
97 Cal.Rptr.2d 871 (2000)
23 Cal.4th 692
3 P.3d 248
The PEOPLE, Plaintiff and Respondent,
v.
Philip Louis LUCERO, Defendant and Appellant.
No. S012568.
Supreme Court of California.
July 13, 2000.
As Modified on Denial of Rehearing August 30, 2000.[*]
Certiorari Denied February 26, 2001.
*881 Peter Dodd, under appointment by the Supreme Court, Hornbrook, for Defendant and Appellant.
Daniel E. Lungren and Bill Lockyer, Attorneys General, George Williamson, Chief Assistant Attorney General, Gary W. Schons, Assistant Attorney General, William M. Wood, Esteban Hernandez and Vincent L. Rabago, Deputy Attorneys General, for Plaintiff and Respondent.
Certiorari Denied February 26, 2001. See 121 S.Ct. 1190.
KENNARD, J.
This is the second time this case is before us. In 1981, defendant Philip Louis Lucero was sentenced to death after a jury found him guilty of two counts of murder (Pen.Code, § 187[1] and one count of arson (§ 451, subd. (c)), and found true an alleged multiple-murder special circumstance. In 1988, we affirmed the judgment of guilt, including the special circumstance finding, but we reversed the judgment of death, holding that the trial court had improperly excluded certain mitigating evidence at the penalty phase of trial. (People v. Lucero (1988) 44 Cal.3d 1006, 245 Cal.Rptr. 185, 750 P.2d 1342.) At retrial, the jury again imposed the death penalty. This appeal, like the earlier one, is automatic. (§ 1239.) We affirm the judgment of death.

I. FACTS

A. Prosecution's Evidence
The prosecution's case-in-chief at the penalty retrial consisted solely of evidence of the two murders of which defendant was convicted.
The murder victims, seven-year-old Linda Christine Hubbard (Chrissy) and 10-year-old Teddy Engilman (Teddy), lived in Yucaipa, a town in San Bernardino County. On April 12, 1980, Chrissy asked her father if she could go with Teddy to a nearby park. He agreed, and the two girls left around 4:00 p.m. Lisa Willis, an acquaintance of Teddy's older sister, saw the two girls at the park.
Defendant lived in a house across the street from the park. Teddy's brother had shown Chrissy a shortcut to the park that passed alongside defendant's house. Between 4:30 and 4:45 p.m., Ruth Schultz, who lived next door to defendant, heard the goose in defendant's yard cackle. From her window, she saw Teddy and Chrissy outside defendant's backyard, and she saw defendant walking toward them. He told the girls the goose would not hurt them and they could come into the yard.
At 5:00 p.m., the Hubbards discovered that Teddy and Chrissy were not in the park and had not returned home. They called the sheriffs office, and a search for the girls began. At 6:45 p.m., Delores Gwaltney, who lived across the street from defendant, saw him drive away from his house. Defendant returned five or 10 minutes later but soon left again. Shortly thereafter, Gwaltney saw that defendant's house was on fire. She telephoned defendant at his father's home and told him about the fire. Defendant seemed unconcerned. San Bernardino Sheriffs Deputy Charles Long, who had been looking for Chrissy and Teddy, also saw the fire and rescued defendant's dog from defendant's enclosed front porch.
Dennis Draeger, Chief of the Calimesa Volunteer Fire Department, together with Captain Charles Bryant and Firefighter Steven Beightler, both of the California Department of Forestry, were among those who arrived to put out the fire in *882 the house, they saw a large bloodstain on the living room carpet. Defendant soon arrived. Captain Bryant asked him about the origin of the bloodstain, but defendant had no explanation. Defendant then left to examine his dog, and when he returned he told Bryant the dog had a cut on its leg that could have caused the stain. Firefighter Beightler had seen the dog and it appeared uninjured. In defendant's conversations with Captain Bryant and Chief Draeger, he seemed unconcerned about the fire but wanted to know how long the firefighters intended to stay in his house.
About 9:00 o'clock that evening, Donald Burton was rummaging through a dumpster behind a nearby market when he saw an object that he thought was a mannequin. When he touched the object's leg, it was warm and felt like a child's leg. He called the San Bernardino County Sheriffs Office. Sheriffs deputies summoned to the scene found the bodies of Chrissy and Teddy in the dumpster, wrapped in plastic garbage bags. They were fully dressed, but Teddy's shoes were missing. Defendant was arrested later that night. Deputy Sheriff Dennis O'Rourke saw what appeared to be bloodstains on defendant's T-shirt and pants leg, and the sock on his left foot was saturated with blood.
Deputy Sheriffs Ronald Durling and James Stalnaker examined defendant's car. They found bloodstains on the driver's side door, the armrest, the dashboard, the steering wheel, and the gearshift lever. There was a pool of blood on an inner tube stored in the trunk of the car. Homicide Detective Larry Malmberg, Deputy Carl Swanlund, and criminalist Phillip Kellet searched defendant's house. In the living room, they found Teddy's shoes (partly covered by a comforter), a bloodstained sheet, an electrical cord, several large soft drink bottles, and pieces of another bottle. Other fragments of the broken bottle were in the garbage bag in which Teddy was found. A price of rope was in the doorway, and in the kitchen were garbage bags similar to the ones used to wrap Chrissy and Teddy.
A pathologist, Dr. Harry Scott, conducted an autopsy of the two girls. He found a large bruised area on Teddy's right eye and cheek, a laceration of her right earlobe, and a penetrating wound through her right lip that had knocked out three of her teeth. Her skull was fractured in several places as a result of being hit several times with a blunt object, which could have been a soft drink bottle. Dr. Scott determined that the blows to Teddy's head had knocked her unconscious, and that while unconscious she had aspirated blood from the wound to her face which caused her death. Chrissy had abrasions on her wrists that could have been caused by being tied up and abrasions on the left side of her neck. She had been strangled to death. Based on the marks on Chrissy's neck, Dr. Scott testified she could have been strangled with a necklace she was wearing.
Serologist Daniel Gregonis testified that the blood found on defendant's sock, on the carpet and sheet in his house, and on the inner tube in the trunk of his car was human blood, none of which could have come from defendant. He concluded that the blood was consistent with Teddy's ABO blood type and her serum protein and enzyme types, a profile that appears in 5.4 percent of the population.
Deputy Sheriff Charles Wideen, an arson expert, investigated the fire in defendant's house. He concluded that the fire had started in one of the bedrooms, and that it had been deliberately set by a person pouring a flammable liquid, like gasoline, on and beneath the bed, and lighting it. In a storage shed on defendant's property, Deputy Wideen found a partially full gasoline can. Deputy Wideen concluded, based on indentations in the *883 dust on the carpet where he round the can, that it had been recently moved.

B. The Defense Case
Defendant presented expert testimony that the bodies of Chrissy and Teddy showed no signs of sexual assault.
Relatives and family members testified about defendant's childhood. Defendant spent his earliest years in a poor section of Denver, Colorado. His father was an alcoholic who had little time for his children. At the age of five, defendant and his mother moved to Texas, but the next year defendant's father came and took him back to Denver. Except for one brief visit, defendant never saw his mother again until after his arrest in this case, when he was 33 years old.
Back in Denver, defendant was raised by his great-aunt, an elderly woman who lived in Goat Hill, a shantytown on the outskirts of Denver. They lived in a shack without electricity, running water, or indoor plumbing. Defendant essentially raised himself. He had little communication with his great-aunt, because she spoke only Spanish and he spoke only English. He became a loner.
When defendant was 11, he and his father moved to California. At the age of 17, lying about his age, he enlisted in the Army, where he remained for the next seven years.
Defendant served three tours of duty in Vietnam. Although the defense offered no witnesses who remembered defendant while he was there, several men who had served in the same units as defendant testified that the units came under sniper and mortar fire in their encampments and that they suffered casualties when their supply convoys were attacked and when they went on "search and destroy" missions. Defendant was wounded and awarded a Purple Heart. He also received a Combat Infantry cadge for having been under enemy fire. On cross-examination, the prosecutor elicited testimony that defendant had been court-martialed for falling asleep on guard duty, that he had been disciplined for having a Vietnamese woman in his quarters and for being in villages that were off-limits, and that he had misappropriated a truck.
After his release from the Army, defendant moved to Lake Tahoe. He married his stepsister Sharla, and they moved to Vista, a city in San Diego County. They had a son, and defendant got a job as a machinist. Defendant was a hard worker but he remained a loner. Five years later, the family moved to Yucaipa, in San Bernardino County, where defendant got a job with an engineering company. He was fired about a year before the murders in this case because he was unable to adapt to the company's specialized equipment.
Dr. Tom Williams, a psychologist, testified that defendant suffered from posttraumatic stress disorder (PTSD), caused by his war experiences in Vietnam. Dr. Williams based this conclusion on defendant's description of these experiences, which included three particularly traumatic episodes: he shot and killed a man who had attacked him with a grenade, his supply truck ran over a land mine, and he had to load into body bags the bodies of a platoon of American soldiers killed in action. Dr. Williams also relied on the results of two Minnesota Multiphasic Personality Inventory (MMPI) tests, one given by him, the other by Dr. Craig Rath. Williams expressed no opinion as to whether defendant killed Chrissy and Teddy because of PTSD, and the defense offered no evidence that PTSD played any causal role in the killings.
Dr. Harvey Dondershine, a psychology professor at Stanford University who had worked for 11 years at the National Center for Post Traumatic Stress Disorders, *884 testified that PTSD is a recognized form of mental illness and described its characteristics. He had not examined defendant, and he expressed no view on whether defendant suffered from PTSD.
Several correctional officers, counselors, and an administrator testified about defendant's behavior while he was incarcerated at San Quentin during his appeal after his first trial in this case. They described defendant as a respectful, quiet, and thoughtful inmate who stayed out of trouble. He interacted well with other inmates and with staff. Defendant took up art while in prison; his teacher, Eva De Bona, described his work as "highly original" and deserving of gallery or museum exhibition.

C. Prosecution's Rebuttal
The prosecution played to the jury a tape recording of a police interview with defendant on the night the killings occurred. Defendant discussed his whereabouts that day, denied knowing anything about the two missing girls, and denied any knowledge as to the cause of the fire in his house. He said nothing that directly inculpated him in the murders of the girls.
Dr. Jay Ziskin, a psychologist, testified that diagnoses by psychologists and psychiatrists are generally unreliable; that there is controversy in the mental health field as to whether PTSD exists as a distinct mental disorder, and if so what criteria should be used to diagnose it. According to Dr. Ziskin, the answers defendant gave in the MMPI test administered by Dr. Rath did not match a PTSD profile established by prominent psychologists, and his answers in the MMPI test administered by Dr. Williams suggested he was faking his symptoms.

II. Trial Issues

A. Trial Court's Failure to Grant Defendant's Motion for Mistrial
The defense called San Bernardino Sheriffs Lieutenant Ross Dvorak to testify regarding defendants demeanor on the night of his arrest. In response to the question, "How would you characterize [defendant's] demeanor?" Dvorak replied that at the beginning of the investigation defendant was "pretty cordial" but "[a]s time went on, it became more and more of a cat and mouse game to the point where [defendant] shut down the interview by saying, `I want to talk to my attorney.'" Defense counsel made no objection to Dvorak's testimony at the time, but soon afterwards, during a bench conference on an unrelated matter that occurred while the prosecutor was still cross-examining Dvorak, counsel asserted that Dvorak's reference to defendant's invocation of his Miranda rights (Miranda v. Arizona (1966) 384 U.S. 436, 86 S.Ct. 1602, 16 L.Ed.2d 694) had been improper and should be stricken. The trial court took no action on the matter, and six other witnesses testified that afternoon.
Before testimony resumed the next morning, defendant moved for a mistrial, claiming prejudice from Lieutenant Dvorak's testimony that during the investigation defendant had invoked his Miranda rights. The trial court denied the motion, stating: "The time to make an objection was at the time the response came out, if it did prejudice the jury in any way. Frankly, it doesn't." Thereafter, at defendant's request, the court told the jury to disregard the testimony in question, which the court ordered stricken from the record.
Defendant argues that the trial court should have granted his motion for mistrial. He relies on Doyle v. Ohio (1976) 426 U.S. 610, 96 S.Ct. 2240, 49 L.Ed.2d 91, which holds that the prosecution may not penalize a defendant for invoking Miranda rights during interrogation by using the invocation against the defendant at trial. The Attorney General asserts that defendant did not preserve the issue for appeal because his objection to the challenged testimony and his request for a mistrial *885 were untimely, b or the sake of argument, we assume that defendant's motion for a mistrial was timely. Nevertheless, we find no error.
"`A mistrial should be granted if the court is apprised of prejudice that it judges incurable by admonition or instruction. (People v. Woodberry (1970) 10 Cal.App.3d 695, 708, 89 Cal.Rptr. 330.) Whether a particular incident is incurably prejudicial is by its nature a speculative matter, and the trial court is vested with considerable discretion in ruling on mistrial motions.'" (People v. Hines (1997) 15 Cal.4th 997, 1038, 64 Cal.Rptr.2d 594, 938 P.2d 388.) Ordinarily, evidence that a suspect has invoked the right to remain silent creates the danger that the jury will draw an impermissible inference of guilt from the testimony. (See generally United States v. Newman (9th Cir.1991) 943 F.2d 1155, 1157.) Here that danger was not present, as defendant's guilt was not in issue in this penalty retrial. Defendant argues that the jury might have inferred from defendant's invocation of his Miranda, rights that he was acting in a cold and callous manner immediately after the killings, and that he therefore should be sentenced to death. But neither the prosecutor nor Lieutenant Dvorak suggested that the jury should draw this inference. As a result, the trial court did not abuse its discretion when it concluded that any prejudicial effect arising from Lieutenant Dvorak's testimony could be cured by an admonition to the jury to disregard it.

B. Admission of "In Life" Photograph of Murder Victim Teddy Engilman
Over defendant's objection, the trial court admitted a photograph of victim Teddy Engilman taken before her death, ruling that it was relevant to assist the jury in determining the extent of the beatings defendant had inflicted on her. Defendant argues the photograph was irrelevant and served no purpose other than to generate sympathy for the victim, and it therefore should have been excluded.
The Attorney General contends this issue has not been preserved for appeal because defendant did not object at trial. We disagree; defendant's pretrial objection was sufficient to preserve the issue. (People v. Morris (1991) 53 Cal.3d 152, 187-191, 279 Cal.Rptr. 720, 807 P.2d 949.) But we find no error. A photograph of a murder victim while alive is relevant at the penalty phase of a capital trial as a "circumstance of the crime," because it portrays the victim as seen by the defendant before the murder. (People v. Cox (1991) 53 Cal.3d 618, 688, 280 Cal. Rptr. 692, 809 P.2d 351.) Defendant points out that we have repeatedly cautioned about the dangers of admitting photographs of murder victims while alive. (See, e.g., People v. Osband (1996) 13 Cal.4th 622, 677, 55 Cal.Rptr.2d 26, 919 P.2d 640; People v. DeSantis (1992) 2 Cal.4th 1198, 1230, 9 Cal.Rptr.2d 628, 831 P.2d 1210; People v. Poggi (1988) 45 Cal.3d 306, 323, 246 Cal.Rptr. 886, 753 P.2d 1082.) In those cases, however, the photographs were admitted at the guilt phase of trial. As we recently explained, they are "generally admissible" when, as here, the prosecutor seeks to introduce them at the penalty phase. (People v. Carpenter (1997) 15 Cal.4th 312, 400-401, 63 Cal.Rptr.2d 1, 935 P.2d 708.) Thus, here the admission of the photograph was proper.
Defendant also argues admission of the photograph violated the federal Constitution because it rendered the trial "fundamentally unfair." Because defendant failed to object on this ground at trial, he may not now raise this issue on appeal. In any event, we discern no fundamental unfairness from the trial court's admission of the photograph.


*886 C. Prosecution's Cross-examination Regarding Feigned Mental Illness
As previously mentioned, Dr. Harvey Dondershine testified that PTSD is a recognized form of mental illness, and he described its characteristics. On cross-examination, the prosecutor asked him whether he was familiar with the "Rosenhan study," which showed that psychiatrists can mistakenly diagnose a patient as mentally ill. Dondershine said he knew of the study, and the prosecutor then elicited from him how it had been conducted: eight medical students feigned mental illness to obtain admission to hospital psychiatric wards, but the day after admission each no longer pretended to be mentally ill. Nevertheless, they were incorrectly diagnosed as mentally ill.
Defendant asserts the prosecutor's questions were not permissible cross-examination. He relies on Evidence Code section 721, subdivision (b), which, at the time of defendant's trial, provided that an expert could not be cross-examined regarding the "content or tenor of any ... technical ... publication unless: [¶] (1) The witness referred to, considered, or relied upon such publication in arriving at or forming his opinion; or [¶] (2) Such publication has been admitted in evidence." (Stats.1965, ch. 299, § 2, p. 1312.) He contends that here Dr. Dondershine did not rely on the Rosenhan study in forming his opinion and the study was not admitted into evidence. Because defendant did not object to the challenged cross-examination, he has not preserved the issue for appeal. (People v. Price (1991) 1 Cal.4th 324, 457, 3 Cal.Rptr.2d 106, 821 P.2d 610.)
Anticipating this conclusion, defendant accuses his counsel of incompetence for not making such an objection. Assuming for the sake of argument that an objection would have been meritorious, defense counsel's decision not to object may have been motivated by legitimate tactical considerations. (See generally People v. Pope (1979) 23 Cal.3d 412, 425, 152 Cal.Rptr. 732, 590 P.2d 859 [if "counsel's omissions resulted from an informed tactical choice within the range of reasonable competence, the conviction must be affirmed"].) Counsel knew the prosecutor intended to call Dr. Jay Ziskin to testify that psychological diagnoses are not valid or reliable, and he could reasonably assume that Dr. Ziskin would rely on the Rosenhan study in support of this conclusion. Counsel may have decided that it would be better for the defense if the jury learned of the Rosenhan study from defense witness Dr. Dondershine rather than from prosecution witness Dr. Ziskin.

D. Defendant's Loss of Sleep
On the morning of August 1, 1989, the second day of testimony, defense counsel told the trial court that the previous day defendant was left in a holding cell at the courthouse until after midnight and did not return to his cell until 12:30 a.m. The court told counsel that if this happened again it would "correct" the problem. Thereafter, on two separate occasions counsel informed the court that defendant had not been returned to his cell until 10:45 p.m.
Defendant contends that his lack of sleep on these occasions violated his federal constitutional rights to the effective assistance of counsel and to be present at trial. But defendant never asked the trial court to postpone the trial to give him additional time to sleep. As for defense counsel's alleged incompetence for not seeking a continuance to enable defendant to have more rest, counsel may have reasonably believed that defendant was sufficiently rested and no continuance was necessary.

E. Proceedings in Defendant's Absence
During its deliberations, the jury sent a note to the trial court, asking: "Was *887 there any official Medical Diagnosis that [defendant] has PTSD?" Defendant was not present when the court and counsel discussed the question, nor was he there when the court answered the question by telling the jury that the diagnosis of PTSD by defense witness Dr. Williams was the only such diagnosis in the record. Defendant asserts the court violated his federal constitutional right to be personally present during all phases of his trial by conducting these proceedings in his absence. (See People v. Waidla (2000) 22 Cal.4th 690, 741-743, 94 Cal.Rptr.2d 396, 996 P.2d 46.)
The Attorney General points out that at trial defense counsel waived defendant's right to be present during the proceedings in question. Defendant responds that the waiver was invalid because he did not personally waive his right to be present. We need not resolve this dispute, because any violation of defendant's right to be present was harmless.
"A criminal defendant's right to be personally present at trial is guaranteed by the Sixth and Fourteenth Amendments of the federal Constitution].... (People v. Jones [ (1991) ] 53 Cal.3d [1115,] 1141 [282 Cal.Rptr. 465, 811 P.2d 757]; People v. Douglas (1990) 50 Cal.3d 468, 517 [268 Cal.Rptr. 126, 788 P.2d 640].) A defendant, however, `does not have a right to be present at every hearing held in the course of a trial.' (People v. Price, [supra,] 1 Cal.4th 324, 407 [3 Cal.Rptr.2d 106, 821 P.2d 610].) A defendant's presence is required if it `bears a reasonable and substantial relation to his full opportunity to defend against the charges.' (People v. Freeman (1994) 8 Cal.4th 450, 511 [34 Cal.Rptr.2d 558, 882 P.2d 249].) The defendant must show that any violation of this right resulted in prejudice or violated the defendant's right to a fair and impartial trial. (People v. Jackson (1980) 28 Cal.3d 264, 310 [168 Cal.Rptr. 603, 618 P.2d 149].)" (People v. Hines, supra, 15 Cal.4th at pp. 1038-1039, 64 Cal.Rptr.2d 594, 938 P.2d 388.)
Here, the trial court's answer to the jury's question that the only diagnosis of PTSD in the record was that made by defense witness Dr. Williams was correct, and defendant's presence would not have affected that answer. As a result, defendant's presence would not have contributed to the fairness of the procedures, and his absence during the jury's inquiry did not prejudice him or violate his right to a fair and impartial trial. (See People v. Waidla, supra, 22 Cal.4th at p. 742, 94 Cal.Rptr.2d 396, 996 P.2d 46.)

F. Failure to Offer Defendant Allocution
Defendant contends the trial court should, on its own initiative, have allowed him at this penalty retrial the opportunity to address the jury "in allocution," that is, without being subject to cross-examination by the prosecutor. He acknowledges that we have repeatedly held there is no right of allocution at the penalty phase of a capital trial. (See, e.g., People v. Clark (1993) 5 Cal.4th 950, 1036-1037, 22 Cal. Rptr.2d 689, 857 P.2d 1099; People v. Nicolaus (1991) 54 Cal.3d 551, 583, 286 Cal. Rptr. 628, 817 P.2d 893; People v. Keenan (1988) 46 Cal.3d 478, 511, 250 Cal.Rptr. 550, 758 P.2d 1081.) But he insists that these cases do not address his claim that failure to permit allocution violates the right of a capital defendant to equal protection of the law, because a defendant in a noncapital case may at the time of sentencing address the court without being subject to cross-examination at the time of sentencing. We rejected such a claim in People v. Clark, supra, 5 Cal.4th at pages 1036 to 1037, 22 Cal.Rptr.2d 689, 857 P.2d 1099, albeit without analysis, merely observing that the defendant in that case had cited no authority in support of the contention.
In any event, defendant's equal protection claim fails at the threshold, because he *888 cannot show that he was denied a right granted to defendants in noncapital cases. Although one decision of the Court of Appeal has held that a noncapital defendant is entitled to allocution as a matter of right (In re Shannon B. (1994) 22 Cal. App.4th 1235, 27 Cal.Rptr.2d 800; but see, contra, People v. Sanchez (1977) 72 Cal. App.3d 356, 359, 140 Cal.Rptr. 110; People v. Wiley (1976) 57 Cal.App.3d 149, 166, 129 Cal.Rptr. 13; People v. Cross (1963) 213 Cal.App.2d 678, 682, 28 Cal.Rptr. 918), no court has held that in a noncapital case a trial court must, on its own initiative, offer the defendant allocution. Thus, here the trial court did not violate defendant's right to equal protection when it did not, on its own initiative, make defendant such an offer.

G. Prosecutorial Misconduct
Defendant accuses the prosecution and its witnesses of prejudicial misconduct. He cites six such instances, which we discuss below.

1. Reference to Defendant's Invocation of the Right to Remain Silent
As previously explained (see issue H.A., ante ), when defendant called Lieutenant Ross Dvorak to testify regarding defendant's demeanor during interrogation, Dvorak mentioned that defendant had ended the interrogation by invoking his right to counsel. Defendant argues that Lieutenant Dvorak's reference to defendant's invocation of his rights constituted misconduct by the prosecutor. (See Doyle v. Ohio, supra, 426 U.S. 610, 96 S.Ct. 2240, 49 L.Ed.2d 91 [prosecutor's cross-examination of a defendant about his invocation of Miranda rights violated due process].) We disagree. The record contains no evidence that the prosecutor was in any way responsible for Dvorak's comment. Defendant points out that a prosecutor must "guard against statements by his witnesses containing inadmissible evidence" (People v. Warren (1988) 45 Cal.3d 471, 481, 247 Cal.Rptr. 172, 754 P.2d 218, italics added), and a prosecutor who believes that a prosecution witness may mention an inadmissible matter "must warn the witness to refrain from making such a statement" (id. at p. 482, 247 Cal.Rptr. 172, 754 P.2d 218). This obligation arises when the witnesses are called by the prosecution. Here, the defense, not the prosecution, called Dvorak to testify.
Defendant also asserts that Lieutenant Dvorak committed misconduct by mentioning defendant's invocation of his right to counsel during interrogation. Any possibility of prejudice was negated when the trial court struck the testimony and told the jury to disregard it.

2. Defendant's Tape-recorded Statement
After defendant presented evidence that he was suffering from PTSD when he killed the two young girls, Teddy and Chrissy, the prosecutor offered into evidence a tape recording of the interrogation of defendant by San Bernardino County Sheriffs detectives on the night of the murders. Defendant said nothing inculpatory during the questioning, but he made some statements that were demonstrably false. Defendant objected to the recording, asserting that the prosecutor intended to use it only to show that he had lied during the interrogation. The prosecutor responded that the recording was admissible to show that defendant was not mentally impaired by PTSD on the night of the killings. The trial court overruled the objection. During closing argument, the prosecutor discussed defendant's lies in the recording. Defendant contends the trial court admitted the recording solely for the limited purpose for which it was offered, and the prosecutor committed misconduct by using it for a different purpose *889 in closing argument: to show that defendant had a bad character because he was a liar.
Because defendant did not at trial object to the prosecutor's argument, he is barred now from raising the issue. (People v. Price, supra, 1 Cal.4th at p. 440, 3 Cal.Rptr.2d 106, 821 P.2d 610.) In any event, an objection would have been groundless. As is apparent from the discussion in the preceding paragraph, the trial court did not admit the tape-recorded statements for a limited purpose; therefore, the prosecutor could use them in closing argument for any legally permissible purpose, as he did here. The prosecutor mentioned defendant's lies in the statement twice, each time for a permissible purpose: first, as evidence that defendant was callous and cold-blooded in his attitude towards the murders shortly after he committed them, casually asking the investigating officers for coffee while lying to them about his knowledge of the young girls' whereabouts; second, as a basis for arguing that defendant had falsely answered questions in the MMPI test on which Dr. Williams relied in concluding that defendant was suffering from PTSD. There was no prosecutorial misconduct.

3. Cross-examination of Defense Expert Williams
Defense witness Dr. Tom Williams, a clinical psychologist and an expert on PTSD, testified that defendant suffered from PTSD. He was not asked, and he expressed no view on, whether the disorder played any role in defendant's commission of the murders.
On cross-examination, the prosecutor asked Dr. Williams a series of questions about defendant's possible motives for committing the crimes. He also asked whether Williams knew that defendant had lied to the sheriffs deputies who questioned him on the night of the murders. Defendant argues these questions were impermissible because they were beyond the scope of Dr. Williams's testimony on direct examination. He asserts: "Under the guise of cross-examining Dr. Williams on his expert opinion, the prosecution was improperly allowed to place before the jury prejudicial evidence and inferences which were not germane to the formation of Williams's expert opinion."
The Attorney General contends defendant waived this issue by failing to object to these questions. After reviewing the record, we conclude that defendant objected to the prosecutor's questions regarding defendant's motives for the murders, but not to the questions regarding his lies to the interrogating officers. Thus, he has preserved the right to challenge the prosecutor's questions on the former subject, but not the latter.
The prosecutor's questions about motive were proper. Even though Dr. Williams did not explicitly testify that the murders were attributable to PTSD, it was possible that the jury might infer, based on his testimony, that PTSD played some role in the killings. As defense counsel said in a discussion in chambers, "I think it is a question for the jury to determine whether or not [defendant] was suffering from PTSD or a flashback or a triggering or something at the time of the homicides." The prosecutor's cross-examination of Dr. Williams about defendant's possible motive for the killings was intended to rebut the inference that they were attributable to PTSD. The questions fell within the subject matter of Dr. Williams's testimony on direct examination and were therefore permissible.
The prosecutor's questions regarding defendant's false statements to the police served a different purpose. Dr. Williams had based his conclusion that defendant suffered from Vietnam-related *890 PTSD on defendant's description of his war experiences in Vietnam and on defendant's answers in tests given by Drs. Williams and Rath. The prosecutor's questions about defendant's false statements tested Dr. Williams's belief in the truthfulness of defendant's account of his Vietnam experiences and his test answers. As a result, any objection to the prosecutor's questions about defendant's lies would have been meritless. (See People v. Coddington (2000) 23 Cal.4th 529, 613, 97 Cal. Rptr.2d 528, 2 P.3d 1081 ["When ... psychiatric experts' opinions ... are based in substantial part on statements made to them by the defendant, inquiry into the basis for the experts' belief that the defendant was honest and their knowledge of past deceitful conduct is permissible"].) Defense counsel was not incompetent for failing to object in this instance.
Finally, defendant raises a claim of prosecutorial misconduct based on the following: On cross-examination, defense witness Dr. Williams testified that he had told defendant that anything defendant said about the murders could be revealed in court. The prosecutor then asked: "Did you explain to him that his lawyers might not ask ... questions [about the murders], but a prosecutor sure might?" The trial court sustained defendant's objection to the question. Contrary to defendant's claim of prejudice, the question was harmless: it can hardly have come as a shock to the jury to learn that once the prosecutor knew that defendant had discussed the murders with Dr. Williams, he would question Williams in court about the matter.

4. Defendant's Reclassification While in Prison
During the defense's presentation of evidence, defense counsel told the trial court the prosecution might mention that defendant had been disciplined at San Quentin Prison when a "shank" (an inmate-made weapon) was found in his cell. He asked that the court hold a hearing under Evidence Code section 402 before permitting the prosecution to introduce evidence about this incident. The prosecutor agreed not to cross-examine witnesses about the incident before resolution of the issue in chambers.
Later that day, before a hearing on the shank incident, defendant called Richard Martinez, a former San Quentin Prison employee familiar with defendant's conduct in prison. Martinez testified that defendant was not a threat to other inmates or guards and was classified as a "Grade A" inmate, meaning he did not pose a disciplinary problem. On cross-examination, the prosecutor asked if Martinez had been involved in any disciplinary proceedings involving defendant, and Martinez said he had. The prosecutor then asked the trial court for a conference in chambers.
Outside the jury's presence, defendant moved for a mistrial, complaining that the prosecutor had broken his promise not to bring up the shank incident before an inchambers resolution. The court heard testimony in chambers from Martinez, who explained he had been involved in a disciplinary proceeding when defendant failed to present himself for a cell count, that he knew of but had not been personally involved in the shank incident, and that as a result of the latter incident defendant had been demoted to a "Grade B" category. Defendant then withdrew his motion for mistrial, but still objected to Martinez's being permitted to testify regarding the shank. The trial court ruled that Martinez could testify that defendant had been disciplined for failing to present himself for a head count, and that as a result of another incident defendant had been demoted to Grade B, but that Martinez could not mention the reason for the reclassification. Martinez then gave testimony that was consistent with the trial court's ruling.
*891 Thereafter, to prevent the jury from speculating about the reasons for the reclassification, defendant offered evidence explaining that a shank had been found in defendant's cell in a location and under circumstances suggesting it might have been placed there by another inmate, without defendant's knowledge.
Defendant now argues the prosecutor's question to Martinez about any disciplinary proceedings against defendant breached his promise not to inquire into the shank incident without a hearing on its admissibility. But the prosecutor did not ask Martinez about the shank incident; he inquired into a matter involving defendant's failure to appear for a head count. There was no prosecutorial misconduct.
Defendant also faults the trial court for permitting the prosecutor to introduce evidence that defendant's disciplinary status had been reclassified from Grade A to Grade B, thereby forcing the defense to elicit details of the shank incident. Defendant argues that had the court held a hearing concerning the admissibility of the shank incident as evidence in aggravation, it might well have excluded the evidence. He points out that at a later hearing on his motion to modify his death sentence, the trial court noted that the evidence did not show beyond a reasonable doubt that defendant had possessed the shank. We find no error. Defendant presented testimony that he was not a disciplinary problem while in prison. The prosecution was entitled to rebut that mitigating testimony with evidence of disciplinary violations that led to defendant's disciplinary reclassification from Grade A to Grade B, regardless of whether that evidence was independently admissible as evidence in aggravation.

5. Prosecutor's Closing Argument
In closing argument to the jury, the prosecutor commented that defendant's "brutality and callousness" during the killings of the two young girls was "equal, if not surpassed, by the defendant's conduct afterwards." Pointing out that defendant had thrown the bodies in a dumpster like "two pieces of garbage," the prosecutor said: "This is what aggravation is all about."
Defendant contends this argument was misconduct because it asked the jury to consider defendant's lack of remorse for the killings as a factor in aggravation. (See People v. Champion (1995) 9 Cal.4th 879, 943, 39 Cal.Rptr.2d 547, 891 P.2d 93 [prosecutor may discuss subject of remorse but may not argue lack of remorse as aggravating factor].) He further asserts that the prosecutor's comment violated his Fifth Amendment privilege against self-incrimination, because, in his view, the jury was likely to regard it as a comment on defendant's failure to testify and to express remorse. (See generally Griffin v. California (1965) 380 U.S. 609, 85 S.Ct. 1229, 14 L.Ed.2d 106 [prosecutor may not comment on a defendant's failure to testify].) Anticipating our rejection of this argument on the ground that his counsel did not object at trial to the prosecutor's argument (People v. Price, supra, 1 Cal.4th at p. 440, 3 Cal.Rptr.2d 106, 821 P.2d 610), defendant claims the failure to do so constituted ineffective assistance of counsel.
The prosecutor's argument was proper. Defendant's callous method of disposing of the girls' bodies in a dumpster was a circumstance of the murders that the jury could properly consider in aggravation (§ 190.3, factor (a)), and the prosecutor was entitled to argue that the aggravated circumstances of the crime warranted the death penalty. Nor do we find anything in the prosecutor's remarks that could be construed as a commentary on defendant's failure to testify. Thus, an objection by defense counsel would have been fruitless.


*892 H. Jury Instruction Issues

I. Instructions Defining Extenuating Circumstances
A standard instruction (CALJIC No. 8.88) told the jury how to weigh the aggravating and mitigating evidence offered at the penalty phase. The instruction defined a mitigating circumstance as "any fact, condition or event which, as such, does not constitute a justification or excuse for the crime in question, but may be considered as an extenuating circumstance in determining the appropriateness of the death penalty." (Italics added.) During its deliberations, the jury asked, "We, the jury, in the above entitled action, request the following: Exact definition of extenuating circumstances." After consulting with counsel, the trial court gave this written answer: "Extenuating circumstances: Such as render a crime less aggravated, heinous, or reprehensible than it would otherwise be, or tend to lessen its guilt. Such circumstances may ordinarily be shown in order to reduce the punishment." "Extenuation: That which renders a crime less heinous than it would be without it. It is opposed to aggravation." The source for these two definitions was Black's Law Dictionary. (See Black's Law Dict. (5th ed.1979) p. 524.)
Defendant now challenges the definitions given by the trial court in answer to the jury's question. The Attorney General argues that he is barred from doing so by the doctrine of invited error, noting that the trial court told the jury that "we decided on the definitions" (italics added), referring to the court, the prosecutor and defense counsel, and the prosecutor later stated (without contradiction from the defense) that "both parties approved" the court's answer.
The doctrine of invited error bars a defendant from challenging an instruction given by the trial court when the defendant has made a "conscious and deliberate tactical choice" to "request" the instruction. (People v. Wader (1993) 5 Cal.4th 610, 658, 20 Cal.Rptr.2d 788, 854 P.2d 80; see also People v. Cain (1995) 10 Cal.4th 1, 38, fn. 14, 40 Cal.Rptr.2d 481, 892 P.2d 1224; People v. Cooper (1991) 53 Cal.3d 771, 831, 281 Cal.Rptr. 90, 809 P.2d 865.) Our cases do not address, however, whether a defendant's approval of a court's instruction, as occurred here, is equivalent to a request. It is also unclear from the record whether in this case defendant's approval of the trial court's definitions of "extenuation" and "extenuating circumstances" was the result of a conscious and deliberate tactical choice. But we need not decide whether the doctrine of invited error bars defendant's challenge, because, as we shall explain, we find that the court properly answered the jury's question.
Defendant complains that the trial court's definitions of "extenuation" and "extenuating circumstances" were inaccurate because they did not tell the jury that mitigating evidence not directly related to the crime itself, such as defendant's character, his history, and his accomplishments, could be considered in determining punishment. But the jurors' question did not indicate that they were confused about whether they could consider defendant's mitigating evidence; they merely asked the trial court to define the term "extenuating circumstances." The jury had no reason to be confused about whether it could consider defendant's mitigating evidence, for the trial court had instructed the jury that among the factors to be considered in weighing the evidence was this: "Any other 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 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 *893 trial." (Italics added.) Thus, the jury was aware it could consider defendant's mitigating evidence even if it did not believe that the evidence extenuated the gravity of the murders he committed.
Defendant argues the trial court's definition of "extenuation" was wrong because, by stating that "extenuation" was "opposed to aggravation," the court effectively defined "mitigation" as "the opposite of aggravation." This juxtaposition, he claims, is inaccurate because mitigation is "open-ended" (that is, the jury is free to consider any evidence to be mitigating), while the jury may consider evidence as aggravating only if it is relevant to an aggravating factor listed in section 190.3. We are not persuaded that the court's definition of "extenuation" would have caused any confusion by the jury as to whether it could consider aggravating evidence not mentioned in section 190.3. The trial court gave the jury a modified version of CALJIC No. 8.85, a standard instruction describing the aggravating and mitigating factors the jury could consider in deciding whether to impose the death penalty. We find nothing in the court's definition of the word "extenuation" that would have caused the jury to disregard this instruction.

2. Trial Court's Failure to Instruct on Sympathy
Defendant faults the trial court for not instructing, on its own initiative, that the jury could consider sympathy for defendant as a mitigating circumstance. We have, however, repeatedly held that such an instruction need not be given at the penalty phase of a capital trial (see, e.g., People v. Champion, supra, 9 Cal.4th at p. 943, 39 Cal.Rptr.2d 547, 891 P.2d 93; People v. Clark (1992) 3 Cal.4th 41, 163, 10 Cal.Rptr.2d 554, 833 P.2d 561), and we see no reason to reconsider that holding. Moreover, here the trial court implied that the jury could consider sympathy for defendant when it instructed the jurors that they could consider "any sympathetic or other aspect of the defendant's character or record 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" (italics added), and that the jurors were free to "assign whatever moral or sympathetic value" (italics added) they deemed appropriate to the aggravating and mitigating factors they were permitted to consider.

3. Trial Court's Failure to Instruct on Defendant's Lack of a Violent Record
The trial court instructed the jurors that in determining whether to impose the death penalty, they should "consider, take into account and be guided by the following factors, if applicable: [¶] ... [¶] (b) The presence or absence of criminal activity by the defendant, other than the crimes for which the defendant has been tried in the present proceedings, which involved the express or implied threat to use force or violence." Defendant argues this instruction was inaccurate because it did not expressly tell the jurors that they should regard section 190.3, factor (b) as mitigating if they found that aside from the murders in this case defendant had not engaged in violent criminal conduct. According to defendant, the jury was likely to infer from the court's instruction that lack of a history of violence was a neutral rather than a mitigating factor.
The Attorney General contends that any error was invited by defendant because he helped the trial court in drafting the instruction in question. We find no invited error. Defense counsel did not participate in drafting the instruction, he merely objected to those portions of the instruction that would allow the jury to conclude, based on the evidence that a *894 shank had been found in defendant's prison cell, that defendant had engaged in conduct involving the threat to employ violence. But the trial court's instruction was proper. "We have repeatedly held that `trial courts are not required to identify particular sentencing factors as aggravating or mitigating and that the 1978 death penalty law is constitutional despite the absence of such a requirement.'" (People v. Davenport (1995) 11 Cal.4th 1171, 1229, 47 Cal.Rptr.2d 800, 906 P.2d 1068; see also People v. Earp (1999) 20 Cal.4th 826, 899, 85 Cal.Rptr.2d 857, 978 P.2d 15; People v. Frye (1998) 18 Cal.4th 894, 1026-1027, 77 Cal.Rptr.2d 25, 959 P.2d 183; People v. Howard (1992) 1 Cal.4th 1132, 1196, 5 Cal.Rptr.2d 268, 824 P.2d 1315.) Defendant asserts these cases are distinguishable because in each the defendant contended that all of the factors should be labeled as aggravating or mitigating, while here he claims only that one particular factor should have been so labeled. We find no distinction: if the trial court need not label all the enumerated factors as aggravating or mitigating, it necessarily follows that it need not identify any particular factor as aggravating or mitigating.

4. Instructions on Factors in Section 190.3
As previously mentioned, the trial court gave a modified version of CALJIC No. 8.85, a standard instruction describing the section 190.3 factors the jury should consider in deciding whether to impose the death penalty. Defendant argues this instruction was deficient in several respects. We are not persuaded.
First, defendant complains the trial court told the jury that one factor it could consider in deciding whether to impose the death penalty was based on section 190.3, factor (a), "the circumstances of the crime of which the defendant was convicted in the present proceeding...." According to defendant, the prosecutor introduced "a vast array of irrelevant evidence" as part of the circumstances of the crimes: that Chrissy lived with her family in Yucaipa on the day of the murder, that Teddy lived with her family nearby, that Chrissy's father told the girls they could go to the park, that Teddy's brother had shown Teddy a shortcut to the park, and that the necklace defendant used to strangle Chrissy had been given to her by her mother as a present shortly before her death.
Defendant contends the evidence just described had no bearing on his moral culpability and the jury should not have considered it in determining whether to impose the death penalty. He asserts the court's instruction that the jury could consider the "circumstances of the crime" was unconstitutionally vague, in violation of the Fifth, Sixth, Eighth, and Fourteenth Amendments to the federal Constitution and the parallel sections of our state Constitution, because it allowed the jury to consider this allegedly irrelevant evidence.
We disagree. As both the United States Supreme Court and this court have said, an instruction that the jury may consider the circumstances of the offense at the penalty phase of a capital case is not unconstitutionally vague. (Tuilaepa v. California (1994) 512 U.S. 967, 977-979, 114 S.Ct. 2630, 129 L.Ed.2d 750; People v. Hawkins (1995) 10 Cal.4th 920, 964, 42 Cal.Rptr.2d 636, 897 P.2d 574; People v. Cain, supra, 10 Cal.4th 1, 68, 40 Cal.Rptr.2d 481, 892 P.2d 1224.) We trust that the jury, assisted by the arguments of counsel, were able to determine which facts were relevant to the penalty determination and which were not. To the extent defendant argues that facts relating to the victims can never be relevant to penalty, he is wrong. "A State may legitimately conclude that evidence about the victim ... is relevant to the jury's decision as to whether or not the death penalty should be imposed." (Payne v. Tennessee (1991) 501 *895 U.S. 808, 827, 111 S.Ct. 2597, 115 L.Ed.2d 720; see also People v. Clark, supra, 5 Cal.4th 950, 1033, 22 Cal.Rptr.2d 689, 857 P.2d 1099.)
Defendant also criticizes the trial court's instruction, as part of CALJIC No. 8.85, that the jury could consider section 190.3, factor (b) in deciding whether to impose the death penalty.[2] Defendant claims this portion of the instruction was unconstitutionally vague and ambiguous because it permitted the jury to consider in aggravation the evidence that defendant at one time had a shank in his prison cell. Defendant notes that the shank was found in a location where it could have been planted by another inmate, and that at the hearing on defendant's motion for modification of the death sentence, the trial court found that the evidence did not show beyond a reasonable doubt he had been in possession of the shank.
The United States Supreme Court has already rejected the contention, now being made by defendant, that factor (b) of section 190.3 in our capital sentencing scheme is unconstitutionally vague. (Tuilaepa v. California, supra, 512 U.S. at pp. 977-980, 114 S.Ct. 2630.) Nor was the trial court's factor (b) instruction erroneous for permitting the jury to consider defendant's possible possession of a shank while in prison. The court correctly instructed the jurors they should consider this evidence only if they found beyond a reasonable doubt he had indeed possessed it. We assume the jurors obeyed the court's instruction.
Also included in CALJIC No. 8.85 was factor (d) of that instruction: "Whether or not the offense was committed while the defendant was under the influence of extreme mental or emotional disturbance." Defendant argues this portion of the instruction (as well as § 190.3, factor (d), on which it is based) was constitutionally deficient because (1) it did not tell the jury whether factor (d) was an aggravating or a mitigating factor; (2) the word "extreme," as used in the instruction, was unconstitutionally vague; (3) the word "extreme" prevented the jury from considering mental or emotional disturbances that are not extreme. We have in the past rejected each of these contentions. (People v. Musselwhite (1998) 17 Cal.4th 1216, 1266-1268, 74 Cal.Rptr.2d 212, 954 P.2d 475; People v. Holt (1997) 15 Cal.4th 619, 698, 63 Cal.Rptr.2d 782, 937 P.2d 213; People v. Ashmus (1991) 54 Cal.3d 932, 1001-1002, 2 Cal.Rptr.2d 112, 820 P.2d 214.)
Defendant further contends that CALJIC No. 8.85 and section 190.3 (on which the instruction is based) are unconstitutionally vague for various reasons: "[T]hey do not limit the jury to consideration of only the listed factors in aggravation; they fail to guide the jury's discretion; they permit the prosecutor to argue non-statutory aggravating evidence as aggravating evidence; and they allow the penalty process to proceed in an arbitrary, capricious, death-biased and unreviewable manner...." Not so. (Tuilaepa v. California, supra, 512 U.S. at pp. 971-973, 114 S.Ct. 2630; People v. Millwee (1998) 18 Cal.4th 96, 163-164, 74 Cal.Rptr.2d 418, 954 P.2d 990; People v. Musselwhite, supra, 17 Cal.4th at pp. 1266-1268, 74 Cal. Rptr.2d 212, 954 P.2d 475; People v. Bacigalupo (1993) 6 Cal.4th 457, 470-477, 24 Cal.Rptr.2d 808, 862 P.2d 808.)

III. Ineffective Assistance of Counsel
Defendant asserts he was denied the effective assistance of counsel, based on various acts and omissions by his attorney.
*896 "To prevail on a claim of ineffective assistance of counsel, defendant `must establish not only deficient performance, i.e., representation below an objective standard of reasonableness, but also resultant prejudice.'" (People v. Hart (1999) 20 Cal.4th 546, 623, 85 Cal.Rptr.2d 132, 976 P.2d 683.) Prejudice occurs only if the record demonstrates "a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." (Strickland v. Washington (1984) 466 U.S. 668, 694, 104 S.Ct. 2052, 80 L.Ed.2d 674.) "When ... the record sheds no light on why counsel acted or failed to act in the manner challenged, the reviewing court should not speculate as to counsel's reasons.... Because the appellate record ordinarily does not show the reasons for defense counsel's actions or omissions, a claim of ineffective assistance of counsel should generally be made in a petition for writ of habeas corpus, not on appeal." (People v. Diaz (1992) 3 Cal.4th 495, 557-558, 11 Cal.Rptr.2d 353, 834 P.2d 1171.)
With these principles in mind, we review defendant's claims of ineffective assistance of counsel.

A. Defense Counsel's Failure to Request Special Instructions
According to defendant, counsel was incompetent for failing to request special instructions on a variety of subjects. We discuss each in turn.
As previously discussed, the trial court gave a standard instruction, CALJIC No. 8.85, describing the factors the jury could consider in its penalty deliberations, including the following: "Any other 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 defendant's character or record 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 contends his counsel should have asked for a pinpoint instruction to explain to the jury the scope of this part of CALJIC No. 8.85. Defendant suggests an instruction such as the one given in People v. Noguera (1992) 4 Cal.4th 599, 647, 15 Cal.Rptr.2d 400, 842 P.2d 1160, where the trial court told the jury that the mitigating factors listed in CALJIC No. 8.85 were "only examples" and the jury could consider "other circumstances as reasons for not imposing the death penalty," or an instruction drawing the jury's attention to defendant's background, history, and character, his capabilities or lack of same, and his accomplishments or lack of same, as was given by the court in People v. McLain (1988) 46 Cal.3d 97, 114, 249 Cal.Rptr. 630, 757 P.2d 569. The trial court was under no obligation to give such an instruction, which would have been essentially duplicative of CALJIC No. 8.85, and counsel need not request unnecessary and duplicative instructions.
Defendant faults his counsel for not requesting an instruction drawing the jury's attention to categories of mitigating evidence offered by the defense, such as defendant's deprived childhood, his military service, his artistic abilities, his role as a father, and his behavior in prison. As we have held in the past, instructions of this type are "argumentative," and therefore should not be given, because they "`invite the jury to draw inferences favorable to one of the parties from specified items of evidence.'" (People v. Hines, supra, 15 Cal.4th at pp. 1067-1068, 64 Cal.Rptr.2d 594, 938 P.2d 388.)
Defendant asserts that in the absence of special instructions of the kind described above, CALJIC No. 8.85 was misleading, confusing and likely to lead to an arbitrary verdict of death. To the contrary. We have held that this instruction correctly describes the jury's role in *897 evaluating evidence presented at the penalty phase. (People v. Musselwhite, supra, 17 Cal.4th at pp. 1266-1268, 74 Cal. Rptr.2d 212, 954 P.2d 475.) Counsel was not ineffective for not requesting additional instructions elaborating upon CALJIC No. 8.85.
Defendant argues defense counsel should have sought an instruction that the jury could consider in mitigation the fact, if true, that the killings of the two young girls were not premeditated. According to defendant, we approved such an instruction in People v. Bonillas (1989) 48 Cal.3d 757, 792, 257 Cal.Rptr. 895, 771 P.2d 844. We did not. The trial court in Bonillas gave such an instruction, but we expressed no view as to whether the court should have given it. Moreover in Bonillas, unlike this case, the jury made no determination at the guilt phase that the murder the defendant had committed was premeditated, because the murder conviction there was based on the felony-murder rule. Here, by contrast, the guilt phase jury necessarily found premeditation when it convicted defendant of first degree murder. Assuming for the sake of argument that the instruction the trial court gave in Bonillas was appropriate there, it would have been improper here. Defendant also makes the closely related claim that counsel should have requested an instruction that if the jury had lingering doubts about premeditation, these doubts could be the basis for sentencing defendant to life in prison without possibility of parole. Even if such an instruction would have been proper, defense counsel may have had tactical reasons not to request it, as we explain in part III.D., post.
Defendant faults counsel for failing to request an instruction that the jury could consider his lack of a history of violence and his lack of prior felony convictions as factors in mitigation. The trial court, however, gave the jury a standard instruction, CALJIC No. 8.85, stating that it could consider the "presence or absence of criminal activity by the defendant ... which involved the express or implied threat to use force or violence," and the "presence or absence of any prior felony conviction...." (Italics added.) This instruction told the jury that if it found an absence of evidence that defendant had a history of violent criminal activity or prior felony convictions, it could consider that fact in mitigation. Defense counsel cannot be faulted for not requesting an instruction that would duplicate the one given by the court.
Defendant argues the trial court's instruction mentioned in the preceding paragraph was inadequate because it merely stated that the jury "shall consider, take into account and be guided by" the presence or absence of a violent criminal history and prior felony convictions, and that counsel should have asked for an instruction that the jury must consider those factors. To the extent there is a difference between the instruction given by the trial court and that proposed by defendant, the trial court's instruction more accurately describes the jury's role in evaluating the aggravating and mitigating circumstances. (See § 190.3 ["In determining the penalty, the trier of fact shall take into account any of the [relevant] factors...."].)
The trial court told the jury to "determine ... which penalty is justified and appropriate by considering the totality of the aggravating circumstances with the totality of the mitigating circumstances." Defendant notes that this instruction did not expressly say that one mitigating factor is sufficient to outweigh all aggravating factors, and he faults counsel for not requesting a clarifying instruction. But such a clarifying instruction would have been argumentative unless it also told the jury that one aggravating factor is sufficient to *898 outweigh all mitigating factors. Counsel may reasonably have concluded that not only was such clarification unnecessary, but it would have done more harm than good, because it would have supported the prosecutor's argument that one aggravating factor (the circumstances of the crime) outweighed all of the factors in mitigation.

B. Defense Counsel's Elicitation of Prejudicial Evidence
As previously explained (see pts. II.A. and II.G.1, ante ), Lieutenant Ross Dvorak, called by the defense to testify regarding defendant's demeanor on the night of his arrest, mentioned that defendant had ended his interrogation by invoking his right to counsel. Defendant asserts his counsel was ineffective because he did not object to the testimony and did not ask that the statements be stricken. Defense counsel did, however, object to the testimony in a conference in chambers while Dvorak was still on the stand, explaining that he "hesitated to do it before the jury because it clangs the bell again." The next day, the trial court told the jury at defense counsel's request to disregard Dvorak's comment because it had been stricken from the record. Defendant also contends counsel should have objected sooner. Even if he should have, there is not a reasonable probability that the trial's outcome would have been different if counsel had objected and sought an admonition immediately after Dvorak's comment regarding defendant's request for counsel, instead of, as counsel did, asking in chambers that the comment be stricken.
Defendant faults counsel for not seeking to exclude certain testimony by Lieutenant Dvorak. After Dvorak mentioned that defendant had invoked his right to counsel, defense counsel asked if defendant had been calm during the interrogation. Dvorak replied that defendant was "[m]aybe a little too calm." When counsel asked Dvorak what he meant, Dvorak replied that defendant had been playing "cat and mouse," his answers had been "self-serving," and he had been "pretending he didn't understand some of our questions." It is this testimony that defendant insists his counsel should have asked the trial court to exclude. This testimony, however, was responsive to the question asked, so a motion to strike the testimony would not have been well taken. In any event, any conceivable incompetence of counsel in this regard was harmless, because a tape recording of defendant's interrogation was played to the jury, which could draw its own conclusions as to whether he had been playing a cat-and-mouse game or giving self-serving answers during the interrogation.

C. Defense Counsel's Failure to Object to Prosecutor's Questions
Defendant argues his counsel was ineffective on five occasions for not objecting to certain questions by the prosecutor. We disagree, and discuss each instance below.
1. Defendant asserts counsel should have objected to testimony that on the day Chrissy and Teddy were killed, they were playing at Chrissy's house and asked Chrissy's father for permission to go to the park. He claims this evidence was irrelevant and "erroneously allowed [the prosecution] to present to the jury a picture of the victims as two playful children who were innocently engaged in a trip to the local park." That defendant killed "two playful children who were innocently engaged in a trip to the local park" was a circumstance of the murders and was therefore admissible. (See generally People v. Edwards (1991) 54 Cal.3d 787, 833, 1 Cal.Rptr.2d 696, 819 P.2d 436 [a circumstance of the crime is one "`which surrounds materially, morally, or logically' the crime"].) Thus, an objection by defense *899 counsel to the testimony in question would have been unavailing. "Counsel may not be deemed incompetent for failure to make meritless objections." (People v. Coddington, supra, 23 Cal.4th at p. 625, 97 Cal. Rptr.2d 528, 2 P.3d 1081.)
2. We reject defendant's contention that counsel should have objected when, after the defense introduced evidence that defendant had participated in the condemned-workers program at San Quentin Prison, the prosecution elicited testimony that the program had been terminated because some workers in the program had illegally passed items to other inmates. Defense witnesses testified that defendant never violated any rules while he was a member of the program. Counsel may reasonably have concluded that evidence of other inmates violating the rules of the program was favorable to the defense, when contrasted to defendant's obedience of those rules.
3. Defendant contends counsel should have objected when, after defendant offered evidence that he had served three tours of duty in Vietnam, where he was awarded a Purple Heart and a Combat Infantry Badge, the prosecutor elicited testimony that he had been court-martialed for falling asleep on guard duty, had been disciplined for having a Vietnamese woman in his quarters and for being in villages that were off-limits, and had misappropriated a truck. According to defendant, he introduced evidence of his military service in Vietnam for the primary purpose of showing that he suffered from PTSD, and evidence of his misdeeds while in the military was irrelevant to this purpose and therefore inadmissible. But defendant also relied on his service in Vietnam to show that, as mentioned elsewhere in his brief, he "had served his country above and beyond the call of duty in war" and that his "sendee for his country in Vietnam was both lengthy and, for the most part, exemplary." Defense counsel stressed this point in closing argument: "We know that Sonny Lucero did serve his country. He did receive a Purple Heart and other ribbons." The prosecution was entitled to reduce the mitigating impact of the evidence that defendant had served three tours of duty in Vietnam and was awarded two medals by showing that his conduct while serving in Vietnam was not exemplary.
4. Defendant characterizes as irrelevant the testimony of Chrissy's father that a necklace Chrissy wore when she died was a present from her mother. Dr. Harry Scott, who conducted the autopsy, testified that Chrissy was strangled, possibly by a necklace. Chrissy's father identified a necklace that was introduced into evidence as the one Chrissy had been wearing the day she died. Thus, his testimony that the necklace was a present from Chrissy's mother was relevant to show his familiarity with the necklace, which strengthened the reliability of his identification of the necklace as the one Chrissy had worn.
5. Defendant complains about counsel's lack of an objection when, after defense witness Isabel Rivera asked the jury to spare defendant's life, the prosecutor asked Rivera whether she had met the victims or knew their names, and whether she knew how they had died, questions to which Rivera gave negative answers. According to defendant, the prosecutor's questions were rhetorical, argumentative, and beyond the scope of direct examination. Defense counsel, however, had no basis for objection. The prosecutor was entitled to ask questions designed to show that Rivera's belief that defendant's life should be saved did not take into account the circumstances surrounding the murder, because she was unfamiliar with all of the facts of the case. An objection by defense counsel would not have been appropriate.
*900 Defendant also faults counsel for not objecting to three comments by the prosecutor in closing argument. We disagree. In each instance, the prosecutor's argument was proper.
1. In closing argument, the prosecutor told the jury: "[Y]ou sit in this case only as the conscience of the community. [¶] And by your decision in this case, you will tell the defendant ... what you think about his conduct on April the 12th, 1980." (Italics added.) Defendant argues this statement had the effect of diminishing the jurors' sense of personal responsibility for their decision whether to impose the death penalty, by suggesting that jurors should make the penalty determination based on what they thought the community would regard as an appropriate punishment, rather than what the jurors themselves regarded as appropriate. The prosecutor, however, never suggested that the jury should abrogate its responsibility to personally determine whether death was the appropriate penalty. It was proper for the prosecutor to describe the jurors as the "conscience of the community." (People v. Jones (1997) 15 Cal.4th 119, 185-186, 61 Cal.Rptr.2d 386, 931 P.2d 960; see also People v. Lang (1989) 49 Cal.3d 991, 1041, 264 Cal.Rptr. 386, 782 P.2d 627.)
Inapposite is defendant's reliance on United States v. Koon (9th Cir.1994) 34 F.3d 1416, reversed in part on other grounds sub nom. Koon v. U.S. (1996) 518 U.S. 81, 116 S.Ct. 2035, 135 L.Ed.2d 392. There, the federal appellate court held: "An appeal to the jury to be the conscience of the community is not impermissible unless it is `specifically designed to inflame the jury.'" (Koon, supra, 34 F.3d at p. 1444.) In this case, when the prosecutor's statement is considered in context, it is clear that it was intended not to inflame the jurors but only to remind them of their role in the judicial process. We find no error.
2. In closing argument, the prosecutor told the jury: "You also know from the testimony of a number of people in [defendant's] unit, Smallwood, Noel, Painter, Sharp and Williams that people that had the same type of experience in Vietnam did not turn out like the defendant, did not end up like the defendant." Defendant contends that by asking the jury to compare him to others who had allegedly similar life experiences, the prosecutor violated his right to individualized sentencing, which the Eighth Amendment requires in capital cases. He argues that many of the others may not have had his experience of a deprived childhood, and he faults counsel for not objecting. When, as here, a defendant asserts that the death penalty should not be imposed because the defendant has experienced hardship, the prosecutor may properly point out that others with similar experiences did not commit murder. There was no reason for counsel to object.
3. Defendant also complains about counsel's lack of objection to the prosecutor's comment in closing argument that "going to Vietnam and having bad experiences and returning to this country and remembering them, that does not give anyone a blank check to commit murder," adding, "you can't find the answer to this crime" in defendant's deprived childhood. The prosecutor did no more than urge the jury to discount defendant's mitigating evidence. This was proper (see People v. Hamilton (1989) 48 Cal.3d 1142, 259 Cal. Rptr. 701, 774 P.2d 730); an objection would have been futile.

D. Defense Counsel's Failure to Argue Lingering Doubt
Defendant contends his trial counsel was incompetent for not asking the jury to spare defendant's life because of a "lingering doubt" about his guilt, and for not requesting the trial court to instruct the jury that lingering doubt could be a mitigating circumstance.
*901 Defendant does not dispute that the evidence that he killed the two young girls was overwhelming, nor does he suggest that his counsel should have argued there was a lingering doubt about his identity as the killer. Rather, he contends the jury could have had a lingering doubt as to whether he killed the two girls with premeditation and deliberation, without which he would have been guilty only of second rather than first degree murder. (§ 189.)
The record does not reveal why defense counsel did not argue lingering doubt or request an instruction on it. Counsel may have had tactical reasons. Although the jury might have had a lingering doubt as to whether defendant acted with premeditation when he committed the first of the two murders, it was unlikely to have had such a doubt as to whether he premeditated before committing the second murder.[3] Thus, defense counsel may have decided that it would be better to say as little as possible about the murders and to focus instead on defendant's service in Vietnam and his deprived childhood. (See generally People v. Hawkins, supra 10 Cal.4th 920, 968, 42 Cal.Rptr.2d 636, 897 P.2d 574.)

E. Cumulative Effect of Errors
Defendant asserts the cumulative effect of counsel's alleged errors and omissions resulted in prejudice sufficient to undermine confidence in the outcome of this case, and we should therefore reverse the judgment of death. As we have explained, in each instance defendant has failed to show that counsel's performance was deficient. Therefore, defendant's claim of cumulative prejudice must also fail.

IV. Miscellaneous Issues

A. Defense Motion for Modification of Death Verdict
Defendant argues the trial court committed six prejudicial errors in denying his motion to modify the jury's verdict of death. (§ 190.4, subd. (e).) There was no prejudicial error, as discussed below.
The trial court noted that at the penalty phase the defense had offered evidence that defendant had "a physically and emotionally deprived childhood"; that he "served, with some major exceptions, well as a soldier in the service of his country"; that he had "done well ... on death row"; and that he "has developed and shows some artistic ability." But the trial court concluded that "none of these factors offered in mitigation extenuate the defendant's unexplained and totally without reason homicidal conduct as evidenced by the circumstances surrounding the killing of totally innocent children." (Italics added.)
According to defendant, the trial court here erroneously believed that it could not consider his mitigating evidence because that evidence did not extenuate the murders he committed. We recently rejected a similar claim in People v. Williams (1997) 16 Cal.4th 153, 66 Cal.Rptr.2d 123, 940 P.2d 710. There, the trial court, after reviewing the defendant's mitigating evidence at the penalty phase of his capital trial, commented that this evidence did not "extenuate the gravity of the crime" the defendant had committed. (Id. at p. 281, 66 Cal.Rptr.2d 123, 940 P.2d 710.) We rejected the defendant's contention that the trial court had failed to consider his evidence in mitigation. We pointed out that the trial court had accurately instructed the jury that it could consider all of the defendant's mitigating evidence, and we concluded that the court's comments showed its consideration of that evidence in ruling on the defendant's modification motion. (Id. at pp. 281-282, 66 Cal. Rptr.2d 123, 940 P.2d 710.)
As in People v. Williams, supra, 16 Cal.4th 153, 66 Cal.Rptr.2d 123, 940 P.2d *902 710, the trial court's comments here do not demonstrate a belief that it could not consider defendant's evidence in mitigation. As in Williams, the court here instructed the jury to consider "any sympathetic or other aspect of the defendant's character or record 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," and it is reasonable to assume the court followed its own instruction when it ruled on defendant's motion for modification of the death verdict. In its ruling, the court described defendant's evidence in some detail, and it never said that it would not consider this evidence or that this evidence was not mitigating. In context, the trial court's comment that defendant's evidence in mitigation did not "extenuate" the murders of the two young girls merely reflected its view that the circumstances of the murders were so egregious as to warrant the death penalty notwithstanding the evidence in mitigation. Nothing before us indicates that the trial court was unaware of its duty to consider defendant's mitigating evidence.
Defendant next contends the trial court "double counted" the two murders as both a special circumstance and as an aggravating circumstance of the crime. (People v. Melton (1988) 44 Cal.3d 713, 765-768, 244 Cal.Rptr. 867, 750 P.2d 741 [holding double counting improper]; but see People v. Millwee, supra, 18 Cal.4th at p. 164, fn. 35, 74 Cal.Rptr.2d 418, 954 P.2d 990 [limiting Melton's holding].) As support, he cites this comment by the trial court: "The circumstances of the crime of which the defendant stands convicted and the existence of the special circumstance found to be true substantially outweigh ... the factors in mitigation." We perceive no double counting. The trial court's comments simply expressed its view that the mitigating evidence was substantially outweighed by the evidence pertaining to a statutory aggravating factor "The circumstances of the crime of which the defendant was convicted in the present proceeding and the existence of any special circumstances found to be true...." (§ 190.3, factor (a).)
In explaining the reasons for its denial of defendant's modification motion, the trial court said that the victims "were two young girls ... who constituted absolutely no threat to the defendant, who were respectively killed by beating and strangulation, which could only evidence a deliberate intent to kill in the most heinous manner." (Italics added.) Seizing on this comment, defendant argues that the trial court erred by considering the "heinous" nature of the crimes as a factor in aggravation. He points out that the United States Supreme Court has held that Oklahoma's "especially heinous, atrocious, or cruel" aggravating circumstance is unconstitutionally vague, as it does not offer the jury sufficient guidance in deciding whether to impose the death penalty. (Maynard v. Cartwright (1988) 486 U.S. 356, 363-364, 108 S.Ct. 1853, 100 L.Ed.2d 372.) But the aggravating circumstance addressed in Maynard was one that determined eligibility for the death penalty, which requires greater precision than the factors that govern the sentence-selection process, at issue here. (See Tuilaepa v. California, supra, 512 U.S. at pp. 971-975, 114 S.Ct. 2630; People v. Bacigalupo, supra, 6 Cal.4th at pp. 474-78, 24 Cal. Rptr.2d 808, 862 P.2d 808.) In any event, the trial court merely used the word "heinous" in passing, as part of its explanation why it found the circumstances of the offense an aggravating factor. It did not find that the heinousness of the murders was a separate aggravating factor.
Defendant claims the trial court did not know what standard to apply in ruling on defendant's motion to modify the death verdict. He points to this comment *903 by the court: "[T]he Court finds that the jury's finding at the trial and the verdict reached, that the aggravating circumstances substantially outweigh the mitigating circumstances, are not necessarily contrary to the law or evidence presented during this penalty trial." (Italics added.) Defendant contends this comment reflects the trial court's mistaken belief that modification was proper only if the verdict was "necessarily" contrary to the law or evidence. But at the outset of the modification hearing the court accurately described its statutory obligations. And at the end of the hearing the court concluded, "[Considering all of the evidence, the Court's assessment is that the factors in aggravation beyond reasonable doubt outweigh those in mitigation and that the finding by the jury is neither contrary to law or evidence." This statement indicates a standard more favorable to defendant than the law required, because the trial court did not have to reach this conclusion beyond a reasonable doubt. In our view, notwithstanding its imprecise language, the court applied the proper standard, independently reweighing the aggravating and mitigating evidence to determine that the weight of the evidence supported the jury's verdict of death. (See generally People v. Espinoza (1992) 3 Cal.4th 806, 830, 12 Cal.Rptr.2d 682, 838 P.2d 204.)
The trial court, while commenting on defendant's evidence in mitigation, said that the method defendant chose to dispose of the bodies showed that he had no remorse for the crimes. Defendant argues the trial court erroneously considered his lack of remorse after the murders as a factor in aggravation. The trier of fact may properly consider remorse in determining penalty, so long as it does not treat lack of remorse as a separate aggravating factor. (People v. Ervin (2000) 22 Cal.4th 48, 103, 91 Cal.Rptr.2d 623, 990 P.2d 506; People v. Champion, supra, 9 Cal.4th at p. 943, 39 Cal.Rptr.2d 547, 891 P.2d 93.)
Here, the trial court's comment shows only that it found no mitigating evidence that defendant showed remorse for killing the young girls. It did not treat lack of remorse as a separate factor in aggravation.
Finally, defendant contends the trial court improperly failed to consider the cumulative weight of the factors in mitigation, instead weighing each separately against all of the evidence in aggravation. We disagree. After carefully reviewing the trial court's explanation of its reasons for its denial of defendant's modification motion, we find no evidence that the trial court considered the mitigating factors in piecemeal fashion.
In sum, the trial court properly denied defendant's motion for modification of the jury's death verdict.

B. Effect of Passage of "Three Strikes" Law
Defendant contends the "Three Strikes" law (§ 667, subds.(b)-(i)) abolished the death penalty for those defendants convicted of murder with special circumstances and having one or more prior convictions for serious or violent felonies. Although defendant himself does not fall into this category, he argues that if the death penalty may not be imposed on those with prior serious or violent felonies, to impose the death penalty on defendants with no such convictions, such as himself, would violate equal protection principles. We have held, however, that the Three Strikes law does not abolish the death penalty for those with prior convictions for serious or violent felonies. (People v. Alvarez (1996) 14 Cal.4th 155, 246-247, 58 Cal.Rptr.2d 385, 926 P.2d 365; see also People v. Williams (1995) 40 Cal.App.4th 446, 457-458, 46 Cal.Rptr.2d 730.) It therefore follows that imposition of the death penalty on those who have no such convictions does not violate equal protection. Defendant argues that our opinion in Alvarez *904 ignored subdivisions (c) and (f)(1) of section 667, each of which states that the penalties specified by the Three Strikes law, which do not include death, shall be applied "[notwithstanding any other law...." Those provisions, however, do not override subdivision (e) of section 667, which states that the increased penalties called for by the Three Strikes law shall be imposed "in addition to any other enhancement or punishment provisions which may apply...."

C. Proportionality Review
Defendant asks us to invalidate his death sentence on the ground it was not proportional to his moral culpability. He points to his deprived childhood, his lack of a criminal record, and his military service during the Vietnam War. He also stresses the weakness of the evidence that the murders were premeditated, noting that in the appeal from his first trial we described the evidence of premeditation as "far from overwhelming," although we found it sufficient to support defendant's murder convictions. (People v. Lucero, supra, 44 Cal.3d at p. 1020, 245 Cal.Rptr. 185, 750 P.2d 1342.)
"`The cruel and unusual punishments clause of the Eighth Amendment to the United States Constitution prohibits the imposition of a penalty that is disproportionate to the defendant's "personal responsibility and moral guilt." [Citations.] Article I, section 17 of the California Constitution separately and independently lays down the same prohibition.'" (People v. Marshall (1990) 50 Cal.3d 907, 938, 269 Cal.Rptr. 269, 790 P.2d 676; see also People v. Padilla (1995) 11 Cal.4th 891, 961-962, 47 Cal.Rptr.2d 426, 906 P.2d 388.) To determine whether a sentence is cruel or unusual under the California Constitution as applied to a particular defendant, a reviewing court must examine the circumstances of the offense, including motive, the extent of the defendant's involvement in the crime, the manner in which the crime was committed, and the consequences of the defendant's acts. The court must also consider the personal characteristics of the defendant, including his or her age, prior criminality, and mental capabilities. (People v. Dillon (1983) 34 Cal.3d 441, 479, 194 Cal.Rptr. 390, 668 P.2d 697.) If the penalty imposed is "grossly disproportionate to the defendant's individual culpability" (ibid.), so that the punishment "`"shocks the conscience and offends fundamental notions of human dignity"'" (People v. Cox, supra, 53 Cal.3d at p. 690, 280 Cal.Rptr. 692, 809 P.2d 351), the court must invalidate the sentence as unconstitutional.
Here, defendant, acting alone, brutally killed two innocent and defenseless children by strangling one with the necklace she was wearing and by striking the other in the head with blows so hard that they knocked out three of her teeth and fractured her skull in several places. The record contains no explanation for these horrific deeds. Although defendant offered some evidence he suffered from PTSD when he killed the girls, there was no evidence the disorder played any role in the killings. Based on these facts, the punishment in this case is not "grossly disproportionate to the defendant's individual culpability" (People v. Dillon, supra, 34 Cal.3d at p. 479, 194 Cal.Rptr. 390, 668 P.2d 697), nor does it "`"shock[ ] the conscience and offend[ ] fundamental notions of human dignity."'" (People v. Cox, supra, 53 Cal.3d at p. 690, 280 Cal. Rptr. 692, 809 P.2d 351.)

D. Constitutionality of California's Death Penalty Statute
Defendant contends that California's death penalty scheme fails, either in theory or in practice, to sufficiently narrow the class of offenders eligible for the death *905 penalty, and therefore violates the Eighth Amendment to the United States Constitution and article I, section 17 of the California Constitution. Assuming for the sake of argument that defendant may raise this claim following a penalty retrial (see People v. Davenport, supra, 11 Cal.4th at p. 1225, 47 Cal.Rptr.2d 800, 906 P.2d 1068), we have repeatedly rejected the contention (see, e.g., People v. Frye, supra, 18 Cal.4th at p. 1029, 77 Cal.Rptr.2d 25, 959 P.2d 183; People v. Bacigalupo, supra, 6 Cal.4th at p. 467, 24 Cal.Rptr.2d 808, 862 P.2d 808; People v. Wader, supra, 5 Cal.4th at p. 669, 20 Cal.Rptr.2d 788, 854 P.2d 80). We are not persuaded that we should reconsider our previous rulings on this issue.
Defendant asserts that the multiple-murder special circumstance, which formed the basis for his death sentence, is "particularly deficient in terms of a narrowing function" for two reasons. First he claims it encompasses an "overly broad class of defendants of disparate and varying culpability." To the contrary, the multiple-murder special circumstance focuses on a narrow group of killers: only those who have murdered more than one person. Second, defendant asserts the multiple-murder special circumstance improperly focuses on the nature of the act committed rather than the defendant's mental state. We are not persuaded. One who is mentally prepared to commit repeated acts of murder, or to commit a murderous act that results in the death of two or more persons, is more dangerous to society and more deserving of the ultimate punishment than one who has killed once. (See generally People v. Coddington, supra, 23 Cal.4th at p. 656, 97 Cal.Rptr.2d 528, 2 P.3d 1081 [holding multiple-murder special circumstance constitutional].)
Defendant maintains that California's death penalty scheme is constitutionally defective because the enumerated aggravating and mitigating factors are vague, arbitrary and result in unreliable sentences. We have repeatedly rejected this contention. (People v. Millwee, supra, 18 Cal.4th at pp. 163-164, 74 Cal.Rptr.2d 418, 954 P.2d 990; People v. Freeman, supra, 8 Cal.4th 450, 525, 34 Cal.Rptr.2d 558, 882 P.2d 249; People v. Webb (1993) 6 Cal.4th 494, 535, 24 Cal.Rptr.2d 779, 862 P.2d 779.)
Defendant argues that California's death penalty law violates the state and federal Constitutions because: (1) jurors do not have to find aggravating factors true beyond a reasonable doubt; (2) jurors need not find that aggravating factors outweigh mitigating factors beyond a reasonable doubt; (3) jurors need not return unanimous, written findings specifying the aggravating factors on which they relied; and (4) the statutory scheme does not provide for comparative or intercase proportionality review of a death sentence. He asserts that most other states have varying combinations of these procedural protections, and that California's failure to employ any of these safeguards violates the Fifth, Sixth, Eighth, and Fourteenth Amendments to the federal Constitution. We have repeatedly held that each of these safeguards is not constitutionally required (see, e.g., People v. Samayoa (1997) 15 Cal.4th 795, 862, 64 Cal.Rptr.2d 400, 938 P.2d 2 [beyond-a-reasonable-doubt finding for aggravating circumstances not required; finding beyond a reasonable doubt that aggravation outweighs mitigation not required]; People v. Osband, supra, 13 Cal.4th at p. 710, 55 Cal.Rptr.2d 26, 919 P.2d 640 [unanimous, written findings not required]; People v. Majors (1998) 18 Cal.4th 385, 432, 75 Cal.Rptr.2d 684, 956 P.2d 1137 [proportionality review not required] ), and we find no federal constitutional violation when we consider them collectively.

DISPOSITION
The judgment of death is affirmed.
*906 GEORGE, C.J., and BAXTER, J., WERDEGAR, J., CHIN, J., and BROWN, J., concur.
Dissenting Opinion by MOSK, J.
I dissent.
For the reasons that I stated when this cause was originally before us (see People v. Lucero (1988) 44 Cal.3d 1006, 1033-1036, 245 Cal.Rptr. 185, 750 P.2d 1342 (conc. & dis. opn. of Mosk, J.)), I would exercise the authority that we possess under sections 1181, subdivision 7, and 1260 of the Penal Code (see generally People v. Hines (1997) Cal.4th 997, 1081-1082, 64 Cal.Rptr.2d 594, 938 P.2d 388 (cone, opn. of Mosk, J.)), and would set aside the multiple-murder special-circumstance finding and the verdict of death, and remand the matter to the superior court for resentencing.
NOTES
[*]   Mosk, J., dissented.
[1]  All further statutory references are to the Penal Code unless otherwise stated.
[2]  Section 190.3, factor (b) states that at the penalty phase a jury may consider "[t]he presence or absence of criminal activity by the defendant which involved the use or attempted use of force or violence or the express or implied threat to use force or violence." (Italics added.) The trial court's instruction in this case omitted the italicized words. Defendant does not contend the omission was erroneous.
[3]  Defendant was eligible for the death penalty so long as at least one of the two murders was premeditated. (§ 190.2, subd. (a)(3).)
