Opinion
LUCAS, C. J.Defendant Melvin Meffery Wade appeals from a judgment imposing the death penalty following his conviction of first degree murder *981(Pen. Code, § 187; all further statutory references are to this code unless otherwise indicated), accompanied by two special circumstances findings (§ 190.2, subds. (a)(14) [murder especially heinous and cruel], (a)(18) [torture murder]). The appeal is automatic (§ 1239, subd. (b).) As will appear, although we must set aside one of the special circumstance findings, we nonetheless affirm the judgment of death.
I. Facts
A. Procedural History
Trial commenced on February 1, 1982. Following the presentation of the prosecution’s case-in-chief, the trial court permitted defendant to enter a plea of not guilty by reason of insanity. As indicated, the jury convicted defendant of first degree murder (§§ 187, 189) and found both special circumstances to be true. By stipulation, the issue of defendant’s sanity was submitted to the jury on the evidence introduced during the guilt phase. The jury found defendant to be sane at the time of the offense.
Following the penalty phase, the jury returned a verdict of death.
B. Guilt Phase Evidence
Defendant was 24 years old at the time of the offense. In April 1981, defendant and his wife, Irabell “Cookie” Strong, were living in a one-bedroom apartment at the Mission Motel in San Bernardino. Four of Cookie’s five children—Penny (age twelve), Joyce (age ten), Alexis (age nine), and Syeeta (age eight)—were also living with them.1
According to Cookie, defendant was kind to the children at first, but as time went by he began to abuse them more and more. Defendant was easily upset and was “quick to hit” the children and punish them. He beat them with his fists, hit them with a paddle, made them stand on one foot for extended periods of time, and ordered them to kneel on top of a dresser and take cold showers. He also forced Joyce and Alexis to drink their own urine and mixtures of milk and salt to induce vomiting.
On the morning of April 10, after accusing 10-year-old Joyce of smelling and not properly washing herself, defendant began punching her with his fists. He proceeded to beat her with a wooden board that had been broken off of the frame of their couch.2
*982That afternoon, defendant ordered Joyce to get inside an old army duffel bag. He told Penny to clip the bag shut. Defendant then hoisted the bag into an attic crawl space above the bedroom ceiling. While Joyce was shut away in the crawl space, defendant lectured the family, complaining that they had “turned a sweet and gentle man into a mad man” and had brought humiliation and degradation upon him.
Approximately three to four hours later, Joyce freed herself from the bag and asked if she could come down. As she started to get down, defendant reached for her but fell. He accused her of causing him to fall and grabbed her as she was hanging from the crawl space. He punched her and threw her body against the wall, making a dent.
Defendant then began beating Joyce again with his fists. The beating apparently continued throughout the evening. During this time, defendant consumed a bottle of wine and shouted that he was “Michael the Archangel” and that he would kill Joyce because she was a “devil.”
Defendant then told Joyce to take her shirt off and stand up against the wall with her arms extended. He beat her again with the board across the chest, stomach and other parts of her body. Throughout the beatings, Joyce cried and asked defendant to stop, telling him that she was sorry and that she would be good.
At one point during the evening, defendant wrapped a dog leash around Joyce’s neck and attempted to hang her from a nail on the wall. When he was unable to do this, he dropped her on the floor. When Joyce did not move, defendant claimed that she was “just putting on” so he kicked her in the side. At that point, she apparently was breathing. Defendant then picked her up and let her body drop to the floor. Defendant then stomped on her stomach.
The motel manager, hearing a disturbance in the apartment occupied by defendant and his family, eventually called the police. Police officers Tom Germany and Keith Thompson responded to the call at 3:35 a.m. At the apartment, they saw defendant, Cookie and three children. Defendant stated that they were having a family dispute and told one of the children to pack his clothing so he could leave. The police officers stayed for approximately 15 minutes and left after Cookie told them that everything would be all right.
Soon thereafter, the manager again heard a woman yelling and saw Cookie running, pursued by defendant. Defendant struck Cookie in the face and ran away as the manager approached. Cookie asked the manager to call *983the police because one of her children was badly injured. The manager called the paramedics and the police. Upon their arrival, they found Joyce dead on the bedroom floor.
A subsequent autopsy revealed that Joyce died from cranial, cerebral, abdominal and soft-tissue injuries. The pathologist who performed the autopsy testified that the injuries acted in concert to produce the death, although any one of the major injuries to the head, abdomen or neck could have caused the death.
Moments after the police arrived, defendant returned. He walked through the parking lot with his hands up in the air and said: “Here I am. I’m the one you want. I guess I hit her too hard. I guess I hit her too hard.” Defendant was then placed under arrest.
Following his arrest, defendant gave a statement to the police.3 He asked if Joyce were dead and said that he had killed an innocent person but that he did not mean to hit her so hard. He admitted hitting Joyce with his fists, striking her with a paddle, and hitting her head against the wall. He also admitted putting her in the crawl space to punish her. He denied using a dog leash on her or making her stand against the wall. Defendant said that he loved Joyce, but that she had been a constant discipline problem. He also related that he was under pressure, was seeing a psychiatrist, had been a prisoner of war in Vietnam, and was on welfare.
Four doctors—psychiatrists Ralph Allison, Ethel Chapman and Robert Summerour and clinical psychologist Craig Rath—were called by the defense to testify about defendant’s psychiatric background and his mental state at the time of the offense. They testified in great detail about defendant’s background. They reported that from the age of three, defendant was physically and sexually abused by his mother’s boyfriend, Jack. Jack would also lock defendant in a closet for hours. While in the closet, defendant would talk to an imaginary friend. Gradually, this friend, called “Othello,” began to talk back to him.
At the age of 12, defendant began to experience blackouts. He described events in his past which he could not explain, such as finding himself in bed with a 46-year-old woman, who kept calling him “Othello.” Throughout the 1970’s, defendant received psychological counseling. He also attempted suicide three times.
*984The defense doctors attempted to determine if defendant was a multiple personality. Each of them testified they encountered a personality called “Othello.” Drs. Rath and Allison also reportedly spoke with personalities named “Joe” and “Michael.” When the doctors asked to speak with “Othello,” defendant would close his eyes, lower his head and, shortly thereafter, the personality of “Othello” would emerge.4
The doctors described Melvin Wade (defendant) as mild-mannered, polite, soft-spoken and cooperative. “Othello,” on the other hand, was hostile, boisterous, arrogant, vulgar and violent; he disliked Melvin intensely.
According to the doctors, “Othello,” also referred to as the “Son of Fire” and “Son of Satan,” was born in Greece and fed on “germs of loneliness and despair.” “Othello” was the devil’s assassin employed by the council of 12 archdemons to kill Cookie. On the day of Joyce’s killing, “Othello” had tried to force Cookie to sacrifice herself by threatening Joyce’s life. “Othello” explained that he really wanted to kill Cookie but Joyce got in the way. “Othello” was also assigned to kill Melvin.
Melvin’s body also contained a personality named “Joe.” “Joe” is “Othello’s” son and secretary, and a “devil in training” “waiting around for a body to occupy.” The doctors described “Joe” as young, weak, friendly, soft-spoken, mischievous and devilish. “Joe” was the personality who surrendered and confessed to the police after the killing. He had apparently “fouled up his part" of the assignment.”
A fourth personality is “Michael the Archangel.” The doctors described “Michael” as angelic, weak and mild. “Michael” holds a rank in the “archangel group” equivalent to “Othello’s” rank as a demon and is “Othello’s” arch-enemy. He tries to help Melvin fight against “Othello.” He is strongest on Sundays and was unable to prevent Joyce’s death because it occurred on a Saturday, “Othello’s” “strongest” day.5 All four defense doctors concluded that defendant suifered from a dissociative disorder. Drs. Rath and Chapman firmly diagnosed him as a multiple personality, unable to harbor malice or to form the intent to kill at the time of the offense. Dr. *985Summerour diagnosed him as having a probable multiple personality dissociative disorder. Dr. Allison, on the other hand, opined that defendant did not have a multiple personality, but rather suffered from “possession syndrome,” an atypical dissociative disorder which occurs when the person believes he is possessed by demons from an outside source. Drs. Rath and Allison concluded that defendant was legally insane at the time of the offense.
The findings of the defense doctors were disputed by the prosecution which called three psychiatrists. These doctors, Robert Flanagan, Frederick Hacker and Anthony Oliver, had also examined defendant.6 Dr. Hacker, while not supporting a multiple personality theory, believed that defendant had not formed an intent to kill at the time of the offense. He described defendant as an “emotionally immature and disturbed person.” Dr. Oliver opined that defendant was a pathological liar and that his multiple personality was malingered. He also diagnosed defendant as being schizotypal and having a mixed personality disorder with antisocial components. Dr. Flanagan stated that defendant was legally sane at the time of the murder.
The prosecution also presented the testimony of Carol Amos, who was defendant’s girlfriend before his marriage to Cookie and who had twin sons by him. Over defense objection, the trial court permitted Ms. Amos to testify about prior acts of child abuse committed by defendant against the twins. This evidence is discussed in greater detail below.
Two employees of the Hordis Glass Company, who had previously worked with defendant, also testified on rebuttal. They described defendant as a quick learner who regularly read books, magazines and newspapers. They never heard defendant call himself “Othello,” “Joe” or “Michael.”
The defense presented two lay witnesses on surrebuttal to corroborate the existence of multiple personalities. From ages 15 to 20, defendant lived with the family of Ella Mae Edwards. Mrs. Edwards testified that she believed defendant was a split personality. He once told her his full name was “Othello Mulct Metheen,” that he had been in the Green Berets, and that he was employed as a hit man.
Ted Sanders, a county jail inmate who observed defendant’s behavior during the period of the trial, described two incidents when defendant’s behavior changed abruptly. On the first occasion, while a number of inmates were watching television, defendant suddenly attacked Sanders and *986threatened to kill him without provocation. Sanders described how defendant’s eyes seemed to grow larger and his voice rougher. When Sanders subsequently mentioned the incident to defendant, he insisted that he had taken no part in it. The second incident occurred three weeks later, when defendant assaulted another inmate in a similar sudden, unprovoked fashion. Again, defendant assertedly could not recall the incident when it was brought to his attention.
C. Penalty Phase Evidence
Defendant was the only witness to testify at the penalty phase. He corroborated the earlier psychiatric testimony about “Othello.” He maintained that he was unaware of killing Joyce, of inflicting any of the previously described “methods of discipline” upon the children, of ever talking to the police about the killing, or of attacking other inmates in the jail. Defendant stated that he loved Joyce and her mother, Cookie. He expressed sadness over Joyce’s death.
Defendant recalled being sexually and physically abused and locked in a closet as a child. He recalled occasions in his life when he had memory lapses. Whenever he questioned “Othello” about these lapses, “Othello” would tell him it was none of his business. Defendant further testified that he did not believe in demons, but that he did believe in God. He asked for God’s forgiveness for what his body had done and expressed his desire not to continue living if he had to coexist with “Othello.”
At defense counsel’s request, “Othello” emerged on the witness stand and testified before the jury. Unlike Melvin, “Othello” used profane language throughout his testimony. He stated that Melvin was his enemy, that he did not believe in God, and that he felt no sorrow for Joyce’s death. He maintained that he was the devil’s disciple and that he wanted the jury to kill Melvin.
II. Guilt Phase Contentions
A. Ineffective Counsel
Defendant’s principal contention is that he was denied his right to the effective assistance of counsel during the closing argument at the guilt phase. Defendant asserts that his counsel’s argument was in essence an apologia for being involved in the case. This claim has no merit.
Our review of the record discloses that trial counsel, faced with defending an appalling crime and responding to the prosecutor’s pointed suggestions *987of a fabricated defense,7 made a tactical choice to candidly admit his client’s guilt, acknowledge the heinous nature of the offense, and concentrate on the theory that defendant indeed was plagued with multiple personalities or dissociative disorders, and was insane or incapable of forming the requisite criminal intent when the offense was committed. The fact that this argument ultimately failed is not a negative reflection on counsel’s competence.
Counsel’s jury arguments proceeded along these lines: The death of young Joyce was a terrible tragedy “intolerable even to contemplate.” After defendant’s arrest, counsel did not volunteer to defend him; instead, counsel was appointed to do so, and he did not “relish” the task. Moreover, counsel’s wife was not pleased with the appointment—she even sent flowers to decorate Joyce’s grave. But after counsel began to investigate the case more thoroughly, he learned of defendant’s multiple personalities, and he eventually became convinced of his client’s mental illness.
In response to the prosecutor’s pronounced skepticism regarding the foregoing defense, counsel explained to the jury that he takes his duty as an attorney quite “seriously,” that the State Bar rules forbid reliance on sham defenses, and that counsel has never knowingly presented “any artifice or untruth” to a judge or jury.
Counsel then thoroughly explored the applicable legal principles, including the definition and legal effect of insanity, and the necessity for proving specific intent to inflict pain. Counsel summarized the expert testimony indicating that defendant had either a multiple personality or dissociative disorder, and observed that although the prosecutor considered the defense to be “showy or sensational,” there was ample evidence to support it and counsel had the duty to present it. “[A]ll we’re saying in this case,” according to counsel, is that defendant “didn’t have the capacity to form the specific intent because he was insane. If that’s sensationalism, if that’s showy, if that’s theatre, [the prosecutor] and I belong in different cultures.”
Counsel then remarked that, although young Joyce was dead, nothing counsel could do would bring her back. But counsel could, by his argument in defense, prevent “a double tragedy.” Counsel again acknowledged the tragic, senseless nature of the crime, observing that such a crime “makes sense to an insane person only.” Thereafter, counsel noted that if his client *988were indeed faking an insanity or diminished capacity defense, he somehow managed to convince Dr. Chapman, a man “with 40 years of psychiatry, college education, medical doctor. He also convinced Dr. Rath, a bright young psychiatrist. He convinced Dr. Summerour .... []f] He convinced Dr. Allison ....[][] Who else did he convince? His lawyer. One who had seen almost every defense in the book . . . .”
Next, counsel attempted to assign or deflect some blame for Joyce’s death to her mother, Cookie Strong, who had failed to come to her daughter’s aid during the lengthy ordeal with defendant. Counsel thereafter returned in his argument to the jury instructions, emphasizing the ones dealing with malice and premeditation, “rash impulse,” intent to inflict pain and intent to kill, diminished capacity, and unconsciousness. Counsel concluded by urging the jury to view the evidence as “dispassionately] as you possibly can,” observing that “no matter what your findings, justice will be the eventual winner.”
We see no basis whatever for holding that counsel’s foregoing arguments constituted ineffective representation. In light of the overwhelming evidence of his client’s guilt, trial counsel had little choice but to candidly acknowledge guilt, concede the heinous nature of the offense, and concentrate instead on convincing the jury of the legitimacy of defendant’s mental defenses. As we observed in an earlier decision affirming a judgment of death, “it is entirely understandable that trial counsel, given the weight of incriminating evidence, made no sweeping declarations of his client’s innocence but instead adopted a more realistic approach .... As stated in a recent case, ‘good trial tactics demanded complete candor’ with the jury. [Citation.] Under the circumstances we cannot equate such candor with incompetence.” (People v. Jackson (1980) 28 Cal.3d 264, 292-293 [168 Cal.Rptr. 603, 618 P.2d 149]; see also People v. Ratliff (1986) 41 Cal.3d 675, 697 [224 Cal.Rptr. 705, 715 P.2d 665]; People v. McGautha (1969) 70 Cal.2d 770, 783-784 [76 Cal.Rptr. 434, 452 P.2d 650], affd. sub nom. McGautha v. California (1971) 402 U.S. 183 [28 L.Ed.2d 711, 91 S.Ct. 1454].)
Defendant complains of trial counsel’s undue candor regarding the heinous nature of the offense, the unusual defense theory, and counsel’s (and his wife’s) own initial skepticism and aversion. Defendant criticizes counsel for seeming to “distance” himself from his client and “downgrade” his defense. The criticism is misplaced: Counsel’s argument carefully developed his own conversion from an initial skepticism to an eventual acceptance of defendant’s peculiar mental state. Clearly, counsel hoped thereby to achieve a similar conversion among the jurors.
In addition, defendant suggests that counsel should have spent more time arguing for a reduction in the degree of the underlying homicide. *989Counsel did question whether the evidence supported a finding of premeditation and specific intent. Moreover, it was clearly a tactical matter whether counsel advocated a reduced degree or instead sought an outright acquittal based on diminished capacity or insanity.8
Defendant was entitled to a “ ‘proper argument on the evidence and applicable law in his favor ....”’ (Herring v. New York (1975) 422 U.S. 853, 860 [45 L.Ed.2d 593, 599, 95 S.Ct. 2550].) Our review of the record convinces us that counsel provided such an argument. We find no legitimate basis for concluding that counsel failed to provide reasonably effective assistance of counsel under the circumstances presented here. (See Strickland v. Washington (1984) 466 U.S. 668, 687-691 [80 L.Ed.2d 674, 693-695, 104 S.Ct. 2052]; People v. McKenzie (1983) 34 Cal.3d 616, 637 [194 Cal.Rptr. 462, 668 P.2d 769].)
B. Prior Offenses
Defendant next contends that reversal of the guilt verdict is required because the trial court erred in admitting evidence of defendant’s prior acts of child abuse.
Over defense objections based on lack of relevance and undue prejudice (Evid. Code, § 352), the trial court permitted Carol Amos, defendant’s former girlfriend, to testify on prosecution rebuttal about prior acts of child abuse committed by defendant against his twin sons.
Ms. Amos related that defendant had initially been nice to the children, but that after he hurt his hand in an industrial accident, he became moody and would frequently beat the boys with his fists and a belt. He would also shove them against the wall, kick them, make them take cold showers and hold their heads under water while giving them a bath.
Ms. Amos said that defendant acted nicely to her and the children when other people were around. She stated that she heard the name “Othello” only once, shortly after she first met defendant, when he told her that his army buddies called him “Othello Mulet Metheen.”
The trial court ruled the proffered evidence admissible because it was “important enough in this case, since it is one of the primary issues as to what this defendant was or was not prior to this date of incident of 4-10, 4-*99011, 1980 [s/c], whether or not it was or was not Melvin and/or Othello, I think that it is sufficiently important that if there is in fact any prejudicial effect, it’s greatly outweighed by the probative value.”
In People v. Thompson (1980) 27 Cal.3d 303, 315 [165 Cal.Rptr. 289, 611 P.2d 883], we held, “[a]s with other types of circumstantial evidence, . . . admissibility [of other crimes evidence] depends upon three principal factors: (1) the materiality of the fact sought to be proved or disproved; (2) the tendency of the uncharged crime to prove or disprove the material fact; and (3) the existence of any rule or policy requiring the exclusion of relevant evidence.”
To be relevant, an uncharged offense must tend logically, naturally and by reasonable inference to prove the issue(s) on which it is offered. (People v. Alcala (1984) 36 Cal.3d 604, 631 [205 Cal.Rptr. 775, 685 P.2d 1126]; People v. Guerrero (1976) 16 Cal.3d 719, 724 [129 Cal.Rptr. 166, 548 P.2d 366], and cases cited; Thompson, supra, 27 Cal.3d at p. 316.) We have long recognized “that if a person acts similarly in similar situations, he probably harbors the same intent in each instance” (Thompson, supra, 27 Cal.3d at p. 319; People v. Pendleton (1979) 25 Cal.3d 371, 376-378 [158 Cal.Rptr. 343, 599 P.2d 649]; People v. Schader (1959) 71 Cal.2d 761, 777 [80 Cal.Rptr. 1, 457 P.2d 841]; People v. Kelley (1967) 66 Cal.2d 232, 242-243 [57 Cal.Rptr. 363, 424 P.2d 947]), and that such prior conduct may be relevant circumstantial evidence of the actor’s most recent intent. The inference to be drawn is not that the actor is disposed to commit such acts; instead, the inference to be drawn is that, in light of the first event, the actor, at the time of the second event, must have had the intent attributed to him by the prosecution. (See Schader, supra, 71 Cal.2d 761, 777.)
The first question to be answered is whether the prior acts were relevant to any material fact in dispute. To place defendant’s relevancy argument in context, it is necessary to review the prosecution’s two theories of murder. Each theory required a different type of intent. The first—that the murder was premeditated—required proof of a specific intent to kill as well as premeditation and deliberation. (See CALJIC No. 8.20 (4th ed. 1979).) The second—murder by torture—required no proof of premeditation or specific intent to kill but proof of a specific intent “to cause cruel pain and suffering for the purpose of revenge, extortion, persuasion or for any sadistic purpose.” (See CALJIC No. 8.24 (4th ed. 1979); People v. Wiley (1976) 18 Cal.3d 162 [133 Cal.Rptr. 135, 554 P.2d 881].)
Defendant argues that the rebuttal evidence was, at most, relevant to prove defendant’s intent to cause cruel pain and suffering but was not relevant to prove the intent required for premeditated murder. He reasons *991that the prior nonfatal beating of his twin sons did not “logically, naturally, and by reasonable inference” tend to prove that he intended to kill Joyce or that he acted with premeditation.
Defendant’s argument misses the point. The multiple personality theory proffered by the defense attempted to demonstrate that “Othello,” not Melvin, assaulted and killed Joyce. The defense reasoned that since Melvin was suffering from a dissociative disorder, he was insane and could not have entertained the requisite intents to kill and torture Joyce. Thus, the principal question for the jury presented by the defense was whether “Othello” existed as a separate personality and whether he, rather than Melvin, killed Joyce. Although the legal theory underlying the defense was somewhat unclear, presumably, if the defense had prevailed, the jury would have either acquitted him as insane or convicted him of a lesser degree of homicide.
The prosecution presented the prior acts of child abuse evidence to rebut this theory. Ms. Amos testified that it was Melvin who became moody and irritable during their relationship and who hit the children with his fists and a belt. During their entire relationship, Ms. Amos had only heard the name “Othello” once when Melvin informed her that his army buddies had given him that name. Further, she testified that Melvin did not have different sets of names for different personalities.
This evidence tended logically, naturally, and by reasonable inference to overcome a material matter sought to be proved by the defense. (Guerrero, supra, 16 Cal.3d at p. 724.) It rebutted the assertion that it was “Othello,” not Melvin, who assaulted and killed Joyce, since it tended to show that Melvin, not “Othello,” had assaulted his children in the past.9 It also helped establish that Melvin entertained the intent to kill and torture Joyce. The evidence was substantially relevant.10
Defendant next argues that the evidence of prior acts of child abuse was cumulative. (Alcala, supra, 36 Cal.3d at pp. 631-632; Thompson, supra, 27 Cal.3d at p. 318.) He points to testimony by defendant’s wife, Cookie, *992and two of her children, Alexis and Penny, to the effect that defendant acted in a rational, deliberate manner during the killing.
The record shows precisely the contrary. Cookie characterized defendant as “crazy” and acting “like a madman” at the time of the killing. She also testified that during the beating, defendant shouted that he was “Michael the Archangel” and that he would kill Joyce because she was a “devil.” Penny opined that defendant acted “strange” on the day of the killing and appeared to be drunk that evening. This testimony hardly portrayed defendant as acting in a rational and deliberate manner.
Defendant also contends that the child abuse evidence was cumulative in light of the testimony by the three prosecution psychiatrists who testified that defendant had the capacity to form the specific intent to kill and torture Joyce. A court, however, is not necessarily required to exclude a lay witness’s testimony simply because there is expert testimony on the same issue, for the nature of a lay witness’s testimony is manifestly different from expert testimony. The child abuse evidence was not “merely cumulative.”
Finally, defendant claims that the evidence should have been excluded under Evidence Code section 352. It is well settled that the trial court is vested with discretion in admitting or rejecting proffered evidence and its decision will not be reversed on appeal “unless there is a manifest abuse of that discretion resulting in a miscarriage of justice.” (People v. Wein (1977) 69 Cal.App.3d 79, 90 [137 Cal.Rptr. 814]; People v. Northrop (1982) 132 Cal.App.3d 1027, 1042 [182 Cal.Rptr. 197], disapproved on other grounds in People v. Smith (1984) 35 Cal.3d 798, 807-808 [201 Cal.Rptr. 311, 678 P.2d 886].)
The trial court, as required, weighed the prejudicial effect against the probative value of the proffered evidence. (See People v. Green (1980) 27 Cal.3d 1, 24-26 [164 Cal.Rptr. 1, 609 P.2d 468].) It found the balance in favor of admissibility. In light of the substantial relevancy of the evidence, it is clear that the trial court did not abuse its discretion in admitting the evidence of prior acts of child abuse.
C. Sufficiency of Evidence of Torture
In a supplemental brief filed after rehearing was granted to the People in this case, defendant for the first time argued that the evidence of defendant’s guilt of torture murder was insufficient. The contention comes far too late. (See Brown v. Superior Court (1982) 137 Cal.App.3d 778, 782 [187 Cal.Rptr. 324]; 9 Witkin, Cal. Procedure (3d ed. 1985) Appeal, § 684, at p. 656, and cases cited.) In any event, as the foregoing statement of facts *993indicates, there was ample evidence of a wilful, deliberate and premeditated intent to inflict extreme and prolonged pain. (See People v. Steger (1976) 16 Cal.3d 539, 549 [128 Cal.Rptr. 161, 546 P.2d 665, 83 A.L.R.3d 1206].)
III. Special Circumstances Contentions
Next, defendant challenges both of the special circumstance allegations which the jury found to be true: that the murder was “heinous, atrocious or cruel” (§ 190.2, subd. (a) (14)), and that it involved torture (§ 190.2, subd. (a)(18)).
In People v. Superior Court (Engert) (1982) 31 Cal.3d 797, 806 [183 Cal.Rptr. 800, 647 P.2d 76], we held that the “heinous, atrocious or cruel” special circumstance provision was unconstitutionally vague. Therefore, as the People concede, this finding must be set aside.
The torture-murder special-circumstance finding requires a more detailed discussion. Section 190.2, subdivision (a)(18), provides a special circumstance if “[t]he murder was intentional and involved the infliction of torture. For the purpose of this section torture requires proof of the infliction of extreme physical pain no matter how long its duration.”
Defendant asserts that, unlike the torture-murder special-circumstance provision in the 1977 death penalty law,11 the present provision is unconstitutionally vague and overbroad in that it fails to “meaningfully narrow the group of those subject to the death penalty and serves only as a vehicle for arbitrary and capricious action, to be used whenever jurors and prosecutors, in their sole and unguided discretion, so desire.”
We considered the same argument in People v. Davenport (1985) 41 Cal.3d 247, 270-271 [221 Cal.Rptr. 794, 710 P.2d 861], In order to preserve the constitutional validity of the statute, Davenport construed section 190.2, subdivision (a)(18), to incorporate “so much of the established judicial meaning of torture as is not inconsistent with the specific language of the enactment.” (Davenport, supra, at p. 267.)
“In sum, we find that the words used in section 190.2, subdivision (a)(18) must be understood in light of the established meaning of torture. Proof of a murder committed under the torture-murder special circumstance therefore requires proof of first degree murder, . . . proof the defendant intended to *994kill and to torture the victim, . . . and the infliction of an extremely painful act upon a living victim. . . .” (Davenport, supra, 41 Cal.3d at p. 271, citations omitted.)12
Defendant contends that, given the Davenport holding, the torture-murder special-circumstance finding in this case must be reversed because the special circumstance instruction failed to inform the jury that the specific intent to torture was an element of the special circumstance. (See, e.g., People v. Leach (1985) 41 Cal.3d 92, 110 [221 Cal.Rptr. 826, 710 P.2d 893].) Although the special circumstance instruction, viewed in isolation, did not, by its express terms, explain that the “infliction of torture” element of the special circumstance included an intent-to-inflict-cruel-pain requirement,13 we believe that in light of the accompanying torture-murder instructions and the argument of counsel on this point there is no reasonable likelihood that the jury was misled on this issue.
In instructing the jury at the guilt/special circumstance phase, the court gave instructions on both torture-murder and on the torture-murder special circumstance. In defining torture-murder, the court made clear that “[a] necessary mental state in murder by torture is the specific intent to cause cruel pain and suffering . . . .” Although in some cases there may be reason to doubt that the jury understood that the “infliction of torture” element in the torture-murder special circumstance embodies the same intent-to-cause-cruel-pain element as in torture-murder, nothing in the present record suggests the jury in this case was likely to have drawn any such distinction in the use of the term “torture” in the two instructions. Indeed, the prosecutor in closing argument specifically explained to the jury that the torture-murder special circumstance required essentially the same showing as torture-murder itself, plus the single additional element of an intent to kill.14 And neither the prosecutor nor defense counsel suggested at any point *995that a torture-murder special circumstance could be established without first proving an intent to torture. Under these circumstances, we are confident that the jury understood the basic elements of the torture-murder special circumstance, and that the special circumstance finding was not based on a mere accidental or unintentional infliction of cruel pain.
IV. Penalty Phase Contentions
A. “No Sympathy” Instruction
The trial court instructed the jury that “As jurors, you must not be influenced by pity for a defendant or by prejudice against him. You must not be swayed by mere sentiment, conjecture, sympathy, passion, prejudice, public opinion, or public feeling.” (CALJIC No. 1.00.)
The penalty jury was also instructed, in the words of section 190.3, subdivision (k), that in determining penalty the jury should take into account “Any other circumstance which extenuates the gravity of the crime even though it is not a legal excuse for the crime.” Defendant contends that this latter instruction was inadequate to cure the defective “no sympathy” instruction, in the absence of clarifying instructions which explain the broad scope of the jury’s sentencing discretion, including the propriety of considering such mitigating or “sympathy” factors as the defendant’s character and background. (See People v. Brown (1985) 40 Cal.3d 512, 541 [220 Cal.Rptr. 637, 709 P.2d 440], vacated sub nom. California v. Brown (1987) 479 U.S. 538 [93 L.Ed.2d 934, 107 S.Ct. 837]; People v. Easley (1983) 34 Cal.3d 858, 878, fn. 10 [196 Cal.Rptr. 309, 671 P.2d 813].)
In Brown and Easley, we disapproved a “no sympathy” instruction similar to the one given here, and we directed further clarifying instructions be given in future cases to better explain to the jury the scope of its sentencing discretion. As for previously tried cases in which a “no sympathy” instruction was given, the guidelines set forth in the United States Supreme *996Court’s decision in Brown require us to review the record in each case to determine whether the jury instructions, taken as a whole, and read in conjunction with the jury arguments, adequately informed the jury of its responsibility to consider all of the mitigating evidence in the case. (See California v. Brown, supra, 479 U.S. 538, 546 [93 L.Ed.2d 934, 943, 107 S.Ct. 837, 842] (conc. opn. by O’Connor, J.), 479 U.S. at pp. 545-546 [93 L.Ed.2d at pp. 941-943, 107 S.Ct. at p. 849] (dis. opn. by Brennan, J., 479 U.S. at p. 561 [93 L.Ed.2d at p. 952, 107 S.Ct. at p. 850] (dis. opn. by Blackmun, J.); see also People v. Ghent (1987) 43 Cal.3d 739, 777 [239 Cal.Rptr. 82, 739 P.2d 1250].)
On the basis of our review of the record, we conclude that there exists “no legitimate basis” (see opn. of O’Connor, J., California v. Brown, supra, 479 U.S. at p. 538 [93 L.Ed.2d at p. 943, 107 S.Ct. at p. 842]) for believing that the jury was misled by the “no sympathy” instruction regarding the propriety of considering defendant’s background and character evidence in making its penalty determination.
In the present case, in addition to giving the “catchall” instruction of subdivision (k), the court preceded its penalty phase instructions by telling the jury that “In determining which penalty is to be imposed on the defendant, you shall consider all of the evidence which has been received during any part of the trial of the cage.” (Italics added.) Thereafter, the arguments of the prosecutor and defense counsel made it clear to the jury that the penalty determination was to be based on a weighing of all of the aggravating and mitigating evidence in the case, and that such evidence included any character or background evidence proffered by defendant.
As the prosecutor explained it, “You balance the bad things about the defendant and about the crime against the mitigating things ... if they exist.” The prosecutor then examined the statutory list of factors, commenting upon their aggravating or mitigating character under the evidence, and explaining that the weight to be assigned to each factor was a jury decision. For example, he agreed that defendant’s lack of any prior felony convictions was a mitigating factor, and he placed “in the middle” (i.e., inapplicable) the presence of any extreme mental disturbance at the time of the offense, reasoning that the evidence failed to establish any such disturbance. (Ibid.) As for defendant’s age (25), the prosecutor left to the jury the question whether it was a mitigating or aggravating factor, observing, however, that defendant was old enough to be responsible for his actions.
On the subject of “sympathy,” the prosecutor simply observed that the evidence of defendant’s unbalanced mental condition was perhaps designed to “cause you to feel sorry for” him. The prosecutor suggested that the *997evidence regarding this condition was inconsistent with defendant’s conduct during the offense, “but perhaps there is some real problem there that he has. It’s intended to get your sympathy and your feelings. That feeling of sympathy is a genuine human emotion but it’s one that can be so easily utilized and abused .... I submit to you that no one had sympathy for the child, Joyce . . . .”
Thus, the prosecutor never suggested to the jury that sympathy for defendant was legally irrelevant, or that the jury should ignore any other relevant character or background evidence in the case. The prosecutor’s reference to weighing the “mitigating things” about defendant and his crime certainly would suggest the contrary to any reasonable juror. Indeed, the prosecutor’s comments indicated that although sympathy might be an appropriate factor in some capital cases, it was inappropriate under the circumstances of the present case.
Defense counsel, relying primarily upon the psychiatric testimony, urged the jury to spare defendant’s life. Counsel’s argument stressed the expert testimony which, in effect, opined that defendant “was a very, very sick young man.” Counsel reaffirmed that even one mitigating circumstance, such as extreme mental or emotional disturbance, could be sufficient basis for a verdict of life imprisonment, even if “everything else is on the aggravating side.”
Although both prosecutor and defense counsel advised the jury that only an “extreme” mental condition would qualify as a mitigating factor under section 190.3, subdivision (d), the other arguments and instructions made it clear that defendant’s mental condition could constitute a “sympathy” factor relevant to the penalty decision. (See People v. Ghent, supra, 43 Cal.3d 739, 776.)
In light of the respective jury arguments, it is inconceivable that the jury failed to understand that it was permitted to consider sympathy, background or character evidence in deciding the appropriate penalty.
B. Counsel’s Penalty Phase Argument
Next, defendant contends that his counsel gave an inadequate closing argument at the penalty phase. Counsel, near the conclusion of his argument, told the jury that defendant had indicated he could live no longer with “that beast from within” (i.e., one of his multiple personalities), and counsel opined that if the jury concluded in its “wisdom” that death was the appropriate penalty, death might give defendant “an escape once again by *998analogy the gift of life . . . to be free from this horror that he and only he knows so well.”
For many of the same reasons previously set forth in our discussion regarding a similar guilt phase contention, we believe counsel’s argument was a reasonable and tactical one, aimed at gaining the jury’s sympathy for defendant, and was not tantamount to advocating his client’s death. (Cf. People v. Deere (1985) 41 Cal.3d 353, 365-367 [222 Cal.Rptr. 13, 710 P.2d 925].) As counsel stated to the jury at an earlier point in his penalty argument, “I’m suggesting that [defendant] be given ... a continued existence until death. Give us an opportunity to examine a person like that, determine whether we can help others who may be like him . . . .” The record thus fails to support defendant’s contention that counsel’s penalty phase argument reflected his incompetence.
C. Effect of Invalid Special Circumstances
The jury found two special circumstances, a “heinous” murder and a “torture” murder. The former finding was invalid under People v. Superior Court (Engert), supra, 31 Cal.3d 797. In light of our determination to uphold the torture-murder finding, the invalid heinous-murder special circumstance was undoubtedly harmless error. (Cf. People v. Allen (1986) 42 Cal.3d 1222, 1281-1282 [232 Cal.Rptr. 849, 729 P.2d 115].) Having reviewed the record, we find no evidence that was submitted to support the heinous-murder special circumstance that was not equally admissible to support the torture-murder special circumstance. The “heinous murder” and “torture-murder” special circumstances were substantially similar, especially as to the type of evidence that would support either of them. Moreover, section 190.3, subdivision (a) expressly provides the jury could consider “[t]he circumstances of the crime of which the defendant was convicted . . . .” The only effect the heinous-murder finding could have had on the jury was thus merely a consequence of the statutory label “special circumstance.” We find that such possibility could not have affected the jury’s verdict. The United States Supreme Court has made clear that a death sentence is valid under these circumstances. (Zant v. Stephens (1983) 462 U.S. 862, 888-889 [77 L.Ed.2d 235, 256-257, 103 S.Ct. 2733].)
D. Instruction to “Disregard Consequences” of Verdict
The jury was instructed, in standard language (CALJIC No. 1.00), to “reach a just verdict, regardless of what the consequences of such verdict may be.” The instruction has been considered inappropriate at the penalty phase (see People v. Brown, supra, 40 Cal.3d 512, 538, fn. 7), but it must be deemed harmless where, as here, the record indicates that the jury fully *999understood the grave consequences of its penalty decision. (See People v. Miranda (1987) 44 Cal.3d 57, 102, fn. 25 [241 Cal.Rptr. 594, 744 P.2d 1127].) In addition, we observe that the instruction does not ask the jurors to wholly ignore the consequences of their decision, but simply asks them to reach a “just” verdict regardless of the consequences of such a verdict.
E. Failure to Delete Inapplicable Mitigating Factors
Defendant contends that the court erred in failing to delete from the standard penalty phase instructions (CALJIC No. 8.84.1) those mitigating factors not applicable in this case. We have rejected that contention in People v. Ghent, supra, 43 Cal.3d 739, 776-777.
F. Sentencing Instructions
Defendant makes familiar arguments regarding the constitutional sufficiency of the 1978 sentencing statutes in failing more explicitly to guide the jury’s discretion and to explain its sentencing responsibilities. We have rejected similar attacks on the 1978 law. (See People v. Allen, supra, 42 Cal.3d at pp. 1276-1280; People v. Brown, supra, 40 Cal.3d 512.) As we explained in Allen, our concern in Brown was that a jury receiving the unadorned standard instruction heretofore used in many capital cases (CALJIC No. 8.84.2) might fail to appreciate the full scope of its “weighing” function, or might fail to realize that inherent in the weighing process was an obligation to determine whether death is the appropriate punishment in that case, regardless of the number of aggravating circumstances.
For the reasons previously discussed, we conclude that nothing in the prosecutor’s argument in this case could have misled the jury regarding the scope of its penalty determination or responsibilities. The jurors were carefully told that the weight to be given a particular sentencing factor was a matter for their own individual judgment. Although the prosecutor did tell the jury that “whatever outweighs the other [i.e., aggravating versus mitigating circumstances] is what directs your judgment ” (italics added), a review of the record as a whole convinces us that no reasonable jury would have understood this statement as divesting it of authority to determine the appropriate penalty in this case.15
*1000G. Other Constitutional Challenges
Defendant asserts the 1978 law is constitutionally deficient in various other respects. All these contentions have been rejected in prior cases. (E.g., People v. Rodriguez (1986) 42 Cal.3d 730, 777-779 [230 Cal.Rptr. 667, 726 P.2d 113].) We likewise reject his argument that death is a disproportionate penalty “for the parent who disciplines his child to death.” The record indicates that, unlike the situation wherein a parent overreacts in heat of anger toward a child, defendant beat and tortured his stepdaughter over an extended period, having ample time to reflect upon the nature of his acts. Under these facts, we cannot hold that the punishment imposed is disproportionate to his individual culpability. (See People v. Allen, supra, 42 Cal.3d 1222, 1285-1286; People v. Dillon (1984) 34 Cal.3d 441, 477-482 [194 Cal.Rptr. 390, 668 P.2d 697].)
H. Habeas Corpus Petition
Shortly before reargument of this case, defendant filed a habeas corpus petition reasserting trial counsel’s incompetence and the disproportionality of the death penalty under the circumstances here. Concluding that these allegations failed to state a prima facie case, we denied the petition without issuing an order to show cause.
The judgment of guilt, the finding of one special circumstance, and the judgment of death are affirmed.
Mosk, J., Panelli, J. Arguelles, J., Eagleson, J., and Kaufman, J., concurred.
A fifth child, LaVert (age seven), was living in Sacramento at the time.
Cookie, Penny and Alexis testified in detail about the events leading to Joyce’s death.
Defendant gave two statements to the police. The first occurred shortly after his arrest when he was transported to the hospital by Officer Thompson. The second statement was given to the police later on the morning of April 11. Both statements were taped and played for the jury.
One of Dr. Allison’s sessions with defendant, during which more than one personality was interviewed, was videotaped and played for the jury.
Several lay witnesses also testified about defendant’s background. His wife Cookie stated that defendant sometimes called himself “Othello Mulct Metheen” and said he was from Greece. On a number of occasions, he also referred to himself as “Michael the Archangel.” At those times, Cookie described defendant as being “dead serious." She also related that defendant had blacked out on several occasions.
Cookie’s daughter Penny testified that defendant said his name was “Othello” sometimes and boasted that he knew many languages. She also stated that defendant had blacked out on a number of occasions.
Drs. Hacker and Oliver had been appointed by the court when defendant entered his plea of not guilty by reason of insanity.
At various points in his argument, the prosecutor described defendant’s defense as “theatrical,” “showy,” “sensational,” “a last-ditch effort,” “no basis in . . . reason or logic,” “totally ridiculous and absurd,” and based on the premise that “The devil made me do it.” Much of defense counsel’s jury argument was in response to these accusations, and was directed toward demonstrating counsel’s gradual acceptance of defendant’s unusual mental state.
Defendant characterizes as incompetent counsel’s failure to present an argument to the jury at the sanity phase. Yet counsel’s earlier guilt phase arguments included a reasonably complete summary of the evidence and legal arguments pertinent to the insanity issue, and counsel reasonably could have deemed it unnecessary or unwise to repeat those matters.
As is evident from the discussion between the court and prosecutor which preceded the trial court’s ruling, the trial court recognized the purpose of this testimony.
Defendant also argues that the relevancy of the prior acts of child abuse evidence depended on whether that evidence shared marks of distinctive similarity with the present offense. Defendant asserts that such distinctive similarity is lacking. The evidence, however, bore marks similar enough to bridge the gap between it and the material fact sought to be proved by the prosecution on rebuttal, i.e., that Melvin, not “Othello,” was the perpetrator of the crime. (See Thompson, supra, 27 Cal.3d at pp. 319-320, fn. 23.) Both instances involved abuse by defendant toward children in his own family. In both, defendant beat them with his fists and kicked them. And in both, he threw their bodies against the wall.
Former section 190.2, subdivision (c)(4), provided a special circumstance if “[t]he murder was willful, deliberate and premeditated, and involved the infliction of torture. For the purpose of this section, torture requires proof of an intent to inflict extreme and prolonged pain.”
We also observed in Davenport that “The very use of the term torture to describe the class of murders to which the subdivision applies necessarily imports into the statute a requirement that the perpetrator have the sadistic intent to cause the victim to suffer pain in addition to the pain of death . . . .” (41 Cal.3d at p. 271.)
The jury was instructed as follows: “To find that the special circumstance, referred to in these instructions as murder involving infliction of torture, is true, each of the following facts must be proved: 1. That the murder was intentional, and 2. That the murder involved the infliction of torture. To prove the infliction of torture, the infliction of extreme physical pain must be proved no matter how long its duration. Awareness of pain by the deceased is not a necessary element of torture.” (CALJIC No. 8.81.18 (4th ed. 1979).)
The prosecutor first reviewed the elements of torture-murder, explaining that “[t]here has to be on the part of the person who committed the acts the intention to cause cruel pain and suffering for the purpose of revenge, extortion, persuasion, or for any sadistic purpose.” He also added, correctly: “The first-degree murder theory of torture does not have any requirement of intent to kill.”
*995The prosecutor then discussed the torture-murder special circumstance. “When we go to the special circumstance, you see that again there’s a torture special circumstance, and basically torture in the special circumstance relates to the same thing as the first-degree murder theory with one exception: There is an additional requirement, and it’s very important. [fl] Under the torture special circumstance, again, there’s a requirement that there was an infliction of cruel pain and suffering, that it was done over a period of time, but again there’s no requirement that there be proof as to the duration. It doesn’t have to be for six hours or four hours or three or two. Any period of time wherein there was this infliction of cruel pain and suffering satisfies the torture. There’s no requirement again that there be any showing of the victim’s awareness of pain. That’s not required. But there is a requirement that is nonexistent in the first-degree murder theory and that is a requirement of intent to kill. That’s required under the special circumstance of torture, intent to kill.” (Italics added.)
Thus, for example, at the conclusion of his penalty phase argument, the prosecutor stated: “This is a situation here, ladies and gentlemen, where the defendant, from what he did to that child and what he represents, deserves, deserves a judgment of death. He deserves it because there are some crimes that are so terrible that society must say that for that crime there must be a most extreme price, that for this crime anyone who commits it must suffer a judgment of death. [fl] Society must say that and it must say that out of a respect for human life. There are some individuals in this society, some persons who have demonstrated their *1000disrespect for society, for the rights of others. The truthfulness and honesty. Have demonstrated their ability to do harm to those that the society must protect above all others. Children. The weak. Those who cannot protect themselves. [H] There are people like that and this defendant who’s in the courtroom at this time is one of those persons that society cannot allow to remain within the society. [][] Society must say that for those actions, for what he has done, for the danger that he presents, he must be sentenced to a judgment of death.”