
25 Cal.Rptr.3d 554 (2005)
35 Cal.4th 334
107 P.3d 229
The PEOPLE, Plaintiff and Respondent,
v.
Gregory Scott SMITH, Defendant and Appellant.
No. S026223.
Supreme Court of California.
March 10, 2005.
As Modified on Denial of Rehearing April 27, 2005.
Certiorari Denied October 31, 2005.
*558 Lynne S. Coffin and Michael J. Hersek, State Public Defenders, under appointments by the Supreme Court, and William Hassler, Deputy State Public Defender, *559 San Francisco, for Defendant and Appellant.
Bill Lockyer, Attorney General, Robert R. Anderson, Chief Assistant Attorney General, Pamela C. Hamanaka, Assistant Attorney General, John R. Gorey, William T. Harter and Susan Sullivan Pithey, Deputy Attorneys General, Los Angeles, for Plaintiff and Respondent.
Certiorari Denied October 31, 2005. See 126 S.Ct. 550.
KENNARD, J.
On October 9, 1991, defendant Gregory Scott Smith pled guilty to (1) first degree murder in violation of Penal Code section 187, subdivision (a);[1] (2) kidnapping in violation of section 207, subdivision (a); (3) arson in violation of section 451, subdivisions (c) and (d); (4) commission of a forcible lewd act upon a child in violation of section 288, subdivision (b); and (5) forcible sodomy in violation of section 286, subdivision (c). Defendant admitted the charged special circumstances that the murder was committed during the commission of a kidnapping, a lewd act upon a child, and an act of sodomy. (See § 190.2, subd. (a)(17).) After the penalty trial, the jury returned a verdict of death. The trial court denied defendant's motions for a new trial and for modification of the verdict, and it sentenced defendant to death. The court imposed concurrent sentences of 11 years on count 2, four years on count 3, six years on count 4, and six years on count 5, but it stayed execution of noncapital sentences pending execution of the death sentence.
This appeal is automatic. (§ 1239, subd. (b).)

I. The Prosecution Evidence

A. Defendant's Prior Relationship with the Victim
From April of 1989 to March 6, 1990, defendant, then 21 to 22 years old, worked for the 31st District Latchkey Project, serving as a teacher's aide at Darby and Chatsworth elementary schools in the San Fernando Valley in Southern California. His behavior as a teacher's aide was inappropriate; he would play with the children as if he were a child, but would get too rough. Defendant was particularly mean to eight-year-old Paul Bailly, a student at Darby Elementary School. On two occasions he tied Paul up with jump ropes. Once Paul asked the school's daycare director to fire defendant. Defendant overheard the request, and said he was going to "get [Paul] back."
On March 6, 1990, Hal Kuhn, executive director of the Latchkey Project, fired defendant because defendant lacked maturity and played too roughly with the children. Defendant was upset and often talked about "getting even."

B. The Investigation of the Murder of Paul Bailly
About 6:30 a.m. on March 23, 1990, Mary Bailly, Paul's mother, dropped him off at Darby Elementary School. At 11:50 a.m., Captain Fred Baugher of the Ventura County Fire Department responded to a fire in the Black Canyon area near Simi Valley and discovered Paul's body in the fire. Paul had been gagged with a cloth gag and duct tape. A set of handcuffs was found at the scene. According to supervising investigator James Allen, the burn pattern on the ground and the condition of the body showed that someone had poured fire accelerant on the corpse and set it on fire. Dr. Frederick Lovell, the Chief Medical Examiner for Ventura County, attributed the cause of death to asphyxiation due to strangling and to aspiration *560 of vomit. In his opinion, the victim had also been forcibly sodomized. The victim was dead before his body was set afire.
On March 24 and 25, 1990, Ventura County sheriff's deputies searched defendant's residence. They found, among other items, a pair of keys that fit the handcuffs found near Paul's body, several rolls of duct tape, and several newspapers. The newspapers, which were about two months old, featured an article about a well-publicized child molestation case in which the defendants were acquitted and another case where the victim had been set on fire by his father.

C. Other Violent Acts by Defendant
1. During 1988-1989, shortly before the March 1990 murder of Paul Bailly, Daniel Kavalsky worked with defendant at the Fallbrook Theater in the San Fernando Valley. He and defendant disliked each other. On one occasion defendant came up to Kavalsky and started choking him. Another person pulled defendant off Kavalsky.
2. In 1984, when Brian Due was about five or six years old, defendant, who was then 16 or 17 years old, approached Brian with one hand in a glove. Defendant said the glove had a mind of its own and defendant could not control it. Defendant then choked Brian with the glove, but released him when he cried.
3. During the summers of 1988 and 1989, Darren Goodman and defendant were counselors at the Griffith Park Boys Camp. Once, when Goodman was a referee at a hockey game, he penalized defendant for holding his hockey stick too high, an act that endangers other players. Defendant responded by striking Goodman in the shins with the hockey stick.
4. Brian Francis was 12 years old when he attended the Griffith Park Boys Camp during the summer of 1988. On one occasion a basketball accidentally hit defendant. When Brian laughed, defendant became angry and threw the ball at Brian as hard as he could. Defendant then chased Brian and tried to pull him into a cabin. When Brian resisted, defendant pulled Brian into the camp office. One of the camp directors observed the incident and fired defendant.

D. Expert Testimony of Dr. Chris Hatcher
Dr. Chris Hatcher, a clinical psychologist, was an expert witness for the prosecution. He described the characteristics of persons who commit crimes such as the sodomy and murder of Paul Bailly.
Dr. Hatcher testified that persons who commit abductions similar to the abduction in this case are carrying out a fantasy in which children are abducted, bound, and sexually assaulted. Characteristic components of the fantasy include forcible sodomy, strangulation, and disfigurement of the victim's body. Dr. Hatcher did not examine defendant or give an opinion on defendant's mental state. (We describe Dr. Hatcher's testimony further when we discuss issues regarding its admissibility and use. See post, 25 Cal.Rptr.3d at 564-567, 107 P.3d at 237-240 et seq.)

II. The Defense Evidence

A. Defendant's Background
Defendant's mother described defendant as developmentally delayed and hyperactive from a very early age. He was six years old before he could put words together in coherent speech. Defendant's mother was affectionate but overprotective toward him. Defendant's father was ashamed of defendant's retardation and verbally abused defendant; the father physically abused defendant's mother.
*561 Janice Foster, an education therapist hired by defendant's parents to help him with learning disabilities, said that at age 16 defendant had the attitude of an eager, friendly eight year old, and intellectually he was like an eight year old. Defendant's mother and his sisters also described defendant's mental retardation.
Defendant had few friends. His closest relationship was with his dog Blue, who was given to him when defendant was four months old. Blue died when defendant was 16 or 17 years old, shortly after defendant and his mother moved from the family home and left Blue behind. Defendant's mother said defendant never recovered from Blue's death, for which he felt responsible.

B. Psychological Expert Testimony
Dr. David Benson, a professor of neurology, tested defendant's IQ at 85-86. He observed signs of brain abnormalities. He diagnosed defendant as mildly to moderately mentally retarded.
After administering a PET scan (positron emission tomography scan) to defendant, Dr. Monte Buchsbaum, a psychiatrist, testified that defendant suffers from brain damage in areas of the brain controlling memory and learning.
In the opinion of Dr. Francis Crinella, a clinical psychologist specializing in developmental neurology, psychological test results confirmed brain damage and were consistent with defendant's life history of "immaturity, explosiveness, conduct disorders, and difficulties in getting along." Defendant's IQ test scores ranged from 51 to 85. Generally, defendant did better on tests that required little abstract reasoning. In Dr. Crinella's view, defendant's brain damage affected his ethical and moral judgment.
Dr. Jerome Evans, a clinical psychologist, said defendant was mentally disabled in various ways throughout his life, and as he got older the disability became worse. Defendant's performance never passed that of an eight to 10 year old. According to Dr. Evans, defendant is incapable of acting remorseful, because he "doesn't know when to try to look good" for others. Persons with defendant's "family background and ... emotional problems ... never succeed at anything.... [E]verything that they try turns out to be a mess or a problem." On cross-examination by the prosecution, Dr. Evans said he had diagnosed defendant as manifesting a schizotypal personality disorder; such persons have peculiar ideas, odd beliefs, magical thinking, and paranoid thoughts.
Dr. John Irwin, a professor of sociology, testified about the conditions of confinement in maximum security prisons.

III. Issues Relating to Jury Selection

A. Juror Removal by Peremptory Challenge
During voir dire, the prosecutor exercised peremptory challenges to excuse Prospective Jurors Donna T. and Donna V. Defendant objected, claiming that the prosecutor was systematically excluding Black jurors, in violation of People v. Wheeler (1978) 22 Cal.3d 258, 148 Cal. Rptr. 890, 583 P.2d 748.[2] We will uphold a trial court finding that the defendant has not established a prima facie case if it is supported by substantial evidence.[3]*562 (People v. Box (2000) 23 Cal.4th 1153, 1189, 99 Cal.Rptr.2d 69, 5 P.3d 130; People v. Mayfield (1997) 14 Cal.4th 668, 726-727, 60 Cal.Rptr.2d 1, 928 P.2d 485.)
Before hearing from the prosecutor on defendant's Wheeler motion, the trial court stated that it was not implicitly finding that the peremptory challenges were for an impermissible purpose. The prosecutor pointed to Donna T.'s responses to his questions during the general voir dire:
Q: "Mrs. [T.], ... do you as you sit there right now feel sorry for the defendant?"
A: "Yes, I do."
Q: "Okay, a lot? A little? Some?"
A: "A lot."
Q: "Okay. And is that because of the situation he's in, or...."
A: "Yes."
The prosecutor noted that Juror Donna T. hesitated when asked if she could vote for the death penalty,[4] and that in answering a question in the jury questionnaire about support for the death penalty, she rated herself as a "five" on a scale of one to ten.
With respect to Prospective Juror Donna V., the prosecutor said he challenged her because of her opposition to the death penalty. During the death-qualifying voir dire she said there should not be a death penalty; she, like Juror Donna T., rated herself at "five" on the death penalty rating scale. The prosecutor said that the mean average for seated jurors was 7.25, although two of the seated jurors had a five rating.
In reply, defense counsel noted that the prosecutor's questioning of Juror Donna T. was short. Regarding Juror Donna V., he said that her problem with the death penalty was her concern that an innocent man might be executed, a circumstance that could not happen here because defendant had already pleaded guilty.
After hearing from both sides, the trial court reiterated its finding that defendant had not made a prima facie showing because the prosecution's peremptory challenges to Prospective Jurors Donna T. and Donna V. were objectively reasonable and unrelated to the jurors' race. It therefore denied defendant's Wheeler motion. We agree with the trial court's conclusion.

B. The Removal of Juror Robert B. After the Jury Was Sworn
After the jury was sworn, but before counsel's opening statements, Juror Robert B. informed the court that he needed to fly to Seattle to deal with a family emergency. His mother was 82 years old, had "shortness of breath," and he had just learned a nurse had been brought in to care for her. Robert B. did not know how long he would have to remain in Seattle, but he was willing to come back and serve on the jury if the trial could be delayed to *563 accommodate him. The prosecutor proposed seating an alternate juror; the defense objected.
The trial court remarked that "perhaps the most prudent course" would be to tell Juror Robert B. to phone the court after he arrived in Seattle and knew how long he had to stay, but ultimately rejected that course of action. Robert B.'s first priority, the court said, would and should be his ailing mother's condition, not his duty of jury service; he could not be expected to go to Seattle, see his mother, and immediately turn around and fly back to California.
In discharging Juror Robert B., the trial court relied on Code of Civil Procedure section 233, which provides: "If, before the jury has returned its verdict to the court, a juror becomes sick or, upon other good cause shown to the court, is found to be unable to perform his or her duty, the court may order the juror to be discharged." Similarly, Penal Code section 1089 provides: "If at any time, whether before or after the final submission of the case to the jury, a juror dies or becomes ill, or upon other good cause shown to the court is found to be unable to perform his or her duty, or if a juror requests a discharge and good cause appears therefor, the court may order the juror to be discharged...."
The decision to discharge a juror and substitute an alternate under Penal Code section 1089 rests within the discretion of the trial court. (See People v. Beeler (1995) 9 Cal.4th 953, 989, 39 Cal. Rptr.2d 607, 891 P.2d 153; People v. Abbott (1956) 47 Cal.2d 362, 371, 303 P.2d 730.) We review such a decision for abuse of discretion. (People v. Beeler, supra, 9 Cal.4th at p. 989, 39 Cal.Rptr.2d 607, 891 P.2d 153.) Because we perceive no functional difference between Code of Civil Procedure section 233 and Penal Code section 1089, and the parties suggest none, we apply the same standard of review of abuse of discretion.
Two Court of Appeal decisions under section 1089 are on point here. As in this case, both decisions involved medical emergencies. In People v. Hall (1979) 95 Cal. App.3d 299, 157 Cal.Rptr. 107, a juror informed the court on a Friday afternoon that he had to take his wife to a physician on Monday morning. The court asked the juror to be in court by 11 a.m., and to telephone if he could not do so. On Monday morning, the juror called the court and said he had to assist his wife the entire day. The trial court then discharged the juror and substituted an alternate juror. The Court of Appeal upheld the trial court's action, observing that the lower court's exercise of discretion was "not rendered abusive merely because other alternative courses of action may have been available to the trial judge." (Id. at p. 307, 157 Cal.Rptr. 107.)
In People v. Bell (1998) 61 Cal.App.4th 282, 71 Cal.Rptr.2d 415, on the morning of the second day of trial, a juror told the trial court that he had to take his son to a doctor because of a medical emergency. The juror expected to be back in court by 1:30 p.m. He agreed to call the court by 10:30 a.m. to update his situation. The trial court, however, expressed doubt that the juror would be able to return that day, and it replaced the juror with an alternate juror to avoid inconvenience to the other jurors, alternates, and witnesses. (See id. at p. 288, 71 Cal.Rptr.2d 415.)
Upholding the trial court's decision, the Court of Appeal in Bell stated: "[T]he [trial] court conducted an adequate inquiry into good cause, and caring for a sick or injured family member surely constitutes good cause. [Citation.] Furthermore, given the uncertain timing of his return *564 and the fact so many jurors, alternates, and witnesses were waiting, the court was well within its discretion to discharge juror No. 2 and replace him with an alternate juror." (People v. Bell, supra, 61 Cal. App.4th at p. 289, 71 Cal.Rptr.2d 415.)
We note also that two decisions of this court have upheld a trial court's discretionary decision to discharge a juror whose family member died unexpectedly, rejecting the defense counsel's suggestions that the court continue the trial until the juror could return. (People v. Ashmus (1991) 54 Cal.3d 932, 986-987, 2 Cal.Rptr.2d 112, 820 P.2d 214; In re Mendes (1979) 23 Cal.3d 847, 852, 153 Cal.Rptr. 831, 592 P.2d 318.)
We conclude that when, as here, a juror has good cause to be absent from trial for an indefinite period, the trial court does not abuse its discretion in replacing that juror with an alternate juror.

IV. Issues Relating to the Admissibility and Use of Evidence of Mental Illness by the Prosecution
A brief overview: clinical psychologist Dr. Chris Hatcher testified that crimes such as those committed in this case are generally committed by sexual sadists who derive sexual pleasure from carrying out a fantasy involving restraint and molestation of a child victim. He did not testify that defendant was such a sadist.
Defendant argues that the introduction of Dr. Hatcher's testimony was an improper attempt by the prosecution to use extreme mental illness as an aggravating factor, contrary to People v. Whitt (1990) 51 Cal.3d 620, 654, 274 Cal.Rptr. 252, 798 P.2d 849, and other cases. (Defendant first raised this issue in an in limine motion before Dr. Hatcher testified, but raised the same issue in connection with defense objections to other testimony, the jury instructions, and the prosecutor's closing argument.) Defendant further contends that admission of Dr. Hatcher's testimony violated his rights under California's death penalty law and under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the United States Constitution.
The Attorney General responds that the testimony was admissible under section 190.3, factor (a), which allows the evidence of the "circumstances of the crime," and that evidence admitted under factor (a) may be either aggravating or mitigating. (See, e.g., People v. Coddington (2000) 23 Cal.4th 529, 640, 97 Cal.Rptr.2d 528, 2 P.3d 1081.)
Thus we face this question: Can the prosecution introduce evidence of a defendant's mental illness as an aggravating consideration if that mental condition relates to the circumstances of the crime? Based upon the precedents of this court, we conclude that it can.

A. Trial Testimony and Rulings

1. Trial court's rulings before Dr. Hatcher's testimony
At trial, defendant moved in limine to exclude Dr. Hatcher's testimony on the ground that evidence relating to mental illness was mitigating character evidence and thus could not be introduced by the prosecution in its case-in-chief and that the prejudicial effect of that evidence outweighed its probative value. After extensive argument, the trial court ruled that Dr. Hatcher's testimony would be admissible on "the nature of the things that are involved" in the crime.

2. Dr. Hatcher's testimony
Dr. Hatcher, a clinical psychologist, specializes in crimes involving the abduction of children. He has interviewed many persons who have committed such crimes, *565 has conducted research on the subject, and is familiar with other studies.
Dr. Hatcher testified that people who commit crimes such as those involved here  the murder of a child accompanied by sexual abuse  go through a developmental process beginning with a fantasy at puberty of being sexually aroused by an image of "someone tied up, restrained, or tortured." Over time, the fantasy becomes more serious and more detailed. Although some individuals can resist the impulse to carry out the fantasy, those that go forward still have a sense of right and wrong. They are able to plan, and they can defer acting until they get the right victim. The "drive and the need to realize the fantasy overcomes any consideration of what might happen to the victim."
According to Dr. Hatcher, the perpetrator will gather instruments of restraint, such as handcuffs. During the crime, the victim is usually restrained and gagged. Unlike ordinary child molesters, sadistic pedophiles are not satisfied with mere sexual contact, but are sexually aroused by the "suffering and the discomfort of the child." Sodomy, strangulation, and disfigurement are common characteristics of this kind of crime.
Dr. Hatcher reviewed various exhibits found in defendant's apartment, including two newspaper articles about a notorious child molestation case in which the defendants were acquitted, and another article about a father who set fire to his young son. He also noted a highlighted list of names found in defendant's residence, photographs of young children also found in defendant's residence, and the rope and duct tape found in defendant's car. He concluded that all of these were consistent with the typical fantasy of persons who commit crimes such as the crime here. Finally, with respect to the crime here, Dr. Hatcher found "a degree of planning, foresight, the development of a period of preparation over a substantial period of time, the focusing of a particular type of fantasy ... regardless of the effect upon others."[5]

B. Admissibility of Dr. Hatcher's Testimony

1. The scope of section 190.3, factor (a)
Section 190.3, factor (a) permits both the prosecution and the defense to introduce evidence of "[t]he circumstances of the crime of which the defendant was convicted in the present proceeding." In People v. Edwards (1991) 54 Cal.3d 787, 1 Cal.Rptr.2d 696, 819 P.2d 436, this court adopted an expansive reading of this language. Edwards explained: "The word `circumstances' as used in factor (a) of section 190.3 does not mean merely the immediate temporal and spatial circumstances of the crime. Rather it extends to `[t]hat which surrounds materially, morally, or logically,' the crime." (Id. at p. 833, 1 Cal.Rptr.2d 696, 819 P.2d 436.) We therefore held that factor (a) authorized evidence of the "specific harm caused by the defendant, including the impact on the family of the victim." (Id. at p. 835, 1 Cal.Rptr.2d 696, 819 P.2d 436.) We also held that evidence of the massive five-day air and ground search for the defendant after the crime was discovered was admissible under factor (a). (Id. at pp. 831-832, 1 Cal.Rptr.2d 696, 819 P.2d 436.)
In other cases we have held that characteristics of the crime fall within the scope of section 190.3, factor (a). People v. Lucero (2000) 23 Cal.4th 692, 714-715, 97 *566 Cal.Rptr.2d 871, 3 P.3d 248, held a photograph of the victim when alive was admissible because it portrayed the victim as seen by the defendant before the murder. People v. Coddington, supra, 23 Cal.4th 529, 640, 97 Cal.Rptr.2d 528, 2 P.3d 1081, said that factor (a) included "the method of killing or evidence of extensive planning." People v. Nicolaus (1991) 54 Cal.3d 551, 581, 286 Cal.Rptr. 628, 817 P.2d 893, held evidence of the defendant's hatred of his wife's religion was admissible as bearing upon the defendant's motive for the crime. (See also People v. Osband (1996) 13 Cal.4th 622, 708, 55 Cal.Rptr.2d 26, 919 P.2d 640 [motive as part of circumstances of crime].)
In light of these precedents, we conclude here that Dr. Hatcher's testimony was admissible under section 190.3, factor (a). It explained the motivation for the crime, and the history and mental condition that produced such motivation. It explained the significance of the methods used to commit the crime  the handcuffs and duct tape, the act of sodomy, the post mortem burning of the body. It also explained how evidence found in defendant's home and car showed that he premeditated the crime, and related to the manner in which it was committed. In short, Dr. Hatcher's testimony was evidence relating to the circumstances of the crime.

2. Evidence of mental illness under factors (d) and (k) of section 190.3
Defendant insists, however, that Dr. Hatcher's testimony falls under factors (d) and (k) of section 190.3, and that such evidence can only be mitigating. Factor (d) authorizes the penalty jury to consider evidence of "extreme mental or emotional disturbance." We have held in previous cases that such evidence can only be mitigating. (E.g., People v. Montiel (1993) 5 Cal.4th 877, 944, 21 Cal.Rptr.2d 705, 855 P.2d 1277; People v. Whitt, supra, 51 Cal.3d 620, 654, 274 Cal.Rptr. 252, 798 P.2d 849; People v. Ghent (1987) 43 Cal.3d 739, 776, 239 Cal.Rptr. 82, 739 P.2d 1250.) In People v. Benson (1990) 52 Cal.3d 754, 276 Cal.Rptr. 827, 802 P.2d 330, we said that no reasonable juror could believe "that extreme mental or emotional disturbance ... were circumstances in aggravation," and hence a jury instruction to that effect was unnecessary. (Id. at p. 802, 276 Cal.Rptr. 827, 802 P.2d 330; see People v. Cox (1991) 53 Cal.3d 618, 675, 280 Cal. Rptr. 692, 809 P.2d 351.)
Factor (k) of section 190.3 authorizes consideration of "[a]ny other circumstance which extenuates the gravity of the crime even though it is not a legal excuse for the crime." Under factor (k), the jury must consider any "`aspect of [the] defendant's character or record ... that the defendant proffers as a basis for a sentence less than death.'" (People v. Easley (1983) 34 Cal.3d 858, 878-879, fn. 10, 196 Cal.Rptr. 309, 671 P.2d 813, quoting Lockett v. Ohio (1978) 438 U.S. 586, 604, 98 S.Ct. 2954, 57 L.Ed.2d 973.) Consequently, even though factor (d) refers to "extreme" emotional or mental disturbance, evidence of mental disorder of less extreme character is admissible under factor (k). (See, e.g., People v. Whitt, supra, 51 Cal.3d at p. 655, 274 Cal.Rptr. 252, 798 P.2d 849.) Evidence admitted under factor (k), like that admitted under factor (d), is mitigating. (See People v. Lewis (2001) 25 Cal.4th 610, 672, 106 Cal.Rptr.2d 629, 22 P.3d 392; People v. Montiel, supra, 5 Cal.4th at p. 944, 21 Cal.Rptr.2d 705, 855 P.2d 1277; People v. Edelbacher (1989) 47 Cal.3d 983, 1033, 254 Cal.Rptr. 586, 766 P.2d 1.)
The Attorney General argues that Dr. Hatcher's testimony does not implicate the principle that evidence of mental illness is mitigating because Dr. Hatcher *567 testified only that a murder such as the one here is usually committed by a sadistic pedophile, not that defendant himself was a sadistic pedophile. The inference, however, is unmistakable: if the nature of the crime shows it was probably committed by a sadistic pedophile, and defendant admits committing the crime, then defendant is probably a sadistic pedophile.[6] Dr. Hatcher's testimony, moreover, acquires relevance only to the extent that it does describe defendant. As the trial judge observed: "[I]t's irrelevant unless you want to argue to somebody that he is a sexual sadist. Otherwise it's meaningless."

3. Admissibility of evidence of mental illness that relates to the circumstance of the crime
The question before us, therefore, is whether on the facts of this case the prosecution could present evidence in its penalty case-in-chief from which the jury could infer that defendant is a sadistic pedophile and argue that inference as an aggravating consideration. Defendant contends that under People v. Boyd (1985) 38 Cal.3d 762, 215 Cal.Rptr. 1, 700 P.2d 782, evidence of mental illness cannot be presented as aggravating evidence. Defendant's assertion misstates the import of Boyd, which does not bar the admission of evidence of defendant's mental condition as aggravating evidence if it is relevant to the circumstances of the crime.
Boyd held that "the 1978 law prevents the prosecution from introducing, in its case-in-chief, aggravating evidence not contained in the various factors listed in section 190.3." (People v. Boyd, supra, 38 Cal.3d at p. 774, 215 Cal.Rptr. 1, 700 P.2d 782; see People v. Clark (1992) 3 Cal.4th 41, 56, 10 Cal.Rptr.2d 554, 833 P.2d 554; People v. Guzman (1988) 45 Cal.3d 915, 963, 248 Cal.Rptr. 467, 755 P.2d 917.) As we have noted, some of those listed factors, including factor (d) ("extreme mental or emotional disturbance") and factor k (any aspect of defendant's character offered as a basis for a sentence less than death) can only be mitigating. Because evidence of mental illness under factors (d) and (k) of section 190.3 cannot be considered aggravating, such evidence cannot be introduced by the prosecution as part of its case in chief at the penalty phase. (People v. Kipp (2001) 26 Cal.4th 1100, 1135, 113 Cal.Rptr.2d 27, 33 P.3d 450; People v. Avena (1996) 13 Cal.4th 394, 438-439, 53 Cal.Rptr.2d 301, 916 P.2d 1000; People v. Coleman (1989) 48 Cal.3d 112, 149, 255 Cal.Rptr. 813, 768 P.2d 32.) But in this case the evidence of defendant's mental illness is pertinent not only to factors (d) and (k), but also to another listed factor  factor (a), the circumstances of the crime. Evidence of the circumstances of the crime is admissible as aggravating evidence in the prosecution's case-in-chief, even though that evidence would have been inadmissible as prosecution evidence if offered only under factors (d) or (k).
This conclusion is supported by two decisions of this court that discuss the scope of prosecutorial argument. In People v. Carpenter (1997) 15 Cal.4th 312, 63 Cal. Rptr.2d 1, 935 P.2d 708, the prosecutor argued that factor (j) of section 190.3  whether the defendant was an accomplice  was aggravating because the defendant acted alone. We observed that even if factor (j) could only be mitigating, "the *568 jury could certainly consider that defendant acted alone as a circumstance of the crime. It mattered little whether the jury considered it in relation to factor (j) or factor (a)." (People v. Carpenter, supra, 15 Cal.4th at pp. 414-415, 63 Cal.Rptr.2d 1, 935 P.2d 708.) In People v. Pollock (2004) 32 Cal.4th 1153, 1185, 13 Cal.Rptr.3d 34, 89 P.3d 353, the prosecutor argued that the defendant's lack of remorse as he fled the scene of the crime was an aggravating factor. Our prior decisions had stated that the presence of remorse is mitigating, but its absence is generally not aggravating. (See People v. Ashmus, supra, 54 Cal.3d at p. 992, 2 Cal.Rptr.2d 112, 820 P.2d 214.) Pollock, however, drew a distinction: Absence of remorse at the crime scene or when the defendant is fleeing the scene is admissible as aggravating evidence because it relates to the circumstances of the crime. (People v. Pollock, supra, 32 Cal.4th 1153, 1185, 13 Cal. Rptr.3d 34, 89 P.3d 353.) Although both Carpenter, supra, 15 Cal.4th 312, 63 Cal. Rptr.2d 1, 935 P.2d 708, and Pollock, supra, 32 Cal.4th 1153, 13 Cal.Rptr.3d 34, 89 P.3d 353, involved prosecutorial argument, it is reasonable to infer that if the prosecutor is permitted to argue that evidence is aggravating, that evidence can be introduced as part of the prosecutor's case-in-chief.
People v. Avena, supra, 13 Cal.4th 394, 53 Cal.Rptr.2d 301, 916 P.2d 1000, also supports this conclusion. There the defendant protested that prosecution evidence of defendant's previous violent crimes, offered under section 190.3, factor (b), should have been excluded because the prosecution cannot introduce evidence of defendant's bad character (factor (k) evidence) in its case in chief. We replied: "The fact that evidence of defendant's previous violent crimes was also indicative of his character or mental condition does not render the evidence inadmissible." (People v. Avena, supra, 13 Cal.4th at p. 439, 53 Cal.Rptr.2d 301, 916 P.2d 1000.)
We distinguish two decisions in which prosecution evidence of mental illness or bad character was held inadmissible in the prosecution penalty case in chief. In People v. Coleman, supra, 48 Cal.3d 112, 255 Cal.Rptr. 813, 768 P.2d 32, a prosecution psychologist testified that the defendant had a passive-aggressive, antisocial personality and was criminally oriented, immature, and defensive. The psychologist did not relate his observations to the crime, but instead used them as a basis to recommend that defendant was dangerous and should not be released. We said that this expert evidence was inadmissible in the prosecution's case-in-chief because it was not relevant to any of the statutory aggravating or mitigating factors other than section 190.3, factor (k). (People v. Coleman, supra, 48 Cal.3d at p. 149, 255 Cal.Rptr. 813, 768 P.2d 32.) We continue to hold that general evidence regarding a defendant's mental state is not admissible in aggravation at the penalty phase. Here, by contrast, Dr. Hatcher's testimony, when considered with the evidence regarding defendant's bizarre behavior while committing the crime, provided evidence from which the jury could infer defendant acted with sexual sadism. This specific evidence of the motivation behind the killing was relevant as a circumstance of the crime.
In People v. Edelbacher, supra, 47 Cal.3d 983, 254 Cal.Rptr. 586, 766 P.2d 1, we said the prosecution acted improperly in arguing that evidence of the defendant's background and history  evidence that did not relate to the circumstances of the crime  showed "`that he's had all the breaks'" (id. at p. 1033, 254 Cal.Rptr. 586, 766 P.2d 1) so the crime could not be blamed on childhood deprivation or hardship. Character evidence relevant only to factor (k), we said, cannot be used affirmatively as a circumstance in aggravation. (People v. Edelbacher, supra, 47 Cal.3d at p. 1033, 254 Cal.Rptr. 586, 766 P.2d 1.) These cases show that evidence of mental illness or bad character is admissible in *569 the prosecution's case in chief only if, as here, it relates to an aggravating factor listed in section 190.3. But if the evidence does relate to an aggravating factor, it is admissible as part of the prosecution's penalty case-in-chief, even if it also bears upon a mitigating factor listed in that section.

4. Defendant's federal constitutional claims
Defendant asserts that admitting evidence of his mental illness as an aggravating consideration violated his rights under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the United States Constitution. Defendant, however, did not raise these contentions in the trial court.
Seeking to avoid the conclusion that his constitutional claims have been forfeited (see People v. Williams (1997) 16 Cal.4th 153, 250, 66 Cal.Rptr.2d 123, 940 P.2d 710), defendant cites People v. Yeoman, supra, 31 Cal.4th 93, 2 Cal.Rptr.3d 186, 72 P.3d 1166, which said: "[N]o useful purpose is served by declining to consider on appeal a claim that merely restates, under alternative legal principles, a claim otherwise identical to one that was properly preserved...." (Id. at p. 117, 2 Cal.Rptr.3d 186, 72 P.3d 1166.) But here defendant's constitutional claim is not identical to his properly preserved claim based on California decisions and statutes. His state law claim is based on decisions interpreting section 190.3 and asserting that factors (d) and (k) can only be mitigating. There are, however, no federal decisions preventing the jury from treating factor (d) or factor (k) evidence as aggravating. (See Tuilaepa v. California (1994) 512 U.S. 967, 976-979, 114 S.Ct. 2630, 129 L.Ed.2d 750.)

C. Defendant's Objection to Dr. Hatcher's Testimony Under Evidence Code Section 352
Defendant contends that Dr. Chris Hatcher's testimony should have been excluded under Evidence Code section 352, which permits the trial court, in its discretion, to exclude evidence "if its probative value is substantially outweighed by the probability that its admission will (a) necessitate undue consumption of time or (b) create substantial danger of undue prejudice, of confusing the issues, or of misleading the jury."
In People v. Box, supra, 23 Cal.4th 1153, 99 Cal.Rptr.2d 69, 5 P.3d 130, we rejected the Attorney General's contention that Evidence Code section 352 did not apply to evidence offered under factor (a) of Penal Code section 190.3. Box explained: "[T]he trial court lacks discretion to exclude all factor (a) evidence on the ground it is inflammatory or lacking in probative value." (23 Cal.4th at pp. 1200-1201, 99 Cal.Rptr.2d 69, 5 P.3d 130.) It retains, however, "its traditional discretion to exclude `particular items of evidence' by which the prosecution seeks to demonstrate either the circumstances of the crime (factor (a)), or violent criminal activity (factor (b)), in a `manner' that is misleading, cumulative, or unduly inflammatory." (Id. at p. 1201, 99 Cal.Rptr.2d 69, 5 P.3d 130; see People v. Michaels (2002) 28 Cal.4th 486, 534-535, 122 Cal.Rptr.2d 285, 49 P.3d 1032.)
Here the issue of the admissibility of Dr. Hatcher's testimony under Evidence Code section 352 is simply another way of looking at the question whether that evidence can be admitted as aggravating evidence. "Prejudice" in section 352 does not refer simply to evidence that is damaging to the defendant. Instead, "`[t]he "prejudice" referred to in Evidence Code section 352 applies to evidence which uniquely tends to evoke an emotional bias against the defendant as an individual and which has very little effect on the issues.'" (People v. Karis (1988) 46 Cal.3d 612, 638, 250 Cal. Rptr. 659, 758 P.2d 1189, italics added.)
Dr. Hatcher's testimony provides a basis from which the jurors could infer that defendant is a sadistic pedophile, and premeditated and committed the crime for the sexual pleasure of the act, an aggravating *570 consideration. If that is a permissible inference, as we have concluded, then the evidence is highly probative.

D. Exclusion of Dr. Hatcher's Testimony as "Profile Evidence"
Defendant argues that Dr. Hatcher's testimony amounted to the improper use of "profile evidence." "Profile evidence," however, is not a separate ground for excluding evidence; such evidence is inadmissible only if it is either irrelevant, lacks a foundation, or is more prejudicial than probative. (Id. at pp. 868-869, 19 Cal.Rptr.3d 229.) In arguing the evidence here was inadmissible, defendant relies on two Court of Appeal decisions, People v. Walkey (1986) 177 Cal.App.3d 268, 223 Cal. Rptr. 132 and People v. Robbie (2001) 92 Cal.App.4th 1075, 112 Cal.Rptr.2d 479.
In Walkey, the prosecution introduced expert evidence that the most important factor in the profile of a child abuser was that he had himself been abused as a child, elicited an admission from the defendant that he had been abused as a child, then argued that the defendant was guilty because he fit the profile of a child molester. (People v. Walkey, supra, 177 Cal.App.3d at pp. 276-277, 223 Cal.Rptr. 132.) The Court of Appeal held the evidence inadmissible and the prosecution's argument improper. (Id. at p. 279, 172 Cal.Rptr. 612.)
In People v. Robbie, supra, 92 Cal. App.4th 1075, 112 Cal.Rptr.2d 479, a prosecution expert testified that many rapists use only minimal force, and described in detail a scenario in which the rapist is in effect acting as if he thinks of the sexual acts as consensual. (Id. at pp. 1082-1084, 112 Cal.Rptr.2d 479.) Not coincidentally, the behavior the expert described matched the testimony of the alleged victim. The expert conceded that the same behavior would be consistent with a truly consensual encounter. The Court of Appeal in Robbie characterized this evidence as inadmissible "profile evidence." It explained: "[The evidence] implies that criminals, and only criminals, act in a given way. In fact, certain behavior may be consistent with both innocent and illegal behavior, as the People's expert conceded here." (Id. at p. 1085, 112 Cal.Rptr.2d 479.) Other cases excluding profile evidence include People v. Castaneda (1997) 55 Cal.App.4th 1067, 1072, 64 Cal.Rptr.2d 395 (drug dealer profile), People v. Martinez (1992) 10 Cal. App.4th 1001, 1006, 12 Cal.Rptr.2d 838 (truck thief profile), and U.S. v. Beltran-Rios (9th Cir.1989) 878 F.2d 1208, 1210 (drug courier profile).
The evidence here is quite different. Profile evidence is objectionable when it is insufficiently probative because the conduct or matter that fits the profile is as consistent with innocence as guilt. The evidence here, however, does not have this problem. Defendant has pled guilty, and the circumstances of Paul Bailly's murder themselves suggest a pathological cause. Dr. Hatcher's testimony did not suggest that this type of crime is committed with any frequency, or at all, by persons who do not have the pathology he described. Defendant's own penalty phase evidence emphasized his mental retardation, but it offered no alternative explanation why defendant would sodomize and kill an eight-year-old boy.

E. Admissibility of Newspaper Articles
While searching defendant's residence on March 24 and 25, 1990, the police discovered copies of three newspapers. Two contained articles about a notorious child molestation case in which the defendants *571 were acquitted. The third contained an article about a father who had set fire to his young son.
The prosecution argued that the articles were admissible to show that defendant had been fantasizing about child molesting and had been planning such a crime. Dr. Hatcher testified that persons who commit such crimes "almost always [have] a collection of newspaper or magazine articles that have direct relevance to the fantasy and to the subsequent assault that's committed." The defense objected to the admission of the newspaper articles as irrelevant and as more prejudicial than probative.
The articles were relevant, both as indicia of defendant's mental condition that led to the crime, and as evidence that defendant was planning, or at least contemplating, such a crime. If defendant's sadistic purpose was an admissible aggravating circumstance, as we concluded earlier in this opinion (ante, 25 Cal.Rptr.3d at 568-569, 107 P.3d at 240-242), then there is no improper prejudicial effect from the evidence of the newspaper articles.

F. Rebuttal Testimony of Dr. Jeffrey Schaeffer
Defendant's expert witnesses testified that defendant was mentally retarded, that he was a "moral imbecile" incapable of appreciating the social context and impact of his behavior, and that he had brain damage. In rebuttal, the prosecution called Dr. Jeffrey Schaeffer. He did not diagnose defendant, but testified over defendant's objection that in defendant's case the four diagnostic categories he would consider were antisocial personality, pedophilia, sexual sadism, and specific developmental disorders. He further testified that there is no correlation between brain damage and committing a premeditated crime of violence. There is also no correlation between learning disabilities or mental retardation and violent crime.
Defendant argues that Dr. Schaeffer's testimony was improper rebuttal because defendant's own experts had never discussed sexual sadism. We disagree. When, as here, a mental health expert offers a diagnosis, this opens the door to rebuttal testimony questioning that diagnosis or suggesting an alternative diagnosis. (See People v. Carpenter, supra, 15 Cal.4th at p. 406, 63 Cal.Rptr.2d 1, 935 P.2d 708.)
Defendant also contends that his evidence of brain damage and retardation was proper mitigating evidence even if those conditions did not cause the murder of Paul Bailly. (See Eddings v. Oklahoma (1982) 455 U.S. 104, 113-114, 102 S.Ct. 869, 71 L.Ed.2d 1; Lockett v. Ohio, supra, 438 U.S. at p. 604, 98 S.Ct. 2954.) We agree with defendant's premise. But rebuttal tending to show that the brain damage and retardation are not related to the crime remains relevant to the jury's evaluation of the defense evidence as it bears upon the appropriateness of the death penalty.
"`The admission of rebuttal evidence rests largely within the sound discretion of the trial court and will not be disturbed on appeal in the absence of "palpable abuse."'" (People v. Kelly (1990) 51 Cal.3d 931, 965, 275 Cal.Rptr. 160, 800 P.2d 516.) We find no abuse of discretion in the trial court's ruling admitting the testimony of Dr. Schaeffer.

G. The Prosecutor's Comments in Closing Argument About Dr. Hatcher's Testimony
As noted earlier, Dr. Chris Hatcher testified about the kind of person who would commit the crimes charged in this case. We concluded that the jury could infer *572 that defendant was such a person. (Ante, 25 Cal.Rptr.3d at 569-570, 107 P.3d at 242.)
In his closing argument to the jury, the prosecutor asked: "Now, what were the inferences we can draw from Dr. Hatcher's testimony about the defendant's motive?" (Italics added.) He then made a series of assertions prefixed with the phrase "we know": "we know" that defendant handcuffed and gagged the victim for sexual pleasure; "we know" that he enjoyed seeing the victim struggle for life; "we know" that he sodomized and strangled the victim "for purposes of sexual pleasure and to produce both terror and struggle." Defendant objected, pointing out that Dr. Hatcher had described a hypothetical perpetrator. The trial court overruled the objection. The prosecutor then resumed his argument by asking the jury again what "inferences" could be drawn from Dr. Hatcher's testimony.
Literally speaking, the prosecutor's argument may have misstated the evidence. "We"  a term that presumably encompassed at least the prosecutor and the jurors  did not "know" defendant's motivation and feelings. "We" could only infer them from Dr. Hatcher's testimony. But this overstatement of the evidence is insignificant, because the prosecutor's argument, taken as a whole, made it clear that he was not talking about proven facts, but about inferences that the jury could draw from Dr. Hatcher's description of the kind of person who commits crimes such as those here. Thus, even assuming that the trial court should have sustained defendant's objection, any error in not doing so would be harmless.

H. The Jury Instructions Relating to Dr. Hatcher's Testimony

1. The instruction limiting the use of Dr. Chris Hatcher's testimony
The trial court gave this limiting instruction: "The testimony of Dr. Chris Hatcher was received in evidence and may be considered by you only for the limited purpose of explaining, if it does, the meaning of certain pieces of evidence offered in this case, to explain the general phenomena of sexual fantasies and to provide information on the subject of the behavior and mental processes of children who are abducted for the purpose of violent sexual assault and persons who commit such crimes. He testified to a generalized body of knowledge. However, should you find that there are facts in this case which are or may be explained by such testimony you may consider the testimony for that purpose. However, such evidence was not received and may not be considered by you, to prove that the defendant is a person of bad character or that he has a disposition to commit crimes. Further, Dr. Hatcher did not examine [defendant] nor did he express any opinion about the defendant or how the crime actually occurred." (Italics added.)
Defendant correctly observes that the inclusion of the italicized phrase permitted the jurors to consider Dr. Hatcher's testimony as information relevant to defendant's mental processes. But this observation simply returns us to the issue previously discussed: May the jury consider, as aggravating evidence under section 190.3, factor (a), evidence of defendant's mental illness insofar as it relates to the circumstances of the crime? Our conclusion that it may do so resolves the controversy over the jury instruction; if the jurors can consider Dr. Hatcher's testimony as evidence relating to defendant's mental processes, it cannot be error to tell them they may do so.

2. Defendant's proposed jury instructions
Defendant proposed five jury instructions relating to mental illness and mitigation. *573 The trial court was not obliged to give any of these instructions, but exercised its discretion to give defendant's proposed special instruction No. 6.
Special instruction No. 6 read, in pertinent part:
"You have been instructed that you may consider, as mitigation, any circumstance which extenuates the gravity of the crime even though it is not a legal excuse for the crime, and any sympathetic or other aspect of the Defendant's character or record as a basis for a sentence less than death, whether or not those circumstances or aspects of the Defendant's character are related to the offense.
"Circumstances surrounding the commission of the crime which you should consider include, but are not limited to, the following:
"1. Whether the Defendant acknowledged responsibility for the crime;
"2. Whether the crime involved a single victim;
"3. Whether the Defendant committed the offense while under the influence of a mental or emotional disturbance, which disturbance need not be extreme nor amount to legal insanity or an inability to form a specific intent. This includes, but is not limited to whether [defendant] has low self-esteem, or suffers from a brain dysfunction, that has affected his ability to learn and may affect his judgment or perception.
"Mitigating factors also include any sympathetic, compassionate, merciful, or other aspect of Defendant's background, character, record, or social, psychological or medical history, that the Defendant offers as a basis for a sentence less than death, whether or not related to the offense for which he is on trial...."
Defendant argues that the trial court erred in rejecting defendant's special instructions Nos. 7 and 8.
Defendant's proposed special instruction No. 7 read: "The term `mental or emotional disturbance' as used in these instructions includes any violent, intense, high-wrought or enthusiastic emotion including, but not limited to, fear, revenge, and the emotion induced by and accompanying or following any intent to commit a felony. [¶] The presence of mental or emotional disturbance may only be considered by you as a factor in mitigation, and may not be considered as an aggravating factor."
The trial court correctly rejected this instruction. Defendant's assertion that any emotion that accompanies an intent to commit a felony constitutes a "mental or emotional disturbance" and cannot be considered as a factor in aggravation is incorrect. As we have explained, the presence of mental or emotional disturbance may be considered as an aggravating factor if admitted as relevant to the circumstances of the crime.
Defendant's proposed special instruction No. 8 read:
"The term `mental disease or defect' as used in these instructions is not limited to evidence which excuses the crime or reduces defendant's culpability, but includes any degree of mental defect, disease or impairment which you may determine is of a nature that death should not be imposed.
"Such a mental disease or defect may be considered by you as a mitigating factor whether or not the mental condition caused the defendant to commit the offense, and whether or not the condition was operative at the time of the offense.
"The presence of mental disease or defect may only be considered by you as a factor in mitigation, and may not be considered as an aggravating factor."
*574 The first two paragraphs of this instruction correctly state the law. (See Eddings v. Oklahoma, supra, 455 U.S. at pp. 113-114, 102 S.Ct. 869; People v. Whitt, supra, 51 Cal.3d at p. 655, 274 Cal.Rptr. 252, 798 P.2d 849.) The third paragraph, however, is inconsistent with our conclusion (ante, 25 Cal.Rptr.3d at 567-569, 107 P.3d at 240-241) that the jury can consider evidence of mental disease or defect as aggravating when that evidence is admitted under section 190.3, factor (a). The trial court therefore correctly rejected the proposed instruction.

V. Issues Relating to the Admissibility of Prosecution Evidence of Children's Reactions to Sadistic Molestation

A. Dr. Hatcher's Testimony
Dr. Chris Hatcher interviewed children who had been sadistically molested, and on the basis of that experience described the stages such children go through. In the first stage, he said, the children felt that the experience is unreal, like watching a television show. Then the children realize that they are in danger and try to avoid it by making friends with the abductor. In the last stage the horrified children are filled with shame at the sodomy and increasingly aware that they may be killed.

B. Defendant's Objections

1. Admissibility of the testimony under Evidence Code sections 702 and 801.
Defendant contends that the admission of Dr. Chris Hatcher's testimony concerning the experiences of child victims violates Evidence Code section 702, which provides that the testimony of a witness is inadmissible unless based on personal knowledge. Dr. Hatcher, however, was testifying as an expert witness pursuant to Evidence Code section 801, and Evidence Code section 702 by its terms does not apply to such testimony.
Defendant, however, points out that Evidence Code section 801 only permits expert testimony on "a subject that is sufficiently beyond common experience that the opinion of an expert would assist the trier of fact." He argues that the experiences of child victims of violent sexual assaults are not sufficiently beyond common experience that expert assistance is required. We disagree. Only a fraction of the general population, and presumably none of the jurors, has been personally victimized. Of course a juror can try to imagine what it would be like for a child to experience such an assault, but this kind of imagining does not substitute for expert testimony.

2. Admissibility of the testimony under Evidence Code section 352
Defendant contends that Dr. Hatcher's testimony should have been excluded under Evidence Code section 352 as more prejudicial than probative. This is an exact counterpart to his argument that Dr. Hatcher's testimony about the characteristics of perpetrators should have been excluded under section 352, and it is rejected on the same grounds. (See ante, 25 Cal. Rptr.3d at 569-570, 107 P.3d at 241-242.)

3. Federal constitutional arguments
Defendant argues that the admission of Dr. Chris Hatcher's testimony violated the Eighth and Fourteenth Amendments to the federal Constitution. He contends that the federal Constitution requires an "individualized" death penalty determination (see Woodson v. North Carolina (1976) 428 U.S. 280, 304, 96 S.Ct. 2978, 49 L.Ed.2d 944), making testimony about the suffering of victims of other crimes inadmissible. We recognize that the jury could *575 not properly punish this defendant for other perpetrators' crimes, but the evidence at issue was not introduced or used for that purpose. Dr. Hatcher's testimony was admissible because the jury could infer that here the victim's experiences were similar to those of victims of other violent molestations, and consider whether to impose the death penalty because of the circumstances of this crime.
Finally, defendant claims that Dr. Hatcher's testimony was so inflammatory that its admission denied him due process of law. (See People v. Boyette (2002) 29 Cal.4th 381, 444, 127 Cal.Rptr.2d 544, 58 P.3d 391.) But penalty trials are different from guilt trials. Emotional appeals are allowed, and evidence that arouses emotions, including evidence of the suffering of the victims and their families, is generally admissible. (See People v. Taylor (2001) 26 Cal.4th 1155, 1171-1172, 113 Cal. Rptr.2d 827, 34 P.3d 937; People v. Bittaker (1989) 48 Cal.3d 1046, 1110, fn. 34, 259 Cal.Rptr. 630, 774 P.2d 659.) Evidence may be excluded under the due process clause or Evidence Code section 352 if it is "unduly inflammatory" (People v. Box, supra, 23 Cal.4th at p. 1201, 99 Cal.Rptr.2d 69, 5 P.3d 130), but that language refers to an extreme situation. Evidence relating to the suffering of the victim and prosecutorial comment on that suffering are appropriate in death penalty cases. (See People v. Wrest (1992) 3 Cal.4th 1088, 1107-1108, 13 Cal.Rptr.2d 511, 839 P.2d 1020; People v. Edwards, supra, 54 Cal.3d 787, 852, 1 Cal. Rptr.2d 696, 819 P.2d 436 (conc. & dis. opn. of Mosk, J.).)

VI. Other Evidentiary Issues

A. Victim Impact Evidence
Defendant argues that the trial court erred when it admitted, over defense objection, testimony by Mary Bailly, the mother of Paul Bailly, the murder victim.[7] She testified: "I don't think the pain will ever go away ... I think the worst part of it is, is what goes on in my mind what happened to him. What he went through is  is just very difficult."
The United States Supreme Court held victim impact testimony admissible in Payne v. Tennessee (1991) 501 U.S. 808, 825, 111 S.Ct. 2597, 115 L.Ed.2d 720. This court then held such evidence admissible in California as relating to section 190.3, factor (a), the circumstances of the crime. (People v. Fierro (1991) 1 Cal.4th 173, 3 Cal.Rptr.2d 426, 821 P.2d 1302; People v. Edwards, supra, 54 Cal.3d 787, 1 Cal. Rptr.2d 696, 819 P.2d 436.) Defendant here points to language in Payne and Edwards that victim impact evidence could be excluded if it is "so unduly prejudicial that it renders the trial fundamentally unfair." (People v. Edwards, supra, 54 Cal.3d at p. 835, 1 Cal.Rptr.2d 696, 819 P.2d 436, quoting Payne v. Tennessee, supra, 501 U.S. at p. 825, 111 S.Ct. 2597.)
People v. Stanley (1995) 10 Cal.4th 764, 832, 42 Cal.Rptr.2d 543, 897 P.2d 481, found no misconduct in a prosecutor's argument on victim impact because "it was not so inflammatory or emotional as to divert the jury's attention from its proper role or invite an irrational, purely subjective response." We do not, however, know of any cases after Payne and Edwards holding victim impact evidence inadmissible, or argument based on that evidence improper. The references in Payne and Stanley to the exclusion of unduly inflammatory victim impact evidence contemplates an extreme case, which is not the *576 situation here. The mother's testimony here is what one would expect in any case involving the murder of a child. It is not significantly different from the testimony of the victim's son and husband held admissible in People v. Taylor, supra, 26 Cal.4th at pages 1171-1172, 113 Cal. Rptr.2d 827, 34 P.3d 937.

B. Evidence of Prison Conditions
The trial court sustained the prosecutor's objection to defense expert evidence offered to show "what occurs in prison and what prison means as a form of punishment." Defendant challenges this ruling.
As defendant recognizes, we have in the past held: "evidence of the conditions of confinement that a defendant will experience if sentenced to life imprisonment without parole is irrelevant to the jury's penalty determination because it does not relate to the defendant's character, culpability, or the circumstances of the offense." (People v. Quartermain (1997) 16 Cal.4th 600, 632, 66 Cal.Rptr.2d 609, 941 P.2d 788; see People v. Daniels (1991) 52 Cal.3d 815, 876-878, 277 Cal.Rptr. 122, 802 P.2d 906.) Defendant asks us to reconsider this issue, contending that jurors cannot be precluded from considering any aspect of a defendant's character and record that he offers as a basis for a sentence of less than death. (See People v. Boyd, supra, 38 Cal.3d 762, 775, 215 Cal.Rptr. 1, 700 P.2d 782; People v. Easley, supra, 34 Cal.3d 858, 878, 196 Cal. Rptr. 309, 671 P.2d 813.) But the evidence defendant offered here is not an aspect of his character and record. Contrary to defendant's contention, it is not the law that jurors must be allowed to consider any evidence a defendant offers on the question whether the death penalty is morally appropriate. Evidence is inadmissible if it does not pertain to a defendant's individual character and record, but pertains solely to the death penalty generally, such as how death is inflicted (see People v. Harris (1981) 28 Cal.3d 935, 962, 171 Cal.Rptr. 679, 623 P.2d 240) or to future conditions of confinement for one sentenced to life without possibility of parole (see People v. Daniels, supra, 52 Cal.3d at pp. 877-878, 277 Cal.Rptr. 122, 802 P.2d 906).

C. Exclusion of Testimony That Witness Believed Defendant Should not be Executed
Defendant's family hired educational therapist Janice Foster to help defendant with his learning problems from 1984 through 1987, when defendant was 15 to 17 years old. Called as a defense witness, she testified that she liked defendant because he was eager and friendly, but that socially and emotionally he was much younger than his chronological age and lacked a fundamental understanding of the effects of his conduct. When asked whether she wanted "to see [defendant] in the gas chamber," she answered: "[he is] a very young person in his mind.... It's horrible when a child dies." The prosecution objected and moved to strike the testimony. The defense made an offer of proof: Foster would testify that she thought the death penalty was not appropriate for defendant because she considered him the equivalent of a child, and killing a child was not appropriate. The trial court, after noting that there was no authority directly on point, granted the prosecutor's motion on the ground that "third party witnesses ought not to be able to testify concerning the justice of one penalty or another."
In People v. Sanders (1995) 11 Cal.4th 475, 46 Cal.Rptr.2d 751, 905 P.2d 420, we concluded that the trial court did not err in refusing to permit the defendant's sister to testify that she did not want him executed. We rejected the argument that the evidence *577 was admissible under factor (k) of section 190.3, which allows admission of evidence relating to any aspect of a defendant's character or record that the defendant proffers as a basis for a sentence less than death. "The specific questions whether family members would prefer that defendant not be executed," we said, "are not ... strictly relevant to the defendant's character, record, or individual personality." (People v. Sanders, supra, 11 Cal.4th at p. 546, 46 Cal.Rptr.2d 751, 905 P.2d 420.) Three years later, however, we held in People v. Ochoa (1998) 19 Cal.4th 353, 456, 79 Cal.Rptr.2d 408, 966 P.2d 442: "A defendant may offer evidence that he or she is loved by family members or others, and that these individuals want him or her to live.... [T]his evidence is relevant because it constitutes indirect evidence of the defendant's character."
This issue arose again in People v. [Gregory Calvin] Smith (2003) 30 Cal.4th 581, 134 Cal.Rptr.2d 1, 68 P.3d 302. There, the defendant's former attorney proposed to testify. The testimony, defense counsel said, was "`not character testimony,'" but former counsel's "opinion regarding the `appropriateness of the death penalty ... given the crime.'" (Id. at p. 632, 134 Cal.Rptr.2d 1, 68 P.3d 302.) We acknowledged that "testimony that defendant deserves to live, provided by someone who had a significant relationship with him, is admissible, not because that opinion is itself important but because the testimony provides indirect evidence of the defendant's character." (Id. at p. 631, 134 Cal.Rptr.2d 1, 68 P.3d 302.) We questioned whether an attorney-client relationship qualified as a significant relationship and led to such indirect evidence of character, but did not decide that question. Instead, we held the evidence was inadmissible because "the opinion of a witness, expert or otherwise, that a life sentence is appropriate is not relevant except to the extent that it might provide insight into the defendant's character." (Id. at p. 632, 134 Cal.Rptr.2d 1, 68 P.3d 302.)
From these cases we can distill a general rule: evidence that a family member or friend wants the defendant to live is admissible to the extent it relates to the defendant's character, but not if it merely relates to the impact of the execution on the witness. Here the relevance of Janice Foster's testimony to defendant's character and personality is clear, because Foster's opinion was based on her familiarity with defendant's emotional and social immaturity, a recognized mitigating consideration.
Admissibility of course requires that the witness have a significant relationship with the defendant. Here, Janice Foster's three-year tutorial relationship with defendant qualifies. Neither the prosecutor's objection to her testimony, nor the trial court's ruling excluding that testimony, was based on the nature of her relationship with defendant.
Instead, the prosecutor's objection and the court's ruling were based on the position that opinion on the appropriateness of the death penalty  either generally or in this particular case  was inadmissible. But People v. Smith, supra, 30 Cal.4th 581, 134 Cal.Rptr.2d 1, 68 P.3d 302, makes it clear that the opinion of a witness who has a significant relationship with a defendant as to the appropriateness of the death penalty for that defendant is relevant "to the extent that it provides insight into the defendant's character." (Id. at p. 632, 134 Cal.Rptr.2d 1, 68 P.3d 302.) Because Foster had such a significant relationship, and her opinion was based on a feature of defendant's character that she had personally observed, we conclude that her opinion was relevant and admissible.
*578 Thus, the trial court erred in excluding Foster's testimony. We use the Chapman test in evaluating the effect of erroneously excluding mitigating evidence; reversal is required "`unless the state proves beyond a reasonable doubt that the error complained of did not contribute to the verdict obtained.'" (People v. Lucero (1988) 44 Cal.3d 1006, 1032, 245 Cal.Rptr. 185, 750 P.2d 1342, quoting Chapman v. California (1967) 386 U.S. 18, 24, 87 S.Ct. 824, 17 L.Ed.2d 705; see People v. Brown (2003) 31 Cal.4th 518, 576, 3 Cal.Rptr.3d 145, 73 P.3d 1137.) Applying this standard, we conclude that the error was harmless. Foster's opinion that defendant should not be executed was relevant only as it provided indirect evidence of defendant's character. But Foster was permitted to provide direct evidence about his character, including his immaturity, and this mitigating factor was argued to the jury. There is no reason to believe that Foster's opinion that defendant's immaturity made the death penalty inappropriate would have affected the verdict.

D. Evidence of Prior Violent Acts
We earlier summarized the evidence of four prior violent acts by defendant. (See 25 Cal.Rptr.3d at 560, 107 P.3d at 234, ante.) Evidence of unadjudicated violent acts is admissible under section 190.3, factor (b). (See People v. Michaels, supra, 28 Cal.4th at p. 541, 122 Cal. Rptr.2d 285, 49 P.3d 1032; People v. Carpenter, supra, 15 Cal.4th at p. 401, 63 Cal.Rptr.2d 1, 935 P.2d 708.)
In two memorandum opinions dissenting from the denial of certiorari, United States Supreme Court Justice Thurgood Marshall questioned whether evidence of unadjudicated violent acts should be excluded as unreliable. (See Robertson v. California (1989) 493 U.S. 879, 110 S.Ct. 216, 107 L.Ed.2d 169; Williams v. Lynaugh (1987) 484 U.S. 935, 108 S.Ct. 311, 98 L.Ed.2d 270.) Citing those opinions, defendant argues that the admission of this evidence violated his rights under the Eighth and Fourteenth Amendments to the federal Constitution. We rejected a similar contention in People v. Koontz (2002) 27 Cal.4th 1041, 1095, 119 Cal.Rptr.2d 859, 46 P.3d 335 and in People v. Kraft (2000) 23 Cal.4th 978, 1078, 99 Cal.Rptr.2d 1, 5 P.3d 68.
Defendant argues that his previous crimes, in particular the alleged false imprisonment of young Brian Francis and the alleged battery of young Brian Due, are such trivial matters that they have little bearing on the appropriateness of the death penalty. He questions whether these acts constituted crimes, maintaining that they are simply incidents of children's play. But defendant's act of holding Brian Francis to a wall and threatening to hit him with a ball if he tried to run constitutes false imprisonment (see § 236; People v. Bamba (1997) 58 Cal.App.4th 1113, 1123, 68 Cal.Rptr.2d 450); and defendant's act of choking Brian Due is a battery (see People v. Rocha (1971) 3 Cal.3d 893, 900, fn. 12, 92 Cal.Rptr. 172, 479 P.2d 372). Whether those acts were serious enough to be given weight in the penalty determination is a matter for the jury to decide.

VII. Issues Relating to the Method of Determining Penalty

A. The Listing of Aggravating and Mitigating Factors
CALJIC No. 8.85 lists the factors to be considered by the jury in making its penalty decision. Defendant contends that the trial court should have deleted those factors inapplicable to this case. We rejected that contention in People v. Sapp (2003) 31 Cal.4th 240, 315, 2 Cal.Rptr.3d 554, 73 P.3d 433, People v. Carpenter, supra, 15 Cal.4th at page 421, 63 Cal.Rptr.2d 1, 935 P.2d 708, People v. Ghent, supra, 43 Cal.3d at pages 776-777, 239 Cal.Rptr. 82, 739 P.2d 1250, and in many other cases.
*579 Defendant proposed a special jury instruction stating that the only applicable aggravating factors in this case were the circumstances of the murder and other criminal activity involving force or violence. The trial court did not err in rejecting this instruction. We have repeatedly said that a trial court need not specify whether factors are aggravating or mitigating. (See People v. Pollock, supra, 32 Cal.4th 1153, 1193, 13 Cal.Rptr.3d 34, 89 P.3d 353; People v. Davenport (1995) 11 Cal.4th 1171, 1230, 47 Cal.Rptr.2d 800, 906 P.2d 1068; People v. Sanders, supra, 11 Cal.4th at p. 561, 46 Cal.Rptr.2d 751, 905 P.2d 420.) In any event, here both the prosecutor and defense counsel said to the jury in closing argument that the circumstances of the crime and other violent criminal activity were the only aggravating circumstances.
The trial court rejected defendant's proposed special instruction No. 4, which stated: "The absence of prior felony convictions is a significant mitigating circumstance in a capital case, where the accused frequently has an extensive criminal past." The trial court, however, did instruct the jury to consider "the presence or absence of any prior felony or misdemeanor conviction."[8] Thus, the jurors were told that they could consider defendant's lack of prior convictions as a mitigating consideration. Whether it was a "significant" consideration was a matter for the jurors to determine.

B. The Weighing of Aggravating and Mitigating Factors


1. Defendant's objections to CALJIC No. 8.88
CALJIC No. 8.88 explains to the jury how it should arrive at the penalty decision. Defendant asserts this instruction violates his rights under the Fifth, Sixth, Eighth, and Fourteenth Amendments to the federal Constitution.
He argues that CALJIC No. 8.88's language, directing the jury to determine whether aggravation "so outweighs" mitigation as to warrant death, is unconstitutionally vague. We rejected that contention in People v. Davenport, supra, 11 Cal.4th 1171, 1231, 47 Cal. Rptr.2d 800, 906 P.2d 1068, and in People v. Breaux (1991) 1 Cal.4th 281, 315-316, 3 Cal.Rptr.2d 81, 821 P.2d 585. The phrase used in CALJIC No. 8.88, or words of similar breadth, are essential to avoid reducing the penalty decision to a mere mechanical calculation. (See People v. Brown, supra, 40 Cal.3d at p. 541, 230 Cal.Rptr. 834, 726 P.2d 516.)
Defendant contends that CALJIC No. 8.88 is incorrect because it refers to whether the death penalty is "warranted" instead of whether it is "appropriate." In People v. Arias (1996) 13 Cal.4th 92, 171, 51 Cal.Rptr.2d 770, 913 P.2d 980, however, we concluded: "By advising that a death verdict should be returned only if aggravation is `so substantial in comparison with' mitigation that death is `warranted,' the instruction clearly admonishes the jury to determine whether the balance of aggravation and mitigation makes death the appropriate penalty."
Defendant also contends that CALJIC No. 8.88 does not convey to the jury that a life sentence is mandatory if aggravation does not outweigh mitigation. We disagree. The standard instruction permits a death penalty only if aggravation is so *580 substantial in comparison with mitigation that death is warranted; if aggravation failed even to outweigh mitigation, it could not reach this level. (See People v. Medina (1995) 11 Cal.4th 694, 781, 47 Cal. Rptr.2d 165, 906 P.2d 2.) Here, moreover, the trial court gave an additional instruction that made the matter quite clear; the court told the jury: "You must return a verdict of life without the possibility of parole if the mitigating circumstances outweigh or are equal to the aggravating circumstances."
Defendant further contends that CALJIC No. 8.88 implies that death is the only appropriate sentence if aggravation is "so substantial in comparison with the mitigating circumstances that it warrants death instead of life without parole." He insists that this language is inconsistent with the principle that the jury can return a life verdict even if aggravating circumstances outweigh those in mitigation. (See People v. Brown, supra, 40 Cal.3d at pp. 538-541, 230 Cal.Rptr. 834, 726 P.2d 516.) There is no inconsistency. A jury is free to return a life verdict even if aggravation outweighs mitigation. But the jury is not free to return a life verdict regardless of the evidence. If aggravating circumstances are so substantial in comparison with mitigating circumstances as to warrant the death penalty, then death is the appropriate penalty. (People v. Arias, supra, 13 Cal.4th at p. 171, 51 Cal.Rptr.2d 770, 913 P.2d 980.)
Finally, defendant argues that the instruction failed to inform the penalty jury of the burden of persuasion. There is no penalty phase burden of persuasion. (See People v. Carpenter, supra, 15 Cal.4th 312, 417-418, 63 Cal.Rptr.2d 1, 935 P.2d 708.) The trial court correctly rejected defendant's proposed supplemental special instruction L, which would have told the jury that if it had a reasonable doubt as to which penalty to impose, it must return a verdict of life imprisonment without possibility of parole. (See People v. Jones (2003) 30 Cal.4th 1084, 1127, 135 Cal. Rptr.2d 370, 70 P.3d 359; People v. Sanchez (1995) 12 Cal.4th 1, 80-81, 47 Cal. Rptr.2d 843, 906 P.2d 1129; People v. Williams (1988) 44 Cal.3d 883, 960, 245 Cal.Rptr. 336, 751 P.2d 395.)

2. Defendant's proposed supplemental instructions
Defendant's proposed special instruction B stated: "The jury has the option to reject death if the evidence arouses sympathy, mercy, or compassion to the point that they jury feels that death is not the proper penalty in this case." This instruction was largely duplicative of defendant's special instruction No. 6, which the trial court accepted. That instruction told the jury that it could consider "any sympathetic, compassionate, merciful, or other aspect of Defendant's background, character, record, or social, psychological or medical history, that the Defendant offers as a basis for a sentence less than death, whether or not related to the offense for which he is on trial." In any event, CALJIC No. 8.88 adequately informed the jurors that they could consider sympathy, mercy, and compassion in deciding whether death was the appropriate penalty. (See People v. Bolin (1998) 18 Cal.4th 297, 343-344, 75 Cal. Rptr.2d 412, 956 P.2d 374.) Thus the trial court did not err in rejecting Defendant's special instruction B.
The trial court also rejected defendant's proposed special instruction H: "The weight to be given to the factors in aggravation and mitigation is a matter for each juror to determine ... [and accordingly] one mitigating factor can sometimes outweigh a number of aggravating factors." The trial court gave a jury instruction based on CALJIC No. 8.88, which told the *581 jurors: "You are free to assign whatever moral or sympathetic value you deem appropriate to each and all of the various factors you are permitted to consider." The instruction then told the jurors: "You may, but are not required to return a judgment of death if each of you are persuaded that the aggravating circumstances are so substantial in comparison with the mitigating circumstances that it warrants death instead of life without parole." In People v. Bolin, supra, 18 Cal.4th at page 343, 75 Cal.Rptr.2d 412, 956 P.2d 374, we held that such instructions satisfied the constitutional requirement to advise the jury of its sentencing discretion.

3. The prosecutor's comment on CALJIC No. 8.88 during closing argument
During closing argument, the prosecutor read CALJIC No. 8.88 to the jury and commented upon it: "There are really two components to this process. One is, is the death penalty appropriate in your mind? And second, do the aggravating factors outweigh the mitigating factors, which is our true burden in this case, proving that the aggravating factors outweigh the mitigating factors. And if it is both appropriate and if the aggravating factors outweigh the mitigating factors, then you should vote for death." The trial court overruled defendant's objection that the prosecutor had misstated the law.
The prosecutor's argument correctly explained the weighing process under CALJIC No. 8.88: the jury weighs the aggravating circumstances as compared to the mitigating circumstances and determines whether the death penalty is appropriate. (See People v. Brown, supra, 40 Cal.3d at pp. 538-539, 230 Cal.Rptr. 834, 726 P.2d 516.) It is true that the prosecutor's "burden"  if such a term applies to a trial in which neither side has the burden of proof  is not merely to show that aggravation outweighs mitigation, but to show it outweighs it to such an extent that death is the appropriate penalty. But there is no indication that the jury was misled thereby. The trial court correctly instructed the jury under CALJIC No. 8.88; we presume that the jury followed that instruction. (People v. Sanchez, supra, 12 Cal.4th at p. 70, 47 Cal.Rptr.2d 843, 906 P.2d 1129.) The prosecutor quoted CALJIC No. 8.88 in his argument to the jury, and he told the jurors that they must decide whether the death penalty was the appropriate punishment whether or not the aggravating factors outweighed the mitigating factors. Looking to the instructions and the prosecutor's closing argument as a whole, we conclude that it is not reasonably likely that the jurors were misled. (See People v. Crew (2003) 31 Cal.4th 822, 848, 3 Cal.Rptr.3d 733, 74 P.3d 820; People v. Bonin (1989) 47 Cal.3d 808, 856-857, 254 Cal.Rptr. 298, 765 P.2d 460.)

VIII. Alleged Prosecutorial Misconduct in Closing Argument
In his closing argument to the jury, the prosecutor made these comments on the arguments of defense counsel: "`You don't do this crime unless there's something wrong with you.' That was one of [defense counsel's] statements.... [T]he logical conclusion from that would be what? It would be the worse the crime, the less people should get the death penalty because the worse the crime, ... the more that's proof that there's something wrong with somebody.... I suppose by [defense counsel's] reasoning, we should say if Hitler were alive, he shouldn't get the death penalty because there must really be something wrong with a guy who commits mass murder and puts millions of people to death in gas chambers."
*582 Defendant objected to the reference to Hitler. The trial court overruled the objection. It observed: "The Hitler argument is prohibited when it comes with respect to a comparison to the defendant, which was not done.... That wasn't done here. It was an extrapolation in argument that may be met with other argument."
We agree with the trial court. The prosecutor was not comparing defendant to Hitler, but was simply testing the logic of the defense argument. (See People v. McDermott (2002) 28 Cal.4th 946, 1003, 123 Cal.Rptr.2d 654, 51 P.3d 874.)

IX. Cumulative Prejudice
Earlier, we identified two errors: (1) the court's refusal to permit witness Foster to testify that she did not want defendant to be executed, and her reasons for that opinion (ante, 25 Cal.Rptr.3d at 576-577, 107 P.3d at 247-249) and (2) the trial court's failure to sustain an objection to the prosecutor's assertion at closing argument that "we know" facts were not matters of direct proof, but only of inference (ante, 25 Cal. Rptr.3d at 571-572, 107 P.3d at 243-244). The first is the most serious error but, as we explained earlier, the exclusion of this evidence could not have affected the outcome of the trial. (See ante, 25 Cal. Rptr.3d at 578, 107 P.3d at 249.) The prosecutor's "we know" comments, even if construed as going beyond the evidence, were effectively cured by his later comments. (See ante, 25 Cal.Rptr.3d at 571-572, 107 P.3d at 243-244.) We conclude that it is not reasonably possible (People v. Michaels, supra, 28 Cal.4th at p. 541, 122 Cal.Rptr.2d 285, 49 P.3d 1032; People v. Jackson (1996) 13 Cal.4th 1164, 1232, 56 Cal.Rptr.2d 49, 920 P.2d 1254) that these errors, individually or in combination, affected the result of the trial.

X. Constitutionality of the California Death Penalty Statute
Citing the Fifth, Sixth, Eighth, and Fourteen Amendments to the federal Constitution, defendant raises numerous constitutional objections to the California death penalty law. All have been previously rejected in decisions of this court.
Neither the breadth of "circumstances of the crime" in factor (a) of section 190.3, nor disagreement about what circumstances are aggravating, results in arbitrary and capricious application of the death penalty. (See Tuilaepa v. California, supra, 512 U.S. at pp. 975-976, 114 S.Ct. 2630; People v. Jenkins (2000) 22 Cal.4th 900, 1050-1053, 95 Cal.Rptr.2d 377, 997 P.2d 1044.)
Defendant has not shown that the California law fails adequately to narrow the class of persons eligible for the death penalty. (See People v. Michaels, supra, 28 Cal.4th at p. 541, 122 Cal.Rptr.2d 285, 49 P.3d 1032; People v. Wader (1993) 5 Cal.4th 610, 669, 20 Cal.Rptr.2d 788, 854 P.2d 80.)
The federal Constitution does not require that a state death penalty law impose a burden of proof on the prosecution to prove death is the appropriate penalty, either beyond a reasonable doubt (see People v. Arias, supra, 13 Cal.4th at p. 190, 51 Cal.Rptr.2d 770, 913 P.2d 980), or by a preponderance of the evidence (see People v. Hayes (1990) 52 Cal.3d 577, 643, 276 Cal.Rptr. 874, 802 P.2d 376). Because no burden of proof is required at the penalty phase (see ante, 25 Cal.Rptr.3d at 578-580, 107 P.3d at 252-253), the law is not invalid for failing to require an instruction on burden of proof. (See People v. Michaels, supra, 28 Cal.4th at p. 541, 122 Cal. Rptr.2d 285, 49 P.3d 1032; People v. Ochoa, supra, 26 Cal.4th at pp. 452-454, 110 Cal.Rptr.2d 324, 28 P.3d 78.) Neither is it invalid because it does not require an *583 instruction that certain factors can only be mitigating. (People v. Espinoza (1992) 3 Cal.4th 806, 827, 12 Cal.Rptr.2d 682, 838 P.2d 204; see also ante, 25 Cal.Rptr.3d at 578-579, 107 P.3d at 249-250.)
The jury is not required to agree unanimously on what aggravating factors exist. (People v. Danks (2004) 32 Cal.4th 269, 316, 8 Cal.Rptr.3d 767, 82 P.3d 1249; People v. Taylor (1990) 52 Cal.3d 719, 749, 276 Cal.Rptr. 391, 801 P.2d 1142.) No written findings are required. (People v. Davenport, supra, 11 Cal.4th at p. 1232, 47 Cal. Rptr.2d 800, 906 P.2d 1068; People v. Yeoman, supra, 31 Cal.4th at p. 165, 2 Cal. Rptr.3d 186, 72 P.3d 1166.)
California's death penalty law is not unconstitutional because it permits the jury to consider evidence of unadjudicated criminal activity (see ante, 25 Cal.Rptr.3d at 578, 107 P.3d at 248-249), does not require the prosecution to prove such activity beyond a reasonable doubt (People v. Ochoa, supra, 26 Cal.4th at p. 453, 110 Cal.Rptr.2d 324, 28 P.3d 78), and does not require the jury to find such activity by a unanimous verdict (People v. Michaels, supra, 28 Cal.4th at pp. 541-542, 122 Cal. Rptr.2d 285, 49 P.3d 1032; People v. Alcala (1992) 4 Cal.4th 742, 809, 15 Cal.Rptr.2d 432, 842 P.2d 1192).
The terms "extreme mental or emotional disturbance" in section 190.3, factor (d), "extreme duress" and "substantial domination" in factor (g) (italics added) do not render the statute invalid. (People v. Jones, supra, 15 Cal.4th at p. 190, 61 Cal. Rptr.2d 386, 931 P.2d 960 [factor (d)]; People v. Visciotti (1992) 2 Cal.4th 1, 73-75, 5 Cal.Rptr.2d 495, 825 P.2d 388 ["extreme duress" in factor (g)]; People v. Adcox (1988) 47 Cal.3d 207, 270, 253 Cal. Rptr. 55, 763 P.2d 906 ["substantial domination" in factor (g)].)
The absence of intercase proportionality review does not invalidate California's death penalty. (See People v. Lenart (2004) 32 Cal.4th 1107, 1131, 12 Cal. Rptr.3d 592, 88 P.3d 498; People v. Michaels, supra, 28 Cal.4th at p. 541, 122 Cal.Rptr.2d 285, 49 P.3d 1032; People v. Anderson (2001) 25 Cal.4th 543, 602, 106 Cal.Rptr.2d 575, 22 P.3d 347.) The death penalty law does not deny capital defendants equal protection because it provides a different method of determining the sentence than is used in noncapital cases. (People v. Cox, supra, 53 Cal.3d at p. 691, 280 Cal.Rptr. 692, 809 P.2d 351; People v. Williams (1988) 45 Cal.3d 1268, 1330, 248 Cal.Rptr. 834, 756 P.2d 221.)
Finally, defendant contends that California's death penalty law violates international norms. But "international law does not prohibit a sentence of death rendered in accordance with state and federal constitutional and statutory requirements." (People v. Hillhouse (2002) 27 Cal.4th 469, 511, 117 Cal.Rptr.2d 45, 40 P.3d 754; see People v. Bolden (2002) 29 Cal.4th 515, 567, 127 Cal.Rptr.2d 802, 58 P.3d 931.)

DISPOSITION
The judgment is affirmed.
WE CONCUR: GEORGE, C.J., BAXTER, WERDEGAR, CHIN, BROWN, and MORENO, JJ.
NOTES
[1]  All statutory references are to the Penal Code unless otherwise noted.
[2]  Defendant did not explicitly contend that the prosecutor's challenges violated the principles of Batson v. Kentucky (1986) 476 U.S. 79, 106 S.Ct. 1712, 90 L.Ed.2d 69, but a state challenge under Wheeler also states a federal claim under Batson. (People v. Yeoman (2003) 31 Cal.4th 93, 117, 2 Cal.Rptr.3d 186, 72 P.3d 1166.)
[3]  In People v. Johnson (2003) 30 Cal.4th 1302, 1318, 1 Cal.Rptr.3d 1, 71 P.3d 270, a majority of this court held that to establish a prima facie showing of a Wheeler violation, the defendant must "show that it is more likely than not the other party's peremptory challenges, if unexplained, were based on impermissible group bias." (Johnson at p. 1329, 1 Cal. Rptr.3d 1, 71 P.3d 270.) The United States Supreme Court has recently granted certiorari. (Sub nom. Johnson v. California (2005) 543 U.S. 1042 [125 S.Ct. 824].) The exact definition of a prima facie case, however, is not critical to our resolution of this appeal. The facts here do not give rise to any reasonable "inference of discriminatory purpose" (Batson v. Kentucky, supra, 476 U.S. 79, 93, 106 S.Ct. 1712, 90 L.Ed.2d 69). (See People v. Cleveland (2004) 32 Cal.4th 704, 732, fn. 5, 11 Cal.Rptr.3d 236, 86 P.3d 302.)
[4]  According to the trial court, it was Donna V., not Donna T., who hesitated. Defendant did not recall any hesitation.
[5]  Dr. Hatcher also testified concerning the experiences of children subjected to sadistic molestation. We discuss that evidence, and defendant's objections to it, in part V of this opinion. (See post, 25 Cal.Rptr.3d at 574-575, 107 P.3d at 245-246 et seq.)
[6]  Even assuming that a limiting instruction could prevent the jury from drawing that inference, the instruction given here did not do so. Although it told the jurors that they could not use Dr. Hatcher's testimony to prove that defendant was a person of bad character or had a disposition to commit crimes, it specifically allowed the jurors to draw inferences about "the behavior and mental processes of ... persons who commit such crimes."
[7]  In a motion in limine in the trial court, defendant contended that the error violated his rights under the due process clause of the Fourteenth Amendment and the cruel and unusual punishment clause of the Eighth Amendment to the federal Constitution.
[8]  CALJIC No. 8.85, incorporating section 190.3, factor (c), directs the jury to consider the presence or absence of prior felony convictions. At defendant's request, the trial court modified this instruction to include misdemeanor convictions.
