheney poured gasoline on Devine's body and set it on fire. Defendant was convicted in the circuit court of Will County of the murder of Devine, and was sentenced to a 60-year term of imprisonment. The appellate court affirmed defendant's murder conviction and sentence. People v. Page, 196 Ill.App.3d 285, 143 Ill.Dec. 46, 553 N.E.2d 753 (1990) (Devine case).
Defendant also confessed to the fall 1985 murder of Charles Howell. Defendant stated that he and Feinberg killed Howell because Howell had been a roommate of Devine, and Devine's disappearance would make Howell suspicious. Defendant and Feinberg decided to murder Howell and bury him in a forest preserve in Park Forest, Illinois. Defendant and Feinberg planned the murder in advance by drawing a map of the area where they would bury Howell, taking shovels from defendant's home and from the home of a neighbor, going to the planned burial site in advance to dig a hole, and luring Howell to the site under the pretense of having a party and engaging in a drug transaction there. Defendant stabbed Howell, and Feinberg hit him in the head with a large stick. Defendant and Feinberg laid Howell in the hole that they had dug, covered him with dirt and branches, and started a fire over the grave with lighter fluid. Feinberg, who had taken Howell's car keys from the pocket of Howell's jeans prior to burying him, gave the keys to defendant as they were leaving the forest preserve. Defendant stated that he wanted the keys because Howell's car was parked in front of defendant's house. After the murder, defendant and Feinberg went to defendant's house, smoked marijuana, and drove around in Howell's car. A few days later, defendant sold Howell's car to a junkyard.
Defendant's statement also included a confession to the murder of John Goodman. Defendant stated that, on May 6, *270 1987, he and Feinberg made plans to rob and kill Goodman. Defendant originated the plan because he had a grudge against Goodman. On Thursday, May 7, 1987, defendant and Feinberg visited Goodman's home in Olympia Fields. When Goodman was in another room, defendant displayed a knife to Feinberg. Defendant then approached Goodman and asked Goodman about some photographs that Goodman had taken of defendant. When Goodman began to laugh, defendant stabbed him in the chest four times. Defendant said that Goodman had not touched him prior to that.
Defendant and Feinberg then put Goodman's body in the bathtub while they wiped the house clean of their fingerprints. They stole credit cards and cash from Goodman's wallet. They wrapped Goodman's body in a sheet and a rug and placed the body in the trunk of Goodman's car. Defendant and Feinberg obtained a shovel and a can of gasoline and left in Goodman's car. After stopping at a tavern in southeastern Wisconsin to eat and play pool, they drove to a rural area in Wisconsin, dug a hole, and buried Goodman's body. They then burned the sheet and rug over the grave.
Defendant further stated that, on May 9, 1987, he and a friend transported some electronic equipment from Goodman's house to defendant's father's house. Defendant described his and his friends' use of Goodman's credit cards during the weekend following the murder. Defendant and Feinberg abandoned Goodman's car at a commuter station the following Tuesday or Wednesday.
As discussed, defendant was convicted of all three murders and received the death penalty for the murders of Goodman and Howell. This appeal follows the dismissal of defendant's post-conviction petition without an evidentiary hearing in the Goodman and Howell cases. For the reasons set forth below, we hold that the trial court properly dismissed defendant's post-conviction petition without an evidentiary hearing. We therefore affirm the judgment of the trial court.

ANALYSIS
The Post-Conviction Hearing Act (725 ILCS 5/122-1 et seq. (West 1998)) provides a remedy to criminal defendants who claim that substantial violations of their federal or state constitutional rights occurred in their trial or sentencing hearing. People v. Towns, 182 Ill.2d 491, 502, 231 Ill.Dec. 557, 696 N.E.2d 1128 (1998). A post-conviction action, however, is a collateral proceeding, not an appeal from the underlying judgment. Towns, 182 Ill.2d at 502, 231 Ill.Dec. 557, 696 N.E.2d 1128. The purpose of the post-conviction proceeding is to allow inquiry into constitutional issues involved in the conviction and sentence that have not been, and could not have been, adjudicated previously on direct appeal. Towns, 182 Ill.2d at 502, 231 Ill. Dec. 557, 696 N.E.2d 1128. The doctrine of res judicata bars consideration of issues that were raised and decided on direct appeal. Towns, 182 Ill.2d at 502, 231 Ill. Dec. 557, 696 N.E.2d 1128; People v. Griffin, 178 Ill.2d 65, 73, 227 Ill.Dec. 338, 687 N.E.2d 820 (1997). Issues that could have been presented on direct appeal, but were not, are waived. Towns, 182 Ill.2d at 503, 231 Ill.Dec. 557, 696 N.E.2d 1128; Griffin, 178 Ill.2d at 73, 227 Ill.Dec. 338, 687 N.E.2d 820.
A defendant is not entitled to an evidentiary hearing on a post-conviction petition as a matter of right. People v. Hobley, 182 Ill.2d 404, 427-28, 231 Ill.Dec. 321, 696 N.E.2d 313 (1998). Rather, an evidentiary hearing is warranted only where the allegations of the post-conviction petition, supported where appropriate by the trial record or accompanying affidavits, make a substantial showing that the defendant's constitutional rights have been violated. Hobley, 182 Ill.2d at 428, 231 Ill.Dec. 321, 696 N.E.2d 313; Towns, 182 Ill.2d at 503, 231 Ill.Dec. 557, 696 N.E.2d 1128. In determining whether to grant an evidentiary hearing, all well-pleaded facts *271 in the petition and in any accompanying affidavits are taken as true. Towns, 182 Ill.2d at 503, 231 Ill.Dec. 557, 696 N.E.2d 1128. Assertions that are nonfactual and nonspecific and that merely amount to conclusions are not sufficient to require an evidentiary hearing. People v. Coleman, 183 Ill.2d 366, 381, 233 Ill.Dec. 789, 701 N.E.2d 1063 (1998). A trial court's determination regarding the sufficiency of the allegations contained in a post-conviction petition is reviewed de novo. Coleman, 183 Ill.2d at 388-89, 233 Ill.Dec. 789, 701 N.E.2d 1063. With these principles in mind, we review de novo the trial court's dismissal of defendant's post-conviction petition without an evidentiary hearing.

I. Ineffective Assistance of Counsel
Defendant first raises a series of challenges to the effectiveness of his counsel during trial, sentencing, and on direct appeal.
To establish a claim of ineffective assistance of counsel, a defendant must first show that counsel's performance was deficient in that it fell below an objective standard of reasonableness. Strickland v. Washington, 466 U.S. 668, 687-88, 104 S.Ct. 2052, 2064, 80 L.Ed.2d 674, 693 (1984). In satisfying this prong, a defendant must overcome the strong presumption that the challenged action or inaction of counsel was the product of sound trial strategy. Strickland, 466 U.S. at 689, 104 S.Ct. at 2065, 80 L.Ed.2d at 694-95.
A defendant must also establish prejudice by proving that there is a reasonable probability that, but for counsel's deficient performance, 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 reasonable probability is a probability sufficient to undermine confidence in the outcome; namely, that counsel's deficient performance either rendered the result of the trial unreliable or rendered the proceeding fundamentally unfair. Strickland, 466 U.S. at 694, 104 S.Ct. at 2068, 80 L.Ed.2d at 698. When challenging a death sentence, a defendant must prove that there is a reasonable probability that, absent counsel's deficient performance, the sentencer would have concluded that the balance of aggravating and mitigating circumstances did not warrant death. Strickland, 466 U.S. at 695, 104 S.Ct. at 2069, 80 L.Ed.2d at 698.
A defendant must establish both prongs of the Strickland test to prevail on a claim of ineffective assistance of counsel. A court, however, may resolve an ineffectiveness claim by reaching only the prejudice prong, as lack of prejudice renders irrelevant the issue of counsel's alleged deficient performance. See Strickland, 466 U.S. at 697, 104 S.Ct. at 2069, 80 L.Ed.2d at 699.

A. Failure to Present Sufficient Evidence of a Voluntary Manslaughter Defense

Defendant argues that trial counsel was ineffective during the Goodman trial for failing to present sufficient evidence to support defendant's voluntary manslaughter theory of defense. At the time of the offense, the homicide statute provided that a person commits voluntary manslaughter if at the time of the killing he either had an actual but unreasonable belief regarding the need for self-defense, or was acting under a sudden and intense passion resulting from serious provocation. Ill.Rev.Stat. 1985, ch. 38, par. 9-2.[1] Serious provocation is conduct sufficient to excite an intense passion in a reasonable person. Ill. *272 Rev.Stat.1985, ch. 38, par. 9-2. This court has recognized the following categories of provocation: substantial physical injury or substantial physical assault; mutual quarrel or combat; illegal arrest; and adultery with the offender's spouse. People v. Garcia, 165 Ill.2d 409, 429, 209 Ill.Dec. 172, 651 N.E.2d 100 (1995); People v. Chevalier, 131 Ill.2d 66, 71, 136 Ill.Dec. 167, 544 N.E.2d 942 (1989).
During the opening argument in the Goodman trial, defense counsel told the jury that defendant had committed the homicide charged, but maintained that defendant was guilty of voluntary manslaughter rather than murder. Later, however, the trial court denied defendant's request that the jury be instructed on voluntary manslaughter, finding that the evidence was not sufficient to support the instruction. The trial court also directed defense counsel not to argue the theory of voluntary manslaughter in summation.
On direct appeal in the Goodman case, defendant argued that his trial counsel was ineffective for presenting the voluntary manslaughter theory of defense. Defendant argued that this theory was not supported by either the law or the facts of the case. This court noted that trial counsel sought to demonstrate that defendant killed Goodman while defendant was acting under a sudden and intense passion resulting from serious provocation. Page, 155 Ill.2d at 261, 185 Ill.Dec. 475, 614 N.E.2d 1160. Trial counsel sought to establish the provocation form of the offense by showing evidence of mutual combat between defendant and Goodman. Page, 155 Ill.2d at 261, 185 Ill.Dec. 475, 614 N.E.2d 1160. Although defendant did not testify, trial counsel was able to elicit evidence, during cross-examination of one of the prosecution witnesses, about an altercation between defendant and Goodman. Trial counsel asked the witness about an inculpatory statement made by defendant prior to his formal confession. In that statement, defendant said that he and Goodman argued for 10 to 15 minutes over some photographs that Goodman refused to surrender. According to defendant, Goodman had taken photographs of defendant and Goodman having a homosexual relationship. Defendant said that he punched and stabbed Goodman when Goodman refused to move from the bathroom doorway, where the two were standing. In addition to this evidence, defendant, in his formal statement, said that he stabbed Goodman after Goodman began laughing at his request for the photographs. See Page, 155 Ill.2d at 261, 185 Ill.Dec. 475, 614 N.E.2d 1160.
This court rejected defendant's argument that trial counsel was ineffective for arguing voluntary manslaughter. We held that trial counsel's decision to present the voluntary manslaughter defense was a matter of trial strategy, and that the record showed that defendant expressly consented to this strategy. Page, 155 Ill.2d at 262-63, 185 Ill.Dec. 475, 614 N.E.2d 1160. We found that, in light of the overwhelming evidence of defendant's involvement in Goodman's murder, defense counsel might reasonably have considered a voluntary manslaughter theory to be the only reasonable course of defense. Page, 155 Ill.2d at 262, 185 Ill.Dec. 475, 614 N.E.2d 1160. We then recounted the overwhelming evidence of defendant's guilt. Defendant confessed in detail to the crimes. An eyewitness saw defendant at Goodman's house shortly before Goodman disappeared. Other witnesses established that defendant was in possession of property belonging to Goodman, including his car and credit cards. Another witness testified that defendant had access to Goodman's house shortly after he disappeared. See Page, 155 Ill.2d at 266, 185 Ill.Dec. 475, 614 N.E.2d 1160.
In these post-conviction proceedings, defendant now argues that his trial counsel was ineffective for failing to present sufficient evidence to support the voluntary manslaughter defense. Defendant has waived review of this argument by failing to raise it on direct appeal. See *273 People v. Towns, 182 Ill.2d 491, 503, 231 Ill.Dec. 557, 696 N.E.2d 1128 (1998). Indeed, this argument is directly contrary to the argument defendant did raise on direct appeal, i.e., that trial counsel was ineffective for presenting the voluntary manslaughter defense.
Defendant, however, appears to argue that his claim is not waived because it is based on evidence outside the original trial record. This exception to the waiver rule in post-conviction appeals refers to those claims that the reviewing court on direct appeal could not have considered because the claim's evidentiary basis was de hors the record. See People v. Whitehead, 169 Ill.2d 355, 372, 215 Ill.Dec. 164, 662 N.E.2d 1304 (1996), overruled in part on other grounds, People v. Coleman, 183 Ill.2d 366, 233 Ill.Dec. 789, 701 N.E.2d 1063 (1998). Defendant argues that there was evidence available to trial counsel to substantiate defendant's voluntary manslaughter defense. Defendant claims that he has now "submitted police reports and evidence of other statements, from numerous individuals, substantiating and establishing the manslaughter defense, including: evidence that the pictures being argued over were evidence of a homosexual attack perpetrated by the victim and his friends; evidence that such tendencies and similar photographs were discovered concerning the victim (as well as additional material involving the defendants); and evidence that in addition to an altercation over the pictures, the victim attempted homosexual contact with the defendant."
The evidence that defendant cites in support of his argument is as follows. Defendant provides his own affidavit which states that "John Goodman had pictures of Gerald Feinberg. Cheyney [sic ] told Gerald that if he helped Cheyney get Andy and Chuck, Cheyney would help Gerald get Goodman for what he had done to him. John Goodman and his friend had drugged Feinberg and performed unnatural sex acts on him. Feinberg was very upset about this, and wanted to get them back."
Defendant attaches the affidavit of Edward Torres, an investigator from the Capital Litigation Division. Torres interviewed Kenneth Berksen, who was once Gerald Feinberg's cellmate at the Cook County jail. According to Torres' affidavit, Berksen stated that Feinberg told him that, on the night of Goodman's murder, Goodman made a sexual advance toward defendant, which enraged defendant and caused defendant to stab Goodman. In this regard, defendant also provides a report from the Olympia Fields police department which relates that Greg Wilson, a friend of Goodman, spoke to a man named John Dixon, who spoke to Feinberg, who said that "Goodman tried to make out with Pat Page, and then they stabbed him."
Defendant also cites numerous other reports from the Olympia Fields police department which discuss relations among defendant, Goodman, and Feinberg. One report recounts that a certain newspaper reporter gave the Olympia Fields police department a photograph of Goodman and defendant. The reporter received the photograph from a third party who had received it from the photographer. The reporter advised police that the source had stated that the photograph was taken one week before Goodman's murder while on a weekend fishing trip in Illinois. Another report discusses information received from Greg Wilson. According to Wilson, defendant had been to Goodman's home and had been videotaped in one of Goodman's "home movies."
An additional report from the Olympia Fields police department describes an interview with Glen Rogers, a friend of Goodman. Rogers stated that he led a homosexual lifestyle which included a relationship with Feinberg, and that approximately one month prior to the interview, Goodman told Rogers that Goodman and Feinberg had a sexual encounter the previous weekend. One report discusses Goodman's homosexual lifestyle and the police department's possession of photographs of *274 Goodman with Glen Rogers and an unidentified nude male. Another report describes a telephone call that the police department received from an individual named Bill Davis. Davis "wanted to know why the S & M angle of this homicide has not been followed up on in the news media." According to Davis, Goodman "used to hang out" at a Chicago bar "frequented by `male hustlers' with homosexual and S & M tendencies." Davis recognized defendant and Feinberg as being patrons of this bar.
The other evidence that defendant cites in support of his current argument references personal details of Goodman's lifestyle. Defendant has attached an affidavit from Appolon Beaudouin, Jr., an investigator for the Capital Litigation Division. This affidavit references Beaudouin's interview with Michelle Kury, defendant's former girlfriend. According to Beaudouin, Kury stated that "Patrick told her that Goodman was into sex videos." Defendant further cites a report from the Olympia Fields police department that lists property recovered from Goodman's home. The list of property references "pornographic homosexual assorted photos" and a "copy of Gay Chicago Magazine for January, 87."
Defendant argues that, had trial counsel presented this evidence, he would have been entitled to a jury instruction on voluntary manslaughter. We hold that defendant has failed to make a substantial showing that he was prejudiced by trial counsel's failure to present this evidence.
Defendant's argument is that this evidence would have supported a defense that he killed Goodman while acting under a sudden and intense passion resulting from serious provocation. Defendant's theory of provocation appears to be that Goodman made unwanted sexual advances toward him on the night of the murder. The only evidence that could have supported this theory is (1) the affidavit from the Capital Litigation Division investigator which recounts that a former cellmate of Feinberg stated that Feinberg told him that, on the night of Goodman's murder, Goodman made a sexual advance toward defendant which enraged defendant and caused defendant to stab Goodman; and (2) the police report which relates that Greg Wilson spoke to a man named John Dixon, who spoke to Feinberg, who said that "Goodman tried to make out with Pat Page, and then they stabbed him." The remaining evidence is simply not evidence that Goodman made an unwanted sexual advance toward defendant on the night of the murder. Indeed, defendant's own affidavit states that Goodman performed unwanted sexual acts on Feinberg, not on defendant.
Even focusing on the evidence that could have supported defendant's theory of provocation, and accepting all of this evidence as true, we hold that defendant has failed to make a substantial showing that trial counsel was ineffective for failing to present this alleged evidence of voluntary manslaughter. Initially, we note that this evidence is hearsay and would likely not have been admissible at defendant's trial. Defendant has failed to provide an affidavit from Feinberg attesting to the information which has been attributed to him, and stating that he would have been willing to testify to this information at defendant's trial. In any event, defendant's theory is that he killed Goodman while he was acting under a sudden and intense passion resulting from serious provocation. Defendant argues that the provocation here is that Goodman made sexual advances toward him. This is not one of the categories of provocation that this court has recognized. See Garcia, 165 Ill.2d at 429, 209 Ill.Dec. 172, 651 N.E.2d 100; Chevalier, 131 Ill.2d at 71, 136 Ill. Dec. 167, 544 N.E.2d 942. Thus, even if evidence that Goodman made a sexual advance toward defendant on the night of the murder had been admitted at trial, this evidence would not have entitled defendant to a voluntary manslaughter instruction.
*275 Defendant, however, argues that, in People v. Saldivar, 113 Ill.2d 256, 100 Ill.Dec. 776, 497 N.E.2d 1138 (1986), and in People v. Lenser, 102 Ill.App.3d 214, 58 Ill.Dec. 463, 430 N.E.2d 495 (1981), the defendants received jury instructions for voluntary manslaughter in cases similar to defendant's case. Although Saldivar and Lenser involved fact scenarios where the victim made a homosexual advance toward the defendants, the question of whether the evidence was sufficient to entitle the defendants to a voluntary manslaughter instruction was not at issue. Also, in Saldivar, the stipulated evidence revealed that the defendant stated that, after the victim made the sexual advance, "a struggle ensued," and the defendant stabbed the victim with a kitchen knife. Saldivar, 113 Ill.2d at 260-61, 100 Ill.Dec. 776, 497 N.E.2d 1138. Thus, it appears that the defendant received the voluntary manslaughter instruction on the basis of mutual combat, not the sexual advance.
Defendant cites additional cases which he contends "discuss what could be termed the `homosexual panic' defense and demonstrate the accepted use of this `defense' to obtain a manslaughter instruction." While these cases likewise involve fact scenarios where the victims made homosexual advances toward the defendants, the defendants' theories of voluntary manslaughter were based on the unreasonable belief in the need for self-defense, not on serious provocation, which is the theory advanced by defendant in this case. See, e.g., People v. Henne, 23 Ill.App.3d 567, 319 N.E.2d 596 (1974); People v. Barnes, 23 Ill.App.3d 390, 319 N.E.2d 248 (1974). These cases, therefore, are inapposite.
For the foregoing reasons, we hold that defendant has failed to make a substantial showing that trial counsel was ineffective for failing to present the alleged evidence of voluntary manslaughter.

B. Failure to Adequately Present Defendant's Motion to Suppress His Confession

Defendant argues that trial counsel was ineffective in both the Goodman and Howell cases in presenting defendant's motion to suppress his confession. We note that defendant was represented by the same two attorneys in both the Goodman and Howell cases. The facts relevant to this issue are outlined extensively in our opinions on direct appeal. See People v. Page, 156 Ill.2d 258, 284-85, 189 Ill.Dec. 371, 620 N.E.2d 339 (1993) (Howell case); People v. Page, 155 Ill.2d 232, 246-59, 185 Ill.Dec. 475, 614 N.E.2d 1160 (1993) (Goodman case). We review those facts necessary to address defendant's argument in this appeal.
Defendant was arrested around 10 p.m. on Saturday, May 16, 1987, and remained in police custody, in Cook County, until May 20, when he was taken before a judge for a bond hearing. Defendant gave law enforcement officers numerous statements with respect to the Goodman murder on May 16, 17, 18, and 19. On May 19, defendant also gave authorities formal statements regarding the murder of Andrew Devine, committed in Will County, and the murder of Charles Howell, committed in Cook County.
The first case to go to trial was the Will County prosecution for Devine's murder. In that proceeding, defendant moved to suppress his statements. Defendant's motion did not specify which statements were being challenged. In his motion, defendant argued that the interrogating officers made unfulfilled promises of leniency; that defendant was led to believe that the only court proceedings in which his statements would be used would be those in which the promises of leniency would be enforced; that the officers did not honor his wishes to consult with an attorney; and that the officers threatened to charge defendant's father with the offenses in the Goodman case.
The Will County trial court held a hearing at which the parties introduced testimony regarding the entire time period during which defendant was in custody. *276 The State presented the testimony of three members of the Olympia Fields police department, the assistant State's Attorney who had questioned defendant in all three cases, and the court reporter who had transcribed defendant's formal statements to the Devine and Howell murders. These witnesses testified that defendant received Miranda warnings and waived these rights prior to each session of questioning, and that defendant was not mistreated while in custody. These witnesses further denied that any promises of leniency were made to defendant or that he or his family members were threatened in any way.
Defendant testified at the suppression hearing. Defendant stated that, shortly after he was taken into custody, the police showed defendant a booking photograph of his father and told defendant that his father would be charged in the Goodman case if defendant did not confess. We note that defendant's father had been arrested when police learned that property belonging to Goodman was in defendant's father's home. Defendant's father was released soon after defendant's arrest. At the suppression hearing, defendant also testified that the police refused defendant's request to contact an attorney or a family member. Defendant further testified that, prior to making the statements regarding the Devine and Howell cases, the assistant State's Attorney promised defendant that he would receive only a 20-year sentence for those offenses if he confessed to the crimes.
Defendant's mother and sister testified on behalf of defendant at the suppression hearing. They stated that during the weekend of defendant's arrest, they repeatedly called the Olympia Fields police department, and their requests to speak with defendant were denied. The defense also presented the testimony of Leila Naszkiewicz, the mother of Michael Naszkiewicz, who had also been arrested in connection with the Goodman murder. Leila Naszkiewicz testified that she too encountered difficulty in attempting to contact her son while he was in police custody.
Following the suppression hearing, the Will County trial court denied defendant's motion to suppress his statements. The trial court held that defendant had given his statements voluntarily. The trial court did not distinguish among the different statements made by defendant.
Subsequently, in both the Cook County Howell and Goodman cases, defendant moved to suppress his statements. The trial court in both cases granted the State's motion to strike defendant's motion to suppress. The trial court in both cases held that the Will County trial court had already resolved the admissibility of defendant's statements, and that defendant was therefore collaterally estopped from challenging that determination.
On direct appeal in the Goodman case, this court extensively reviewed this issue and concluded that the Will County trial court, in rejecting defendant's claims, "necessarily determined issues pertinent to all three sets of statements made by the defendant while in police custody." Page, 155 Ill.2d at 254, 185 Ill.Dec. 475, 614 N.E.2d 1160. This court stated that "we have carefully examined the evidence and arguments presented at the Will County suppression hearing. Our analysis leads us to conclude that the Will County judge's ruling on the admissibility of the Devine statements resolved as well factual issues pertinent to the Goodman and Howell statements." Page, 155 Ill.2d at 257, 185 Ill.Dec. 475, 614 N.E.2d 1160. Likewise, on direct appeal in the Howell case, this court stated that "[w]e have carefully examined the record of the Will County proceedings and the record in the instant case and have found nothing to dissuade us from our earlier conclusion" in the Goodman case that defendant is collaterally estopped from challenging the admissibility of his statements. Page, 156 Ill.2d at 285, 189 Ill.Dec. 371, 620 N.E.2d 339.
*277 Defendant argues in these post-conviction proceedings that trial counsel was ineffective in both the Goodman and Howell cases in presenting the motions to suppress defendant's statements. Defendant contends that he has made a substantial showing that, had trial counsel presented certain other evidence, the trial court would not have held that defendant was collaterally estopped from challenging the admissibility of his statements. Defendant suggests that this new evidence includes "the extensive searches and cooperation with authorities in searching for the Goodman and Howell bodies; their promises relating to these searches; and the additional conversations on these outings."
We review the evidence that defendant now cites in support of his argument that trial counsel was ineffective in presenting his motion to suppress his statements in Cook County. Defendant attaches his own affidavit in which he repeats allegations to which he testified at the suppression hearing. In this affidavit, defendant also states that he rehearsed his statements both before and after the court reporter arrived. Defendant states that, before the court reporter arrived, the assistant State's Attorney reminded defendant that he would help defendant "get 20 [years] or less." However, the assistant State's Attorney told defendant that "since he could not promise me anything, [h]e would have to ask me if there was a promise, that I would have to say no." Defendant further alleges that he "found that Michael Naszkiewicz and Michelle Kury repeatedly asked for attorneys and Michael's mother tried to get an attorney, but the police would not let her." Finally, defendant states that he "was told that my family and I would be killed if I did not take the rap."
Defendant also references an affidavit from the investigator for the Capital Litigation Division, who interviewed Michelle Kury on June 13, 1997. During this interview, Kury stated that she was in the Village of Matteson jail for four days and could not get an attorney or talk to her family for that period of time.
Defendant further cites a report from the Olympia Fields police department which discusses a May 15, 1987, meeting between a police officer and Leila Naszkiewicz, whose son Michael was in custody at the time. Naszkiewicz apparently requested that she be notified when her son had a bond hearing, and requested information regarding representation for her son by the public defender's office. Naszkiewicz was advised that her son was being held on burglary charges but that the charges could change as the investigation progressed.
In this regard, defendant attaches an affidavit from his brother. His brother states that when defendant "was in the Richton Park jail, my mother and I tried to see him and the police almost arrested me for sitting in the parking lot. They held Pat [defendant] for at least 72 hours, and told me that he had not been charged, he did not need a lawyer and did not need to see anyone."
Defendant also attaches an affidavit from his father. His father relates that defendant told him that he confessed to the crimes because the police showed him a picture of his father in a jail cell. Finally, defendant cites two Olympia Fields police department reports which recount that defendant was transported to Wisconsin to search for Goodman's body. These reports also state that defendant voluntarily gave statements after being advised of his Miranda rights.
Defendant fails to explain how any of this evidence would have resulted in a holding by the trial court that defendant was not collaterally estopped from challenging the admissibility of his statements. Most of this evidence is cumulative of the evidence that the trial court considered, and which this court reviewed, in determining that defendant was collaterally estopped from relitigating his motion to suppress his statements. The other evidence, *278 namely, the circumstances surrounding the arrests of Michelle Kury and Michael Naszkiewicz, is simply not relevant to a determination of the voluntariness of defendant's statements.
We therefore hold that defendant has failed to make a substantial showing that, had trial counsel presented this evidence, there is a reasonable probability that the trial court would not have held that defendant was collaterally estopped from challenging the admissibility of his statements.
We note that defendant also suggests in this regard that trial counsel in the Howell and Goodman cases were ineffective for failing to ensure that appellate counsel in the Devine case challenged the admissibility of defendant's statements. In the Devine case, defendant did not receive the death penalty. Thus, defendant's appeal in that case was heard by the appellate court. See People v. Page, 196 Ill.App.3d 285, 143 Ill.Dec. 46, 553 N.E.2d 753 (1990). Appellate counsel in the Devine case did not challenge the admissibility of defendant's statements. Defendant now argues that trial counsel in the Goodman and Howell cases "failed to insure that some level of appellate review was had of these statements," and that as a result of this "failure," the issue of the admissibility of defendant's statements was never reviewed. This, of course, is an improper argument, as we are not reviewing the Devine case. Furthermore, defendant fails to offer any argument to support the notion that a challenge to the admissibility of his statements would have been successful.
As a final matter, defendant suggests that trial counsel were ineffective for failing to adequately present defendant's motion to quash his arrest and suppress evidence. Defendant attaches police reports regarding the taking of defendant into custody, and the obtainment of permission from defendant's mother to search her house.
The Will County trial court denied defendant's motion to quash his arrest and suppress evidence. On direct appeal in the Goodman case, we noted that the trial court in the Goodman case granted the State's motion to strike defendant's motion to quash his arrest and suppress evidence on the basis that defendant was collaterally estopped from challenging the Will County trial court's prior determination. See People v. Page, 155 Ill.2d 232, 248, 185 Ill.Dec. 475, 614 N.E.2d 1160 (1993) (Goodman case). We further noted that the Cook County trial court's disposition of defendant's motion to quash his arrest and suppress evidence was not at issue in the appeal. Page, 155 Ill.2d at 248, 185 Ill. Dec. 475, 614 N.E.2d 1160.
Defendant offers no argument to support his suggestion that trial counsel were ineffective for failing to adequately present defendant's motion to quash his arrest and suppress evidence. We therefore hold that defendant has waived any argument in this regard. See 177 Ill.2d R. 341(e)(7) (stating that an appellant's brief must include an argument, "which shall contain the contentions of the appellant and the reasons therefor").

C. Failure to Present Mitigating Evidence

Defendant argues that he has made a substantial showing that trial counsel was ineffective at sentencing in both the Goodman and Howell cases for failing to present certain mitigating evidence. The alleged mitigating evidence to which defendant cites includes information regarding defendant's involvement in a cult and the interplay of that cult involvement with defendant's psychiatric history. Defendant contends that, had trial counsel presented this evidence at the sentencing hearings, there is a reasonable probability that the jurors would have concluded that the balance of aggravating and mitigating circumstances did not warrant death.
The following is the evidence that was presented in mitigation at defendant's sentencing hearings in the Goodman and *279 Howell cases. In the Goodman case, Arlene Messner-Peters, a social worker, testified regarding a mitigation report that she prepared at the request of trial counsel. She interviewed defendant's family members, reviewed material from the Department of Corrections, and reviewed defendant's confessions. Messner-Peters testified that defendant's childhood was unstable. Defendant's parents were often involved in physical altercations with each other. Defendant's father was an alcoholic and would become abusive toward his wife and children.
Messner-Peters also testified regarding defendant's difficulties in school, both academically and socially. Defendant suffered from a learning disability. Also, a congenital condition affecting defendant's eye muscles had caused defendant's eyes to drift apart and to cross. The children at school teased defendant because of this condition. Defendant also had a history of using marijuana and LSD.
Dr. Gerard Girdaukas, a licensed clinical psychologist, testified that he administered psychological tests to defendant and diagnosed him with a learning disability and with a "non-specific personality disorder." Defendant exhibited symptoms of depression, paranoia, delusional thinking, and organic brain impairment. Dr. Girdaukas concluded that defendant was under the influence of extreme emotional disturbance at the time of the Goodman murder. Dr. Girdaukas recommended that defendant take antipsychotic medication and attend support groups, and he recommended further testing.
Defendant's parents, Paul and Patricia Page, and defendant's sister, Grace Page, testified on defendant's behalf. Their testimony reiterated the evidence regarding defendant's academic and social problems. The testimony also revealed that defendant's parents separated when defendant was eight years old. Defendant lived with each parent at various times in his childhood. The testimony further described defendant's father's alcoholism, abusive behavior, and infidelity.
A neighbor also testified regarding her relationship with defendant's family, and about defendant's good nature. Further, a clergyman, who had visited defendant while he was an inmate at the Cook County jail, testified about defendant's interest in religion and his desire to be baptized.
At the sentencing hearing in the Howell case, defendant presented almost all of the same mitigating evidence that was presented at the Goodman sentencing hearing. However, defendant's mother, sister, and neighbor did not testify at this sentencing hearing.
Defendant claims that trial counsel was ineffective for failing to investigate and present evidence regarding defendant's involvement in a cult. According to defendant, this evidence showed that defendant's involvement in a cult was "so extreme that it was labeled by numerous mental health professionals, years before the murders, as evidencing delusional thought processes and psychotic behavior." Defendant argues that this evidence would have helped to explain to the jurors "how he was associated with these murders (and how others were more culpable) and how he came to be able to be involved in such acts."
Defendant attached to his post-conviction petition a 1981 psychiatric summary report from the Psychiatric Institute of Cook County regarding defendant's fitness for trial of the pending burglary charge against him. The psychiatrist who examined defendant concluded that defendant was fit for trial, stating that defendant "does not display any psychotic behavior nor show any psychotic symptoms." The psychiatrist reported that defendant "relates an interest in the occult [and] talks about getting together with other young men to have some sort of seances involving `black magic.'" Defendant insisted that "being sent to jail is not right and he needs to be in a hospital for his `problem.'" *280 According to the psychiatrist, defendant appeared "quite manipulative."
Defendant also attached a 1981 psychological examination from the Psychiatric Institute which recounts defendant's statements that he has "gone pretty far into the occult" and that he saw devils in inkblots. Defendant next referenced a psychological summary that was conducted by a psychologist who concluded that defendant was not fit for trial on his pending burglary case. Defendant reported to the psychologist that he was experiencing hallucinations and paranoid delusions, and expressed concern about his involvement in witchcraft. Specifically, defendant stated that he was engrossed in the study of black magic, and that he and several friends, led by a 24-year-old warlock, held services, conjured demons, and cast spells. The psychologist concluded that, although defendant's request for psychiatric treatment seemed genuine, defendant "is shrewd enough to seek treatment as a possible alternative to incarceration."
Defendant also provided a May 17, 1987, report from the Olympia Fields police department. The report states that Feinberg told police officers that "there are people who believe that Mr. Patrick Page is the anti-Christ, and that Page derived a power from the location where Chuck Howell's body was buried." The report further recounts that Feinberg "indicated that Patrick Page was the leader of a Satanic cult." Another report from the Olympia Fields police department describes a call that the reporting officer received from Marty Carson, who identified himself as a friend of defendant. Carson stated that he had accompanied defendant to a campfire site where defendant would "party," and from where defendant stated he derived a "special power." Defendant further provided some unattributed notes regarding defendant's involvement in black magic, rituals, and sacrifices.
Defendant attached his own affidavit, which states that "I was involved in certain practices from a young age, and am still in fear of individuals who were involved and may still be involved in these practices." Defendant likewise attached affidavits from his father and brother. These affidavits relate that, when defendant was 16 years old, he was involved in "some kind of cult or devil worship."
Finally, defendant provided reports from a physician and a psychologist regarding the workings of cults. These doctors essentially reviewed the information we have just discussed and postulated that defendant was under the influence of a cult leader at the time he committed the murders at issue. These doctors also generally described the mind-control techniques used by leaders of cults.
After reviewing this allegedly mitigating evidence, we hold that there is no reasonable probability that, had counsel presented this evidence at the sentencing hearings, the juries would have concluded that the mitigating factors were sufficient to preclude the death sentence. See Strickland v. Washington, 466 U.S. 668, 695, 104 S.Ct. 2052, 2069, 80 L.Ed.2d 674, 698 (1984). Contrary to defendant's argument, the jurors likely would have viewed this evidence of cult involvement as aggravating evidence. This evidence describes defendant's involvement in devil worship and ritualistic sacrifices. Even worse, some of this evidence shows that defendant was the leader of the cult engaged in these practices. Significantly, the evidence also shows that the doctors to whom defendant mentioned his cult involvement suggested that defendant was manipulative and might be trying to avoid prison by relying on his cult involvement. In any event, defendant fails to explain how any of this evidence showed a "cult connection to the murders" of Howell and Goodman.
Furthermore, the aggravating evidence in this case far outweighs the mitigating evidence. The State presented defendant's confession to the murders of Devine, Howell, and Goodman. Defendant, Feinberg, and Kenneth Cheney murdered *281 Devine because Devine "ripped off" Cheney in a drug deal. They tied up Devine with an extension cord and transported him to a wooded area, where they stabbed him to death. After the murder, defendant, Cheney, and Feinberg drove to Cheney's home, where they drank alcohol and smoked marijuana.
Defendant and Feinberg later murdered Howell because they were worried that Devine's disappearance would make Howell suspicious. Defendant and Feinberg planned the murder in advance. They drew a map of the area where they would bury Howell, went to the planned burial site and dug a hole, and lured Howell to the site under the pretense of having a party there. Defendant stabbed Howell, and Feinberg hit him over the head with a large stick. They buried Howell and set his grave on fire. After the murder, defendant and Feinberg went to defendant's house, smoked marijuana, and drove around in Howell's car.
A year and a half later, defendant originated the plan to murder Goodman because defendant held a grudge against Goodman. Defendant stabbed Goodman in the chest four times. Defendant and Feinberg stole credit cards and cash from Goodman's wallet before wrapping Goodman's body in a sheet and a rug and placing it in the trunk of Goodman's car. After stopping at a tavern in southeastern Wisconsin to eat and play pool, defendant and Feinberg drove to a rural area in Wisconsin, dug a hole, and buried Goodman's body. They then burned the sheet and the rug over the grave.
The State also presented details of defendant's criminal history. The State introduced certified copies of defendant's conviction following a guilty plea on May 11, 1982, to seven charges of burglary. Defendant was sentenced to five years' imprisonment for the offenses. After defendant had served a portion of this prison sentence, he was assigned to a prerelease center. Residents were allowed to leave the center during the day to work, but were required to return each night. A supervisor from the center testified that defendant signed out on the morning of December 5, 1983, and did not come back until January 2, 1984. Defendant said that he did not return on December 5 because he had gotten drunk and fallen asleep. Because defendant knew that he was on escape status anyway, he decided to stay out for the holidays. Consequently, defendant was returned to the custody of the Illinois Department of Corrections.
A casework supervisor from the Logan Correctional Center testified that defendant was incarcerated at Logan beginning in September 1982, and remained there until May 1983, when he was assigned to the prerelease center. Defendant was returned to Logan in February 1984, and was released on parole two months later. Defendant received 27 disciplinary tickets while an inmate at Logan. Defendant received these tickets for physical or verbal altercations with other inmates, insulting behavior toward the staff, possession of contraband, and failing to go to school.
Captain Robert Maeyama of the Park Forest police department also testified regarding various contacts he had with defendant while defendant was a juvenile. Captain Maeyama stated that he apprehended defendant in connection with several different charges during a period from June 1977 to October 1980. These charges included three batteries or aggravated batteries, two burglaries, a theft, a car theft, and disorderly conduct.
A review of this aggravating evidence shows that defendant is a domineering and remorseless murderer. Given defendant's extensive criminal history, as well as the heinous nature of the crimes in this case, defendant has failed to establish the requisite prejudice under Strickland. There is no reasonable probability that the outcome of defendant's sentencing hearings would have been different had the alleged mitigating evidence at issue been presented.
*282 As a final matter, defendant requests this court to order a limited remand so that he may have a complete neurological examination conducted. Defendant initially filed a motion for funds so that defendant could retain a neurological expert to perform "full neurological testing" of defendant. Defendant argued that the limited evaluation conducted by Dr. Girdaukas showed possible brain damage or neurological disorders. Defendant sought funds to retain an expert to conduct this testing. The trial court denied defendant's motion. In accordance with our preceding discussion, we hold that the trial court did not abuse its discretion in denying this motion.
Defendant, in his reply brief in this court, states that the Capital Litigation Division now has sufficient funds to pay for the requested neurological testing. Defendant, therefore, requests a limited remand "for the purpose of conducting the Neurological Assessment and the Cult-related Psycho-Social investigation."
We decline to order a limited remand in this case. Defendant presented the testimony of Dr. Girdaukas, a licensed clinical psychologist, at both sentencing hearings. Dr. Girdaukas administered numerous psychological tests to defendant and presented his findings to the jurors. There is no reasonable probability that the outcome of defendant's sentencing hearings would have been different had evidence of defendant's cult involvement been presented. We therefore decline to remand this case for the testing defendant now seeks.

D. Failure to Challenge Proportionality of Defendant's Sentence

Defendant argues that appellate counsel was ineffective for failing to challenge the proportionality of defendant's death sentences to the natural life sentences of his codefendant, Feinberg. On direct appeal in the Howell case, appellate counsel argued that the trial court improperly precluded defendant from presenting to the jury, at the second stage of the sentencing hearing, nonstatutory mitigation evidence that his codefendant, Gerald Feinberg, had pled guilty and was sentenced to natural life imprisonment for the murder of Howell. See People v. Page, 156 Ill.2d 258, 270, 189 Ill.Dec. 371, 620 N.E.2d 339 (1993). We noted that defendant was not requesting "that this court undertake a review of the proportionality of his sentence." Page, 156 Ill.2d at 271, 189 Ill. Dec. 371, 620 N.E.2d 339. Rather, defendant was arguing "that his codefendant's sentence and relative degree of participation in the murder should have been considered by the jury at the second stage of his sentencing hearing." Page, 156 Ill.2d at 271, 189 Ill.Dec. 371, 620 N.E.2d 339. We rejected this argument and held that defendant's request to have the jury consider evidence of a codefendant's sentence is neither constitutionally required nor relevant to the jury's examination of the individual defendant's characteristics and the circumstances of his offense. Page, 156 Ill.2d at 270-72, 189 Ill.Dec. 371, 620 N.E.2d 339.
Defendant now contends that appellate counsel in the Howell case should have instead argued that defendant's death sentence is disproportionate to the natural life sentence of his codefendant Feinberg. Defendant also suggests that appellate counsel in the Goodman case was likewise ineffective for failing to challenge the proportionality of defendant's death sentence to the natural life sentence of Feinberg.
Comparative proportionality review in death penalty cases is not required by either the United States Constitution (see Pulley v. Harris, 465 U.S. 37, 104 S.Ct. 871, 79 L.Ed.2d 29 (1984)) or the Illinois death penalty statute (see People v. Palmer, 162 Ill.2d 465, 491, 205 Ill.Dec. 506, 643 N.E.2d 797 (1994)). This court has, however, considered whether a sentence of death in a particular case is disproportionately harsh in comparison with a less severe sanction imposed on a codefendant convicted of the same crime. See, e.g., People v. Burt, 168 Ill.2d 49, 80-81, *283 212 Ill.Dec. 893, 658 N.E.2d 375 (1995); People v. Flores, 153 Ill.2d 264, 294-96, 180 Ill.Dec. 1, 606 N.E.2d 1078 (1992); People v. St. Pierre, 146 Ill.2d 494, 513, 167 Ill. Dec. 1029, 588 N.E.2d 1159 (1992); People v. Bean, 137 Ill.2d 65, 134, 147 Ill.Dec. 891, 560 N.E.2d 258 (1990). Such judicial review acknowledges the necessity to avoid arbitrary or capricious death sentences by insuring that the cases in which death is imposed are rationally distinguished from those in which it is not imposed. St. Pierre, 146 Ill.2d at 513, 167 Ill.Dec. 1029, 588 N.E.2d 1159. The focus of this review is on the particular defendant's involvement in the crime, the nature of the crime, the character and background of the defendant, including any criminal record, and the defendant's potential for rehabilitation. See Burt, 168 Ill.2d at 80, 212 Ill.Dec. 893, 658 N.E.2d 375; Flores, 153 Ill.2d at 294, 180 Ill.Dec. 1, 606 N.E.2d 1078.
The record reveals the following relevant information regarding defendant's involvement in the crimes. In the Goodman case, it was defendant who originated the plan to rob and kill Goodman because defendant held a grudge against Goodman. Defendant stabbed Goodman in the chest four times; Feinberg did not inflict any injuries on Goodman. In the Howell case, defendant stabbed Howell in the chest, and Feinberg hit Howell in the head with a stick.
Moreover, defendant had a substantial criminal history while Feinberg had no criminal convictions. Details of defendant's criminal history were introduced at the sentencing hearings in the Goodman and Howell cases. As we have previously discussed, this criminal history includes defendant's conviction for burglary, and his escape from the prerelease center where he was serving a portion of his sentence for this conviction. Additionally, defendant received 27 disciplinary tickets while an inmate at Logan Correctional Center. These disciplinary tickets were for physical or verbal altercations with other inmates, insulting behavior toward the staff, possession of contraband, and failing to go to school. Furthermore, defendant was charged with numerous offenses while a juvenile, including three batteries or aggravated batteries, two burglaries, a theft, a car theft, and disorderly conduct.
Given defendant's role as the leader in the crimes in this case, defendant's criminal background, and defendant's lack of potential for rehabilitation, defendant's death sentences were not disproportionate to Feinberg's natural life imprisonment sentences. Defendant, therefore, has failed to make a substantial showing that he received ineffective assistance of appellate counsel in this regard.

II. Perjured Testimony
Defendant next argues that his constitutional right to due process was violated at trial because the State failed to correct false testimony.
The State's knowing use of perjured testimony to obtain a criminal conviction constitutes a violation of due process of law. People v. Jimerson, 166 Ill.2d 211, 223, 209 Ill.Dec. 738, 652 N.E.2d 278 (1995). A conviction obtained by the knowing use of perjured testimony must be set aside if there is any reasonable likelihood that the false testimony could have affected the jury's verdict. People v. Olinger, 176 Ill.2d 326, 345, 223 Ill.Dec. 588, 680 N.E.2d 321 (1997), citing United States v. Bagley, 473 U.S. 667, 678-80, 105 S.Ct. 3375, 3381-82, 87 L.Ed.2d 481, 492 (1985).
These principles likewise apply where the State, although not soliciting the false testimony, allows it to go uncorrected. Olinger, 176 Ill.2d at 345, 223 Ill.Dec. 588, 680 N.E.2d 321, citing Napue v. Illinois, 360 U.S. 264, 269, 79 S.Ct. 1173, 1177, 3 L.Ed.2d 1217, 1221 (1959). This is so even where the witness' false testimony goes only to that witness' credibility. Olinger, 176 Ill.2d at 345, 223 Ill.Dec. 588, 680 N.E.2d 321, citing Napue, 360 U.S. at 269, 79 S.Ct. at 1177, 3 L.Ed.2d at 1221.
*284 Defendant's claim revolves around the testimony of Glen Rogers and Greg Wilson, who testified at the Goodman murder trial. Glen Rogers and Greg Wilson testified that on Monday, May 11, 1987, they went to Goodman's house and looked in the windows. They noticed that a television set and stereo equipment were missing. They then called the Olympia Fields police department. Goodman had been murdered the preceding Thursday.
Defendant references the cross-examination of these witnesses. Rogers denied that he had sexual relations with Feinberg at Goodman's house, and also denied that he had any sexual relations with Feinberg other than one time at his own house. Wilson denied that there was any relationship involving cocaine or homosexual conduct between himself and Goodman.
Defendant now argues that the testimony by Rogers and Wilson was false, and that the State should have corrected the testimony. In support of this claim, he attaches a May 14, 1987, report from the Olympia Fields police department. This report describes the reporting officer's meeting with Rogers. Rogers stated that he had two or three sexual encounters with Feinberg during the past two months and three or four sexual encounters with Feinberg during the past year. Defendant also attaches a page of a May 17, 1987, Olympia Fields police department report which recounts that Wilson told the officer that Feinberg had just called Wilson and asked to speak to Rogers, who lived with Wilson. Feinberg wanted to know if Rogers had any cocaine.
Defendant argues that this alleged "homosexual and drug-related conduct went directly to the heart of the [voluntary] manslaughter defense, and it also served to impeach the State's witnesses." As we have discussed, defendant's theory of defense at the Goodman trial was that he killed Goodman while acting under a sudden and intense passion resulting from serious provocation, and therefore committed voluntary manslaughter. The alleged provocation is that Goodman made a sexual advance toward him. The number of sexual encounters between Rogers and Feinberg, and their involvement in possessing or using cocaine, is not relevant to defendant's establishing a voluntary manslaughter defense based on Goodman's alleged sexual overture to defendant.
Furthermore, even if Rogers and Wilson had been impeached at trial with the evidence defendant cites, there is no reasonable likelihood that their testimony could have affected the jury's verdict. The testimony of Rogers and Wilson played a minor role in the State's case, and, as this court stated on direct appeal in the Goodman case, the evidence of defendant's guilt was overwhelming. See People v. Page, 155 Ill.2d 232, 262, 185 Ill.Dec. 475, 614 N.E.2d 1160 (1993). In particular, defendant confessed in detail to the crime, and an eyewitness saw defendant at Goodman's house shortly before Goodman disappeared. Thus, defendant has failed to make a substantial showing of a constitutional violation in this regard.

III. Brady Violation
Defendant also contends that the State violated his right to due process by failing to disclose to the defense all exculpatory evidence as required by Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963). Defendant argues that the State violated the Brady rule by failing to disclose evidence regarding the victim Goodman's past homosexual conduct and evidence regarding defendant's involvement in cult activities.
To establish a Brady violation, the suppressed evidence must be both favorable to the accused and material. Favorable evidence is material in this context "`only if there is a reasonable probability that, had the evidence been disclosed to the defense, the result of the proceeding would have been different.'" People v. Hobley, 182 Ill.2d 404, 432-33, 231 Ill.Dec. 321, 696 N.E.2d 313 (1998), quoting United States v. Bagley, 473 U.S. 667, 682, 105 *285 S.Ct. 3375, 3383, 87 L.Ed.2d 481, 494 (1985). A "`reasonable probability'" of a different result is a "`probability sufficient to undermine confidence in the outcome.'" Hobley, 182 Ill.2d at 433, 231 Ill.Dec. 321, 696 N.E.2d 313, quoting Bagley, 473 U.S. at 682, 105 S.Ct. at 3383, 87 L.Ed.2d at 494. To determine whether evidence is material, a court must consider the cumulative effect of all suppressed evidence favorable to the defense. Hobley, 182 Ill.2d at 433, 435, 231 Ill.Dec. 321, 696 N.E.2d 313. Furthermore, the prosecution cannot escape its duty under Brady by contending that the suppressed evidence was known only to police investigators and not to the prosecutors. Hobley, 182 Ill.2d at 433, 231 Ill.Dec. 321, 696 N.E.2d 313, citing Kyles v. Whitley, 514 U.S. 419, 438, 115 S.Ct. 1555, 1568, 131 L.Ed.2d 490, 508-09 (1995).
The allegedly suppressed evidence to which defendant refers is the evidence of defendant's involvement in a cult, which we previously discussed in addressing defendant's claim that his trial counsel was ineffective for failing to present mitigating evidence. Defendant also references allegedly suppressed evidence of Goodman's "homosexual conduct and contacts with the defendants." This is the evidence that we previously discussed in addressing defendant's claims that trial counsel was ineffective for failing to present sufficient evidence of a voluntary manslaughter defense, and that the State failed to correct perjured testimony.
Defendant has failed to offer any argument as to how there is a reasonable probability that this allegedly suppressed evidence would have changed the result of the proceedings. Moreover, our resolution of defendant's other arguments which reference the allegedly suppressed evidence demonstrates that there is no reasonable probability that this evidence would have changed the result of the proceedings. We therefore hold that defendant has failed to make a substantial showing of a Brady violation.
We also note that defendant offers no basis upon which to conclude that his trial counsel did not in fact possess these police reports. In this regard, however, defendant argues that the post-conviction trial court abused its discretion in denying his motion to depose trial counsel. We hold that the trial court did not abuse its discretion in denying defendant's motion to depose his trial counsel. Because this allegedly suppressed evidence is not material within the meaning of Brady, there is no need to inquire of defense counsel whether they possessed it.

IV. Death Penalty Instructions
Defendant argues that the instructions given to the jury at his sentencing hearings are confusing, misleading, and violate his constitutional rights. Defendant has waived this issue by failing to raise it on direct appeal. See People v. Towns, 182 Ill.2d 491, 503, 231 Ill.Dec. 557, 696 N.E.2d 1128 (1998). Defendant, however, argues that this argument is not waived because its evidentiary basis was de hors the trial record. See People v. Whitehead, 169 Ill.2d 355, 372, 215 Ill.Dec. 164, 662 N.E.2d 1304 (1996), overruled in part on other grounds, People v. Coleman, 183 Ill.2d 366, 233 Ill.Dec. 789, 701 N.E.2d 1063 (1998).
Defendant relies on the studies of Professor Hans Zeisel and Professor Shari Diamond in arguing that we should remand the cause for an evidentiary hearing on the fairness of the instructions. Both the Zeisel and Diamond studies purported to test the ability of potential jurors to comprehend certain Illinois death penalty instructions. The 1990 Zeisel study, which concluded that the instructions resulted in misunderstanding and confusion, formed the basis for a federal district court's holding that the death penalty instructions were constitutionally infirm. See United States ex rel. Free v. Peters, 806 F.Supp. 705 (N.D.Ill.1992). The Court of Appeals for the Seventh Circuit, however, reversed the district court's holding. Free v. Peters, *286 12 F.3d 700 (7th Cir.1993); see also Gacy v. Wellborn, 994 F.2d 305 (7th Cir. 1993). This court has agreed that the Zeisel study does not establish that the Illinois death penalty instructions are unconstitutional. See People v. Jackson, 182 Ill.2d 30, 93, 230 Ill.Dec. 901, 695 N.E.2d 391 (1998); People v. Brown, 172 Ill.2d 1, 55-56, 216 Ill.Dec. 733, 665 N.E.2d 1290 (1996).
Defendant, however, cites the study by Professor Diamond, which was conducted after the Zeisel study. The Diamond study was designed to address two primary objections to the Zeisel study: (1) that the Zeisel study did not use a control group to determine whether revised jury instructions would improve performance and (2) that the Zeisel study did not take into account jury deliberations. The results of the Diamond study confirmed the conclusion of the Zeisel study that the death penalty instructions were confusing.
This court has already rejected the argument that the Diamond study provides a basis for invalidating the Illinois death penalty instructions. See People v. Terrell, 185 Ill.2d 467, 518-19, 236 Ill.Dec. 723, 708 N.E.2d 309 (1998); Jackson, 182 Ill.2d at 93, 230 Ill.Dec. 901, 695 N.E.2d 391; People v. Hobley, 182 Ill.2d 404, 467-70, 231 Ill.Dec. 321, 696 N.E.2d 313 (1998); Brown, 172 Ill.2d at 55-57, 216 Ill.Dec. 733, 665 N.E.2d 1290. Specifically, in Brown, we stated:
"[A]lthough 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." Brown, 172 Ill.2d at 57, 216 Ill.Dec. 733, 665 N.E.2d 1290.
We adhere to our prior holdings and hold that an evidentiary hearing is not warranted on defendant's claim that the death penalty instructions are unconstitutional.
In this regard, defendant also argues that the post-conviction trial court abused its discretion in denying defendant's request for production of the juror cards for the 12 jurors who sat at the guilt and sentencing proceedings in the Goodman case. Defendant seeks to locate and interview the jurors so that he may "support the claim that the instructions used in the instant case were confusing or misled the jury."
This court in People v. Hobley, 182 Ill.2d 404, 467-70, 231 Ill.Dec. 321, 696 N.E.2d 313 (1998), addressed a related issue. In Hobley, the defendant likewise argued that the death penalty instructions are unconstitutional. In addition to citing the Zeisel and Diamond studies, the defendant submitted affidavits from the jurors in his case. Some of the jurors stated that they found the instructions to be confusing; that they felt obligated to impose the death penalty as a result of their guilty verdict; and that they believed that the defendant could be released on parole if they did not impose the death penalty. Hobley, 182 Ill.2d at 470, 231 Ill.Dec. 321, 696 N.E.2d 313. This court held that this information pertains to the method, motive, or process by which the jurors reached their verdict and therefore, may not be used to impeach the jury's verdict. Hobley, 182 Ill.2d at 470, 231 Ill.Dec. 321, 696 N.E.2d 313.
Accordingly, the information defendant seeks pursuant to his motion for production of the juror cards may not be used to support his current argument. Thus, we hold that the trial court did not abuse its discretion in denying defendant's request for production of the juror cards.


*287 CONCLUSION
For the reasons stated, the judgment of the circuit court of Cook County dismissing defendant's post-conviction petition without an evidentiary hearing is affirmed. We direct the clerk of this court to enter an order setting Tuesday, November 14, 2000, as the date on which the sentence of death, entered by the circuit court of Cook County, shall be carried out. Defendant shall be executed in the manner provided by law. 725 ILCS 5/119-5 (West 1998). The clerk of this court shall send a certified copy of the mandate in this case to the Director of Corrections, the warden of Tamms Correctional Center, and the warden of the institution where defendant is confined.
Affirmed.
Chief Justice HARRISON, concurring in part and dissenting in part:
I agree that Page's convictions should not be disturbed. In my view, however, his sentence of death cannot be allowed to stand. For the reasons set forth in my partial concurrence and partial dissent in People v. Bull, 185 Ill.2d 179, 235 Ill.Dec. 641, 705 N.E.2d 824 (1998), the Illinois death penalty law violates the eighth and fourteenth amendments to the United States Constitution (U.S. Const., amends. VIII, XIV) and article I, section 2, of the Illinois Constitution (Ill. Const. 1970, art. I, § 2). Page's sentence of death should therefore be vacated, and the cause should be remanded for imposition of a sentence of imprisonment. Ill.Rev.Stat.1985, ch. 38, par. 9-1(j). Because Page has been found guilty of murdering more than one victim, the term of his imprisonment must be natural life. Ill.Rev.Stat.1985, ch. 38, par. 1005-8-1(a)(1)(c).
NOTES
[1]  Effective July 1, 1987, the legislature amended section 9-2 of the Criminal Code of 1961 and replaced the offense of voluntary manslaughter with the offense of second degree murder. See 720 ILCS 5/9-2 (West 1998). The second degree murder statute incorporates the mitigating factors of sudden and intense passion and unreasonable belief in the need for self-defense. See People v. Tenner, 157 Ill.2d 341, 371-72, 193 Ill.Dec. 105, 626 N.E.2d 138 (1993).
