delivered the opinion of the court:
Defendant, Latasha Pulliam, was indicted on 131 counts of murder, aggravated criminal sexual assault, aggravated kidnapping, and aggravated unlawful restraint. She and her codefendant, Dwight Jordan, were tried simultaneously by separate juries in the circuit court of Cook County. Defendant’s jury convicted her of first degree murder, two counts of aggravated criminal sexual assault, and two counts of aggravated kidnapping. The jury determined that there were no mitigating factors sufficient to preclude imposition of the death penalty. The trial court sentenced defendant to death for first dégree murder. Additionally, the court sentenced defendant to three consecutive prison terms of 60 and 30 years for aggravated criminal sexual assault and 15 years for aggravated kidnapping. Defendant’s death sentence has been stayed pending direct review *269by this court. Ill. Const. 1970, art. VI, § 4(b); 134 Ill. 2d Rs. 603, 609(a).
On appeal to this court, defendant argues that the trial court erred in (1) admitting hearsay; (2) admitting evidence of a book found in defendant’s apartment; (3) allowing testimony concerning a court-ordered fitness examination at both trial and sentencing; (4) allowing various items of evidence in aggravation; (5) preventing a defense witness from testifying; (6) allowing the State to make improper arguments at sentencing; (7) refusing to respond to a question from the jury; and (8) imposing an excessive sentence. Defendant also argues that the death penalty is unconstitutional for a number of reasons. We affirm defendant’s convictions and sentences.
FACTS
On March 21, 1991, defendant was arrested for the murder of six-year-old Shenosha Richards (hereinafter Shenosha). The next day, defendant spoke to law enforcement officers and signed a court-reported confession. On appeal, defendant does not challenge the admissibility of this confession. In the confession, defendant related the following account of the murder.
On March 21, defendant was outside on the street when Shenosha asked to come to her house. Defendant took Shenosha to her third-floor apartment. Upon entering the apartment, she took Shenosha to her bedroom, where Dwight Jordan, her boyfriend and codefendant, was sitting on the bed. She told Shenosha to sit down and watch television. Defendant then went to the kitchen to use cocaine, and remained there for half an hour. When she returned to the bedroom, Shenosha was on the floor crying, with her underwear down to her knees. Jordan was behind her on the floor, fondling his penis in an attempt to achieve an erection. Upon failing to do so, he picked up a white shoe polish bottle and *270inserted it into Shenosha’s rectum. Shenosha continued crying and asked Jordan to stop, saying that she would not tell anyone.
Defendant further confessed that Jordan then told her to get a hammer. After retrieving the hammer, defendant put saliva on it and inserted the straight end into Shenosha’s vagina. As defendant did this, Jordan continued inserting the shoe polish bottle in and out of Shenosha’s rectum. Defendant and Jordan continued this activity for 10 minutes. When they stopped, Shenosha was crying. Defendant put her hand over Shenosha’s mouth, and Shenosha tried to scream. Defendant then took an electrical cord from a television, wrapped it around Shenosha’s neck, and "started to strangle her.”
Defendant stated that she then took Shenosha to an empty apartment down the hall, with the electrical cord still wrapped around her neck. Defendant said that as they entered this apartment, Shenosha fell onto a board with a nail protruding from it. Defendant took Shenosha to the kitchen of the apartment where she started a fire "to scare her.” After defendant put the fire out, Shenosha said that she would not tell anyone, except that she would have to tell her parents. At that point, defendant pulled the cord tighter around Shenosha’s neck and continued tightening it for 10 minutes. Then, because she heard knocking on the door of her apartment down the hall, she put Shenosha in a closet in the empty apartment and threw Shenosha’s shoes out the window.
Defendant said that she looked in the closet a few minutes later and saw that Shenosha was not breathing. Defendant then took the hammer that she had used earlier and hit Shenosha on the head three or four times. Defendant then placed Shenosha in a garbage can, hit her on the head with a two-by-four, and tried to cover her up with garbage.
*271Defendant said that she gave this statement willingly, fully aware of her constitutional rights to remain silent and have the assistance of counsel. Investigators who searched the crime scene recovered Shenosha’s shoes, a hammer, a white shoe polish bottle, and a triangular piece of wood with a protruding nail.
At trial, the medical examiner who performed the autopsy on the victim testified that Shenosha suffered 42 distinct injuries. She sustained two puncture wounds to her chest which damaged her lungs and coronary artery. The examiner testified that these wounds were consistent with being struck by a board with a nail. Shenosha had six lacerations on her head, three of which penetrated through to the skull. These injuries were consistent with being hit with a hammer, or a board such as a two-by-four. She had injuries under her chin which were consistent with ligature strangulation. She sustained lacerations to the skin of her anus which were consistent with a traumatic penetration or sexual assault. Injuries caused by the penetration were at least eight inches deep, consistent with the handle of the hammer or the shoe-polish bottle. She also had lacerations alongside her clitoris and on the lower surface of her vagina extending to her anus which were consistent with penetration of the hammer or the shoe-polish bottle.
In its case in chief, the defense called a psychologist who had examined defendant in 1994. He testified that defendant has an IQ of 69 and that he believed her to be mildly mentally retarded. He further testified that a person with defendant’s degree of mental retardation would be easily influenced by others, would not anticipate the consequences of her actions, and would have difficulty predicting the outcome of a situation.
In rebuttal, the State called a psychologist who had examined defendant in 1991. He testified that he did *272not believe defendant was mentally retarded. He also testified that defendant had malingered, or faked mental illness, during his examination of her, and further opined that she likely did so during the 1994 examination as well.
The jury found defendant guilty of first degree murder (720 ILCS 5/9 — 1(a)(1) (West 1992)), two counts of aggravated criminal sexual assault (720 ILCS 5/12— 14(a)(2) (West 1992)), and two counts of aggravated kidnapping (720 ILCS 5/10 — 2(a)(3) (West 1992)). The jury then found defendant eligible for the death sentence on two grounds: (1) that she committed the murder in the course of other felonies, namely, aggravated criminal sexual assault and aggravated kidnapping (720 ILCS 5/9 — 1(b)(6) (West 1992)); and (2) that the victim was under the age of 12 and her death resulted from exceptionally brutal and heinous behavior indicative of wanton cruelty (720 ILCS 5/9 — 1(b)(7) (West 1992)).
At the second stage of the sentencing hearing, the State offered evidence in aggravation. An employee of the Department of Children and Family Services testified that defendant frequently had been placed in state facilities as a youth, but had often run away. The employee testified that on one occasion, defendant ran away with another girl who was under state care, and that while the two were gone, defendant physically forced the girl to submit to oral, anal, and vaginal sex performed by one of defendant’s former boyfriends. The employee testified that the girl was also forced to perform oral sex on both defendant and her former boyfriend.
The State presented evidence that defendant’s daughter was twice hospitalized, once for injuries consistent with physical abuse, and once for both physical and sexual abuse. The State also offered evidence that defendant, while incarcerated awaiting trial, sexually *273assaulted an inmate. Finally, in order to show defendant’s lack of remorse, the State presented evidence that defendant described to another inmate in great detail her sexual assault and murder of Shenosha.
In mitigation, defendant offered evidence that her parents and other adults physically and sexually abused her as a child. The evidence indicated that defendant gave birth to a child when she was 15 and to another when she was 17, and that the fathers of these children were two separate boyfriends of defendant’s mother. Defendant also offered evidence that her codefendant, Jordan, physically abused her. A second defense psychologist testified that defendant is mildly mentally retarded, with a long history of alcohol and drug abuse.
The jury found no mitigating factors sufficient to preclude imposition of the death sentence. The trial court sentenced defendant to death.
ANALYSIS
Trial
Hearsay
Defendant contends that the trial court erred in allowing testimony concerning certain statements made by various persons about the crime because the statements were hearsay. An out-of-court statement is hearsay only if it is offered to establish the truth of the matter asserted. People v. Simms, 143 Ill. 2d 154, 173 (1991).
Defendant’s first hearsay argument concerns the testimony of the police officer who apprehended her. This officer testified that during his pursuit of defendant, numerous bystanders shouted such things as "There she goes, right there, she’s running.” The officer also testified that after he apprehended defendant, members of the crowd said such things as "They got her, there she is right there, they got her in the car.”
*274A police officer may testify about statements made by others, such as victims or witnesses, when such testimony is not offered to prove the truth of the matter asserted, but is instead used to show the investigative steps taken by the officer leading to the defendant’s arrest. Simms, 143 Ill. 2d at 174. We hold that the statements made by bystanders at the crime scene were not inadmissible hearsay because they were not offered to prove what they asserted, i.e., that defendant fled and that she was taken into police custody. Rather, the statements were offered to explain the steps taken by the police in investigating the crimes and apprehending defendant.
Defendant next argues that the trial testimony of Kenosha, Shenosha’s sister, contained inadmissible hearsay. Kenosha testified that on the day of the murder, a young girl in the neighborhood told her that Shenosha had gone to the movies with Shenosha’s aunt. We hold that this statement was not inadmissible hearsay because it was not offered to prove the truth of the statement. Shenosha had not gone anywhere with her aunt, but rather was in defendant’s apartment at the time. The statement was offered to explain why Kenosha continued looking for Shenosha after talking with the young girl.
Kenosha also testified that while she was looking for her sister, she encountered codefendant Jordan, who told her that defendant "live[s] up there.” This statement also was not inadmissible hearsay, as it was not offered to prove that defendant in fact lived in the apartment Jordan identified. No one disputed this fact at trial. The statement was instead offered to explain why Kenosha and her mother went to defendant’s apartment.
Defendant further contends that some of the testimony given by Emma Richards, Shenosha’s mother, was *275hearsay. Emma testified that the night before the murder, Shenosha asked her if she knew Dwight Jordan’s girlfriend. Emma testified that when she answered yes, Shenosha told her that Jordan’s girlfriend had taken her to a park across the street that day. We reject defendant’s contention that these statements made by the victim were hearsay. The statements were not offered to prove that defendant took Shenosha to the park, but were instead offered to explain why Emma and Kenosha sought out defendant after they discovered that Shenosha was missing.
Emma also testified that while she was searching for her daughter, a neighbor, Leslie Moon, told her that no one had left defendant’s apartment recently. We likewise do not believe this statement was hearsay, because it was offered not to prove that no one had left the apartment, but rather to show why Kenosha and her mother went to the apartment a second time.
Finally, Emma further testified that during her search, Moon told her that she had observed defendant place something in the garbage can on the porch of defendant’s apartment. We agree with defendant that the purpose for offering this statement was to corroborate the State’s allegation that defendant placed the victim’s body in the garbage can. The statement was therefore hearsay, and the trial court erred in admitting it. We do not believe, however, that this error requires reversal of defendant’s conviction. An error in the admission of evidence is harmless if properly admitted evidence is so overwhelming that no fair-minded juror could reasonably have voted to acquit the defendant. People v. Miller, 173 Ill. 2d 167,195 (1996). Because the evidence of defendant’s guilt was overwhelming, we hold that the trial court’s error in admitting this statement was harmless.
Evidence of Book Found in Defendant’s Apartment
At trial, the State was permitted to show the jury *276the cover of a book entitled The Force of Sex. A police officer who investigated the murder testified that he found the book on a coffee table in defendant’s apartment two days after the murder. The officer testified that he did not notice the book when he searched the apartment the day after the murder. He testified that the apartment was not locked between the time of the murder and his discovery of the book. No testimony was offered concerning the nature of the book’s contents, or about who owned or had read the book.
Defendant objected when the State sought to introduce the book into evidence. Defendant argued that the book’s potential for prejudice outweighed any probative value it might have. Defendant also contended that there was insufficient evidence linking her to the book, because there was no testimony that she owned or had read it, and because the apartment had not been secured between the time of the murder and the discovery of the book. The trial court ruled that the cover and title of the book were probative to show the defendant’s state of mind, and overruled defendant’s objections. The jury was allowed to view only the cover of the book and to hear the testimony of the investigating officer about where and when he found it.
Evidentiary rulings are within the sound discretion of the trial court and will not be disturbed on review unless the court has abused that discretion. People v. Boclair, 129 Ill. 2d 458, 476 (1989). The general rule is that physical evidence may be admitted provided there is proof to connect it with the defendant and the crime. People v. Free, 94 Ill. 2d 378, 415 (1983). Evidence may be inadmissible, however, if it has little probative value due to its remoteness, uncertainty or its possibly unfair prejudicial nature. People v. Enis, 139 Ill. 2d 264, 281 (1990).
We hold that the trial court erred in admitting the *277book into evidence. First, because there was no testimony that defendant owned or had read the book, or concerning the nature of its contents, the court had no sound basis for concluding that the book was relevant to the crimes. Second, the fact that the apartment was unsecured for two days before the book was found further diminished the book’s relevance to defendant’s role in the crimes. Given these circumstances, the trial court abused its discretion in admitting the book. Because the properly admitted evidence of defendant’s guilt was so overwhelming, however, we hold that this error was harmless. Miller, 173 Ill. 2d at 195.
Use of Fitness Examination
Defendant contends that because she did not raise the affirmative defense of insanity, the trial court erred in allowing testimony from a state psychologist concerning a 1991 examination which the court ordered to determine her fitness to stand trial. See 725 ILCS 5/104 — 14 (West 1992) (providing that statements made by a defendant during a court-ordered fitness examination may not be admitted against the defendant unless she raises the defense of insanity or the defense of drugged or intoxicated condition). The psychologist testified that during the 1991 examination, defendant stated that she heard voices and acted as though she were talking to an invisible person. The psychologist also testified that defendant said that she saw crack cocaine all over the floor of the examining room, and that if she had a pipe, she would pick up the crack and smoke it. We hold that defendant waived any error in the admission of this testimony by failing to object when the testimony was offered at trial. Miller, 173 Ill. 2d at 191.
Defendant contends, however, that because the trial court’s admission of the testimony concerning the fitness examination was plain error, her failure to object does not constitute waiver. Under the plain error doc*278trine, a reviewing court may consider a trial error not properly preserved by objection when (1) the evidence is closely balanced or (2) the error is so fundamental and of such a magnitude that the defendant was denied her right to a fair trial. Miller, 173 Ill. 2d at 191-92.
As noted earlier, the evidence in defendant’s case was not closely balanced. Furthermore, we do not believe that the alleged error was so fundamental as to deny defendant her right to a fair trial. Defendant herself injected the issue of mental competence into the proceedings by arguing that her low IQ and purported mental retardation absolved her of responsibility for her actions. See Buchanan v. Kentucky, 483 U.S. 402, 422-23, 97 L. Ed. 2d 336, 355, 107 S. Ct. 2906, 2917-18 (1987) (holding that prosecution may constitutionally offer evidence from court-ordered fitness examination when defendant presents psychiatric evidence).
Defendant alternatively contends that her trial counsel’s failure to object to the testimony concerning the fitness examination deprived her of the effective assistance of counsel in violation of the sixth amendment to the United States Constitution. U.S. Const., amend. VI. In order to prove that counsel’s assistance was unconstitutionally ineffective, a defendant must establish a reasonable probability that the result of the proceeding would have been different had counsel not committed the alleged errors. People v. Albanese, 104 Ill. 2d 504, 525 (1984). In light of the overwhelming evidence of defendant’s guilt, we do not believe that the jury’s verdict would have been different if the court had éxcluded the testimony concerning the fitness examination.
Defendant also contends that the trial court erred in allowing the psychologist who conducted the 1991 fitness examination to testify that because of his conclusion that defendant had malingered, i.e., faked mental *279illness, during that examination, she likely did so again during a defense psychologist’s subsequent evaluation of her in 1994. Defendant argues that the state psychologist’s assessment of the 1991 examination was irrelevant to the defense psychologist’s interpretation of the 1994 results.
Defendant was the first to raise the issue of malingering at trial, when her psychologist testified on direct examination that defendant had not malingered during the 1994 evaluation. Only after this testimony was offered did the State counter with its psychologist’s opinion that defendant had malingered in 1991 and had continued to do so since. The latitude to be allowed in the presentation of rebuttal evidence is within the sound discretion of the trial court. People v. Collins, 106 Ill. 2d 237, 269 (1985). Because defendant initially raised the issue of malingering, we do not believe the trial court erred in allowing the State to rebut defendant’s arguments on this point.
Sentencing
Use of Fitness Examination
Defendant contends that testimony concerning the 1991 fitness examination was also improperly admitted during the sentencing phase of trial. At the sentencing hearing, the psychologist who conducted the 1991 examination repeated the testimony he had given earlier at trial. In addition, he further testified that defendant suffered from poly-substance abuse, borderline intellectual functioning, antisocial personality disorder, and sexual sadism. He testified that persons who suffer from sadism enjoy tormenting their victims.
As with the evidence of the fitness examination offered during the first phase of trial, we hold that defendant waived any error in the admission of this evidence at sentencing by failing to object contemporaneously *280when it was offered. Miller, 173 Ill. 2d at 191. We also reject defendant’s argument that the admission of this evidence at sentencing was plain error. The evidence of defendant’s guilt was overwhelming and there was a substantial amount of evidence in aggravation. In addition, because defendant was the first to introduce psychiatric evidence, admission of testimony concerning the fitness examination did not deprive her of a fundamental right. Buchanan, 483 U.S. at 422-23, 97 L. Ed. 2d at 355, 107 S. Ct. at 2917-18. Furthermore, we hold that defense counsel’s failure to object to the admission of this evidence at sentencing did not violate defendant’s sixth amendment right to the effective assistance of counsel because, in light of the evidence against her, defendant failed to establish a reasonable probability that the jury’s verdict would have been different absent counsel’s alleged error. Albanese, 104 Ill. 2d at 525.
Defendant also contends that the psychologist’s testimony at sentencing about sexual sadism improperly converted the mitigating factor of mental illness into an aggravating factor. See Zant v. Stephens, 462 U.S. 862, 885, 77 L. Ed. 2d 235, 255, 103 S. Ct. 2733, 2747 (1983) (holding that certain factors may not constitutionally be labeled as aggravating). Once again, we hold that defendant waived this alleged error by failing to object.
Defendant further contends that the trial court improperly admitted testimony by the psychologist that defendant was sane. Defendant asserts that sanity cannot be an aggravating factor because it applies to every defendant eligible for the death penalty. See Arave v. Creech, 507 U.S. 463, 474, 123 L. Ed. 2d 188, 200-01, 113 S. Ct. 1534, 1542-43 (1993) (holding that if an aggravating circumstance applies to every defendant eligible for the death penalty, the circumstance is constitutionally in firm). We reject defendant’s challenge to this testimony. The State did not affirmatively attempt to use *281defendant’s sanity as an aggravating factor, but rather mentioned it solely to rebut defendant’s argument in mitigation that the jury should refrain from imposing the death penalty due to defendant’s purported mental illness.
Evidence in Aggravation
Defendant contends that the trial court erred in admitting testimony of a fellow inmate in aggravation. First, defendant argues that the testimony was irrelevant and prejudicial. The inmate testified that defendant confessed to committing the sexual assault and murder at issue in the instant case. The inmate also related specific details of the crimes as told to her by defendant. Defendant argues that in eliciting this testimony, the State was improperly relitigating defendant’s guilt. We disagree. Evidence concerning a defendant’s role and participation in the commission of an offense is admissible at sentencing to establish defendant’s character. People v. Turner, 156 Ill. 2d 354, 368 (1993).
The inmate also testified that defendant had stated she could avoid going to prison for the assault and murder by pleading insanity. Defendant argues that the prejudicial nature of this testimony outweighed its probative value. We hold that this testimony was properly admitted at sentencing to show defendant’s lack of remorse for her crimes. People v. Barrow, 133 Ill. 2d 226, 281 (1989).
Second, defendant contends that the trial court improperly admitted evidence that she took her infant daughter to the hospital in 1989. The examining doctor testified that the infant had a severe second-degree burn in a clearly demarcated line around her buttocks. The doctor testified that he believed the burn was caused by someone intentionally dipping the child into scalding water, because there were no burns or splash marks on any other part of her body. Defendant argues that *282because it is plausible that her daughter was burned accidentally, the doctor’s testimony was unduly prejudicial. We disagree. Given the State’s presentation of extensive additional evidence that defendant had a history of sexually and physically abusing her daughter, the testimony concerning the burn injury was admissible.
Third, defendant contends that the trial court erred in admitting evidence that she allegedly sexually assaulted another inmate while incarcerated awaiting trial. A prison guard testified that one morning, several inmates told her that defendant had sexually assaulted an inmate. The guard testified that when she asked the alleged victim if defendant had assaulted her, the inmate nodded slightly, but would not say anything out loud. The guard testified that the alleged victim had marks on her neck, face and arm, and seemed frightened of defendant. The guard further testified that no report was filed about the incident because the alleged victim refused to talk about it.
Defendant argues that this testimony was inadmissible because it was not corroborated by a prison disciplinary report. Evidence is admissible at the aggravation / mitigation phase of a sentencing hearing, however, as long as it is relevant and reliable. People v. Free, 94 Ill. 2d 378, 422 (1983). This determination lies within the discretion of the trial judge. People v. Eddmonds, 101 Ill. 2d 44, 65 (1984). Because the allegations that defendant perpetrated a sexual assault were corroborated by the guard’s testimony that the alleged victim was visibly injured and frightened after the incident, we hold that the trial court did not abuse its discretion in admitting this testimony.
Defendant also argues that the guard improperly testified as to the race of the incarcerated sexual assault victim, describing her as "a real petite little white girl.” *283Because this reference consisted of a single, isolated statement, we hold that it was not intended to incite racial prejudice, and did not in fact have such an effect. People v. Thomas, 137 Ill. 2d 500, 543 (1990). The jury was repeatedly instructed that it was not to be influenced by any person’s race, and we find no error in the court’s handling of this testimony.
Exclusion of Testimony Concerning Mental Disabilities
Defendant contends that the trial court erred in refusing to allow a witness to testify regarding the difficulties faced by mentally handicapped people. The offered witness was a member of the Illinois Human Rights Commission at the time of trial, and had previously served as chair of the Advisory Council for the Education of Handicapped Children of the Illinois State Board of Education. In an offer of proof, she testified that mentally handicapped people have a difficult time learning. She also testified that mentally handicapped parents need support because they have trouble performing basic parenting skills. On cross-examination, she conceded that she was not acquainted with defendant’s case.
The trial court refused to allow the witness to testify before the jury. Defendant argues that this was error because the evidence the witness would have offered was relevant to mitigation. The determination of relevance lies within the discretion of the trial judge. Eddmonds, 101 Ill. 2d at 65. When the witness was introduced to the court, the defense conceded that it had already presented expert testimony substantially similar to the testimony it desired the witness to offer. The defense also conceded that the witness would not be offering expert testimony. The witness admitted that she did not know defendant and had not reviewed her medical history. Finally, the defense failed to notify the court or the State that it would offer the witness until *284the moment it did so. Given the above factors, as well as the trial judge’s observation that there was a significant dispute over whether defendant was in fact mentally retarded, we hold that the trial court did not abuse its discretion in refusing to allow the witness to testify.
State’s Closing Argument at Sentencing
Defendant contends that the trial court erred in allowing the State to make various arguments to the jury at the conclusion of the sentencing phase of trial. Specifically, defendant asserts that the State improperly argued that there was no excuse for defendant’s crimes, that defense counsel was trying to make the jury feel guilty, that the evidence clearly established defendant’s guilt, and that defendant’s daughter was a "cocaine baby.”
We hold that defendant waived these issues by failing to object contemporaneously when the arguments were made. People v. Miller, 173 Ill. 2d 167, 191 (1996). Furthermore, because the evidence in this case was not closely balanced, and because the State’s arguments did not deny defendant a fair trial, we will not address these issues under the plain error doctrine. Miller, 173 Ill. 2d at 191-92.
Court’s Response to Question from Jurors
Defendant contends that the trial court erred in responding to a note the jury sent to the judge during its deliberations on defendant’s sentence. The note consisted of the following question: "What happens if we cannot reach a unanimous decision on either verdict?” Defendant moved that the court respond to this inquiry by giving the jury the following instruction: "According to the law, if you are not unanimous, you are to sign the verdict that says you are not unanimous and it is a no death verdict.” The court overruled this motion, and instead instructed the jury in writing as follows: "You have your instructions. Keep deliberating.”
*285The general rule is that the trial court has a duty to provide instructions to the jury where it has posed an explicit question or requested clarification on a point of law arising from facts about which there is doubt or confusion. People v. Childs, 159 Ill. 2d 217, 228-29 (1994). A trial court may, however, exercise its discretion and properly decline to answer a jury’s inquiries where the instructions are readily understandable and sufficiently explain the relevant law; where further instructions would serve no useful purpose or would potentially mislead the jury; when the jury’s inquiry involves a question of fact; or if providing an answer would cause the court to express an opinion which would likely direct a verdict one way or another. Childs, 159 Ill. 2d at 228.
We believe that the trial court properly exercised its discretion in refusing defendant’s requested instruction and in directing the jury to continue deliberating. Immediately before beginning its deliberations on defendant’s sentence, the jury was instructed as follows: "You may not sign a verdict imposing a death sentence unless you unanimously vote for it.” Because the instructions given to the jury concerning unanimity were readily understandable and sufficiently explained the relevant law, we hold that the court did not err in the manner in which it responded to the jury’s inquiry.
Excessiveness of Punishment
Defendant contends that the death sentence imposed by the jury is excessive when juxtaposed with the evidence in mitigation. Defendant presented evidence that she was physically and sexually abused by her alcoholic mother, sexually abused by her mother’s boyfriends, and physically abused by her boyfriend/codefendant. She also offered evidence that she was depressed and had received psychiatric treatment, and that she suffers from an antisocial personality disorder. She asserts that her low IQ qualifies her as mildly mentally retarded *286and that this factor alone should preclude the imposition of the death penalty.
A capital sentencing jury’s decision will not be lightly overturned, particularly where it is amply supported by the record. People v. Johnson, 146 Ill. 2d 109, 145 (1991). Mitigation evidence of a defendant’s cognitive abilities and mental health does not preclude imposition of a death sentence when that evidence is outweighed by aggravating evidence. People v. Wilson, 164 Ill. 2d 436, 460 (1994). Likewise, evidence that a defendant has been physically or sexually abused or is an alcohol and drug abuser does not invalidate a death sentence when outweighed by aggravating evidence. People v. Taylor, 166 Ill. 2d 414 (1995).
Here, defendant confessed to a brutal rape, torture, and murder of a six-year-old girl. An expert attributed the victim’s death to 42 distinct injuries arising from a combination of strangulation, puncture wounds to the chest, and blunt head trauma. In addition, the State offered evidence in aggravation that defendant had previously assisted in raping one of her friends, that she had sexually and physically abused her child, and that she had sexually assaulted a fellow inmate. Considering all of this evidence, we cannot say that the jury was required to find that the mitigation evidence precluded imposition of the death penalty. See People v. Johnson, 146 Ill. 2d 109, 145 (1991).
Constitutionality of Death Penalty
Defendant contends that the trial court’s imposition of the death penalty is unconstitutional on several grounds. First, she argues that section 9 — 1(b)(7) of the Criminal Code (720 ILCS 5/9 — 1(b)(7) (West 1992)) is facially vague. This section permits the jury to impose a death sentence if the victim was under 12 years of age and the death resulted from exceptionally brutal or heinous behavior indicative of wanton cruelty. We have *287previously rejected this argument, and we decline to reconsider that holding. People v. Odie, 128 Ill. 2d 111, 140 (1988).
Defendant also contends that the Illinois Pattern Jury Instructions given at both stages of her sentencing hearing unconstitutionally failed to guide the jury’s discretion. See Free v. Peters, 806 F. Supp. 705 (N.D. Ill. 1992), aff’d in part and rev’d in part, 12 F.3d 700 (7th Cir. 1993). We have likewise rejected this argument and refuse to reconsider our holding. People v. Williams, 161 Ill. 2d 1, 59 (1994).
Defendant next argues that section 9 — 1(g) of the Criminal Code (720 ILCS 5/9 — 1(g) (West 1992)) is unconstitutional because it places the burden on a criminal defendant to establish that a sentence other than death should be imposed and thereby precludes meaningful consideration of mitigation evidence. We reject this argument, as we have done in the past. People v. Miller, 173 Ill. 2d 167, 200 (1996). In a related argument, defendant asserts that sections 9 — 1(c) and (e) are unconstitutionally vague because they allow the jury to consider aggravating factors other than those enumerated in the statute. We also adhere to precedent in rejecting this contention. Miller, 173 Ill. 2d at 200.
Finally, defendant argues that the death penalty statute as a whole is unconstitutional because it results in arbitrarily or capriciously imposed death sentences. We decline to reconsider our previous rejection of this argument. Miller, 173 Ill. 2d at 201.
CONCLUSION
For the reasons stated, defendant’s convictions and sentences are affirmed. The clerk of this court is directed to enter an order setting Wednesday, September 10, 1997, as the date on which the sentence of death is to be imposed. Defendant shall be executed in the manner provided by law. 725 ILCS 5/119 — 5 (West 1994). The *288clerk shall send a certified copy of the mandate in this case to the Director of Corrections, the warden of State-ville Correctional Center, and the warden of the institution where defendant is now confined.
Affirmed.