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Opinion WERDEGAR, J. Following a mistrial declared when a jury was unable to agree on guilt, a second jury convicted defendant George Edward Marshall of three counts of first degree murder (Pen. Code, § 187; all further statutory references are to the Penal Code unless otherwise indicated) and one count of attempted murder (§§ 664/187), and as to each count found defendant used a firearm during the commission of the offense (§ 12022.5). Following a penalty trial, the same jury sentenced defendant to death. The trial court found the jury’s multiple murder verdicts constituted true findings on the multiple-murder special-circumstance allegations and denied defendant’s motion to modify the verdict. (§ 190.4, subd. (e).) This appeal is automatic. (§ 1239, subd. (b).) Finding no reversible error, we affirm the judgment. Facts I. Guilt Phase A. Crime Scene and Defendant’s Arrest. On the morning of January 1, 1981, defendant’s wife, Cynthia Marshall, her brother Jeffrey Lee, and a boarder, Henry Thomas, were shot to death at defendant’s Locust Street residence in Modesto. A visitor, Annette May, was wounded, but escaped through a bedroom window and sought refuge with a neighbor, who summoned police. Responding officers found the front door of the residence slightly open. Inside they saw an automatic or semiautomatic weapon lying on the living room floor. The body of Cynthia Marshall lay in a pool of blood in the kitchen, and that of Henry Thomas on a waterbed in one of the bedrooms. Defendant, wearing a blue leisure suit and a white hat with a black brim, was found in the master bedroom, holding two small children. The body of 13-year-old Jeffrey Lee lay just inside the door to the master bedroom. Defendant told an officer Jeffrey had “just come in here and fell down.” Defendant was arrested and escorted down the hallway and out of the house. Defendant neither looked into the bedroom where Henry Thomas’s body lay, nor commented on his wife’s lifeless body, although it was in view. To one officer, defendant appeared dazed or in a state of shock. While being transported to the police station, defendant told an officer he was very tired and had arrived home a few minutes before the shootings. Defendant stated he was in the back bedroom with his two children when he heard shots being fired, and immediately locked the bedroom door. Defendant asked, “Is Cindy all right?” The officer responded he did not know. Throughout the booking procedure, defendant appeared calm, quiet and collected. He was transported to the hospital for the taking of a blood sample, and in response to a nurse’s inquiry as to his marital status said, “According to these guys, I’m single.” In Detective McDonough’s opinion, defendant was sober, and he detected no odor of alcohol on defendant’s breath. Defendant did not appear to be under the influence of any drugs. B. Testimony of Annette May. Annette May, 20 years old at the time of the offenses, arrived at the Golden Touch disco, an establishment defendant and his wife operated, around 8 p.m. on New Year’s Eve 1980. While at the disco, May consumed many different kinds of drinks, including beer, champagne, brandy and hard liquor. She saw defendant at the disco wearing a white suit and a white hat. May remained there until about 4:30 a.m., when she left for the Marshall residence with Henry Thomas. She was feeling tired and “high.” Eventually she and Thomas went to sleep in Henry’s bedroom. May awoke when it was “kind of light out.” As she went to the bathroom she saw defendant in his bedroom. She could not see what he was wearing, as he was bending over a pile of clothes. She did not see Cynthia or hear any noise from the kitchen. After May returned to bed, Henry got up and went to the kitchen to get something to eat. She could hear Henry and defendant talking in a normal, friendly tone of voice. As Henry returned to bed, May again fell asleep. The next time May awoke she could hear defendant’s two children, screaming and crying in the living room. She could also hear Cynthia crying and saying, “Why, George,” and “No, George.” May then saw the bedroom door open and heard a gun go off. A number of shots were fired into the room. May fell from the bed onto the floor, in the 20-inch-wide space between the bed and the wall. From there she scooted under the headboard. There was a crack or space between the headboard and the bed through which she could see. May saw defendant enter the bedroom carrying a large, dark gun with a shoulder strap. Defendant looked at the waterbed and approached May. She pretended to be dead and defendant walked away. He picked up one of his children near the bedroom doorway. He was wearing a white suit and a white hat with dark trim. These appeared to be the same clothes he had been wearing earlier at the disco. After a few minutes, May escaped through the bedroom window and ran, naked and bleeding, to seek help from a neighbor, Anna Baker. It was around noon when May arrived at Baker’s house. There was some dispute over whether May identified defendant or responded “I don’t know” when Baker asked who had shot her. C. Forensic Evidence. Post mortem examination revealed each of the victims died as a result of wounds inflicted by a high velocity gun. Four bullets found at the scene were fired from the weapon found in the living room, and seven cartridge cases found in the house had been chambered in it and may have been fired from it. The weapon, a semiautomatic rifle, resembled one that Alvin Green testified he had observed defendant to possess at the disco. Cynthia Marshall’s name, with the Locust Street address, appeared on a receipt for an HK-93 rifle purchased at a sporting goods store in San Leandro in November 1979. The HK-93 had later been exchanged for an HK-91, a higher caliber model. The serial number on the weapon found at the crime scene matched that recorded on the Bureau of Alcohol, Tobacco and Firearms form 4473 filed in connection with the exchange. No usable fingerprints were found on the rifle. Police tested defendant’s hands for gunshot residue, with negative results. The clothes defendant was wearing at the time of his arrest were tested for blood; none was found. Defendant’s blood-alcohol level at 3 p.m., some three hours after his arrest, was .10 percent. D. Testimony of David Moore Regarding Bloodied White Suit. Cynthia Marshall’s uncle, David Moore, testified that the day after the offenses he went to the Locust Street residence, when the house was under a coroner’s seal, and was admitted by a deputy sheriff. His purpose was to retrieve clothes and toys for defendant’s two children. While doing so, he found a clothes hamper in the bathroom and turned it upside down. Going through the clothes, he found a white suit with blood spattered on it, along with some bloody shirts. He did not think his discovery important and did not tell the officers about it until after defendant’s first trial ended in a mistrial. The police never found any bloodstained clothing, but the trial court denied a defense motion to suppress Moore’s testimony concerning the bloodied white suit. E. Events of New Year’s Eve. Evidence indicated that, during the day preceding the crimes, defendant ran errands in preparation for the New Year’s Eve celebration he was planning at the disco. Around 4 p.m. defendant went to his job at Gallo Glass Company and worked an eight-hour shift. A fellow Gallo employee gave him a ride to the disco, dropping him off around 12:30 or 12:45 a.m. Cynthia was at the door, taking admission fees. Defendant began to pour champagne for the disco patrons, drinking as he did so. Defendant’s attire on New Year’s Eve was a subject of dispute. Defendant testified he was initially wearing blue slacks and a blue leisure coat, and at some point changed into a grey coat that he kept at the disco. Two witnesses likewise testified defendant was wearing dark clothing. Other witnesses, however, testified defendant was wearing a white suit on New Year’s Eve. The celebration began to wane after 4:30 a.m., when disc jockey Henry Thomas left the Golden Touch with Annette May. Together they went to the room Thomas rented in defendant’s house. Cynthia had previously gone home by herself, driving defendant’s car. Before leaving the disco she traded defendant $80 in small bills for four $20 bills. Defendant testified she also took some money bags with her. F. Defendant’s Relationship With His Wife. Defendant and Cynthia had been married for two years at the time of the killings, and were the parents of two daughters, Star Child and Jamilah. Both were employed at Gallo Glass Company in Modesto, and during their spare time they operated a disco called the Golden Touch. Defendant and his wife jointly owned their residence, and prior to their marriage defendant had purchased a house on Benson Avenue in Modesto, which they rented out. Defendant testified he loved his wife and got along well with her, apart from brief separations occasioned by transient emotional changes during each of her pregnancies. She was pregnant at the time of her death and, as was her custom, had gone to stay with her mother, from which stay she had returned around Christmas. Prosecution witness Patsy Thomas testified that, sometime after Christmas, she overheard an argument between defendant and his wife, during which Cynthia said, “Well, it doesn’t really matter because I am leaving anyway—this time for good.” Thomas testified defendant replied, “Over my dead body.” Thomas also testified she heard defendant say he had purchased $100,000 of insurance on Cynthia’s life and that Cynthia wanted the money she had put into the disco, as she did not want to be involved in the business. Defendant denied Cynthia had threatened to leave. G. Testimony of Alvin Green Regarding Motive. Alvin Green testified he occasionally worked at the disco as a disc jockey or security guard. Sometime after 4:20 p.m. on New Year’s Eve, he went to the disco to pick up his earnings. Defendant, Green said, indicated to him on that occasion that he and Cynthia were not getting along and might be separating. According to Green, defendant expressed concern that if Cynthia left him, as an ex-felon he would lose everything, because their assets were in her name; he would see her dead before he lost everything. Defendant denied seeing Green at the disco on New Year’s Eve. H. Testimony of Informant Gary Brady. Gary Brady became acquainted with defendant while both were incarcerated in the Stanislaus County jail during the first three months of 1981. Brady testified defendant admitted he had shot his wife, a small child, a man and a woman, with a high-powered rifle. Brady claimed defendant offered him a 1966 Mustang and a house defendant owned if Brady would kill the “bitch” who escaped out the window, his mother-in-law, and one Green. In return for Brady’s testimony, the district attorney’s offices in San Joaquin and Stanislaus Counties promised him he would receive a two-year prison term for a pending robbery charge. Brady had received similar consideration for his testimony in the Fresno County murder prosecution of Clarence Ray Allen. Inmate Andrew Crane testified Brady did not enjoy a good reputation for truthfulness and was considered a “snitch” by other inmates. Defendant likewise testified Brady had a poor reputation for truth-telling, and stated he never discussed his case with Brady. I. Testimony of Kenny Mitchell. In the prosecution’s rebuttal case, Kenny Mitchell testified he had been at the Golden Touch disco on New Year’s Eve and went to defendant’s residence the following morning, ostensibly to arrange a cocaine deal, but in reality to defraud defendant. As Mitchell approached the front door of the residence he heard a gunshot, followed by another gunshot and a woman’s voice saying, “Oh, God. George, what are you doing this for?” The door was open about 18 inches. Inside Mitchell saw defendant, wearing a white suit, apparently with a black gun in his hand, emerging from one room and entering a bedroom. Mitchell then left the area. Mitchell was impeached with prior felony convictions, prior inconsistent statements, admissions he had lied in the past, and a further admission that after leaving the Golden Touch disco after the New Year’s Eve festivities, he had gone to a gambling shack to gamble, drink, smoke marijuana and use cocaine. Additionally, Benson Neal, an inmate in the Stanislaus County jail who was housed in the cell next to appellant, testified that Kenny Mitchell came to his house several days after New Year’s Day 1981. Mitchell was carrying a white calculator, some silver dollars and several rings; he told Neal he had killed three people to get them. Charles Edward Thompson testified Mitchell told him he had made a deal with the district attorney to get two cases dropped in exchange for his false testimony against defendant, urging Thompson to do the same. Albert Ward testified to hearing Mitchell make similar statements. After Thompson and Ward testified, Mitchell was recalled to the stand by the defense. He acknowledged he knew Thompson and Ward and had discussed defendant’s case with them. He said he told Thompson he was not really going to testify, but was just “running a game” on the police. J. Testimony of Defendant. Defendant narrated the events of New Year’s Eve and the morning following. He testified that after most of the disco patrons had left, he got a ride from the disco to his home, where he picked up his car and drove back to the disco. After closing the disco he went to an establishment a few doors away and had a drink. Although he had been drinking throughout the night and could feel the alcohol, he then drove home, a distance of four or five blocks. When he arrived, a little after 7 a.m., Cynthia and his daughter Star Child were waiting for him. He noticed the rifle in the living room beside the closet door. Jeffrey Lee was in the master bedroom, watching television. Defendant poured himself some champagne and went into the master bedroom to play with his children. Eventually he fell asleep. At some point defendant heard someone call his name. He recognized the voice as his wife’s, but he was so tired he did not know whether he was dreaming or not, and did not respond. He heard what sounded like a series of “pops.” Eventually he got up, not knowing what time it was. He opened the bedroom door and saw Jeffrey Lee and Star Child in the hallway. Star Child had a toy in her hand and a frightened look on her face. As defendant reached down to pick her up, he noticed, out of the comer of his eye, the form of a man move from the kitchen into the hallway. He saw the form of a weapon and heard a single shot. Defendant quickly reentered the master bedroom and locked the door. Defendant’s younger daughter, Jamilah, was already in the bedroom, in her crib. Defendant took her out of the crib and placed his daughters on the floor, covering them with his body. He was unaware of Jeffrey being in the room. At some point defendant picked up the telephone and tried to call the private number of the Modesto Chief of Police, but the line appeared to be dead. When defendant heard the police walkie-talkie in the hallway, he yelled out that he and his girls were “back here.” Soon thereafter defendant was taken into custody. II. Penalty Phase A. Prosecution Evidence. The prosecution introduced evidence that in 1975 defendant was convicted of assault with a deadly weapon. Defendant was then operating Uptown Saturday Night, an East Oakland cultural club, and providing housing and financial support for Donald Mitchell, an employee who had fallen on hard times. One night some thefts occurred at the club, and defendant suspected Mitchell. The two men armed themselves and went for a drive in defendant’s car to discuss the matter. The discussion grew heated as the men drove along Skyline Boulevard. Defendant saw Mitchell reach into the pocket containing his gun. Fearing for his life, defendant immediately pulled over and drew his own weapon. He grabbed Mitchell’s hand and tossed his gun onto the passenger side floorboard. Gun in hand, defendant ordered Mitchell out of the car and frisked him. Finding Mitchell was carrying no other weapons, defendant returned his own gun to his pocket. When the men had been talking for several minutes beside defendant’s car, two uniformed Oakland park rangers stopped to investigate. Seeing a gun butt protruding from defendant’s pocket, they took the pistol and discovered it was loaded. They also found Mitchell’s gun on the floor of the car, but noted it was rusty and unloaded. Defendant testified he did not realize Mitchell’s weapon was old and had assumed it was loaded. Defendant served no time in jail for the assault conviction. B. Defense Evidence. The defense presented evidence of defendant’s background and religious beliefs. Defendant was the oldest of 13 children bom to a desperately poor family. From the age of seven, defendant picked cotton in the fields to help support the family. He cared for his younger siblings while his mother was picking cotton and his father was away on his many trips with the merchant marine. His father beat defendant, singling him out among the children for especially severe abuse. Defendant’s parents divorced when he was 10. Although defendant did not complete school as a child, he taught himself to read while in the merchant marine. He has been continuously employed in a variety of jobs and has been self-sufficient since he was 13. A Christian Science minister testified she had visited defendant some 60 times during his incarceration. She described the depth of his religious commitment and his dedication to helping other inmates, both spiritually and by teaching them to read. She indicated that defendant was responsible for settling a number of potentially violent disputes at the jail and that correctional officers have described him as a model prisoner. Discussion I. Guilt Phase Issues A. Double Jeopardy. Defendant was tried twice on three counts of murder and one count of attempted murder. At the first trial, the jury indicated to the trial court it was deadlocked, seven jurors voting to acquit and five to convict. A subsequent vote revealed no change in the jurors’ respective positions. The court asked the jury to continue its deliberations. After three hours, the foreman announced a third ballot had produced an identical result. The trial court called the jurors back into court and inquired whether further deliberations would be useful. After the jury indicated it could not overcome the deadlock, the trial court declared a mistrial and dismissed the jury. At no time did the trial court inquire whether the jury was able to reach a partial verdict of acquittal on any of the charged offenses, nor did the jury hint at such a possibility. Defendant argues that, under the rule of Stone v. Superior Court (1982) 31 Cal.3d 503, 519 [183 Cal.Rptr. 647, 646 P.2d 809] (Stone), the mistrial was without legal necessity and his retrial placed him twice in jeopardy, in violation of the Fifth Amendment to the federal Constitution, as applicable to the states through the Fourteenth Amendment, and article I, section 15, of the California Constitution. The constitutional guarantees against double jeopardy protect a defendant’s “ ‘valued right to have his trial completed by a particular tribunal’ ” and his interest in not being subjected to successive prosecutions for the same offense. (Arizona v. Washington (1978) 434 U.S. 497, 503 [54 L.Ed.2d 717, 727, 98 S.Ct. 824], fn. omitted; Bigelow v. Superior Court (1989) 208 Cal.App.3d 1127, 1135 [256 Cal.Rptr. 528].) “The underlying idea, one that is deeply ingrained in at least the Anglo-American system of jurisprudence, is that the State with all its resources and power should not be allowed to make repeated attempts to convict an individual for an alleged offense, thereby subjecting him to embarrassment, expense and ordeal and compelling him to live in a continuing state of anxiety and insecurity, as well as enhancing the possibility that even though innocent he may be found guilty.” (Green v. United States (1957) 355 U.S. 184, 187-188 [2 L.Ed.2d 199, 204, 78 S.Ct. 221, 61 A.L.R.2d 1119].) When a jury indicates it is unable to reach a verdict, double jeopardy rules bar retrial unless the defendant consents to the discharge of the jury (People v. Compton (1971) 6 Cal.3d 55, 62-63 [98 Cal.Rptr. 217, 490 P.2d 537] [defendant’s mere silence is not consent to declaration of mistrial]), or the trial court determines further deliberations are not reasonably likely to result in a verdict (§ 1140), in which case legal necessity exists for a declaration of mistrial (Arizona v. Washington, supra, 434 U.S. at pp. 503-505 [54 L.Ed.2d at pp. 726-727, 98 S.Ct. 824]). Stone, supra, 31 Cal.3d 503, like this case, involved a homicide prosecution in which the jury was instructed on the charge of murder and uncharged lesser included offenses. The jury in Stone deliberated for seven days, but was unable to reach a unanimous verdict within the options presented to it. (Id. at p. 507.) The prosecution and defense stipulated to an inquiry to determine the jury’s position. The foreman reported in open court that no jurors voted for either first or second degree murder, four voted for voluntary manslaughter, two voted for involuntary manslaughter, six voted for justifiable homicide, and none voted for acquittal. (Ibid.) Each juror expressed the opinion the jury was hopelessly deadlocked and further deliberations would not yield a verdict. (Ibid.) The defense moved the court to accept a verdict of acquittal on the offenses of first and second degree murder. Noting no established procedure existed for such a partial verdict, the trial judge denied the motion and ultimately declared a mistrial. (Id. at pp. 508-509.) Defendant sought a writ of prohibition to prevent retrial. (Id. at p. 509.) We concluded the trial court should have received the jury’s verdict on first and second degree murder, and prospectively held as follows: “[I]n all cases in which the jury has not yet begun deliberations as of the date this decision becomes final, the trial court is constitutionally obligated to afford the jury an opportunity to render a partial verdict of acquittal on a greater offense when the jury is deadlocked only on an uncharged lesser included offense. Failure to do so will cause a subsequently declared mistrial to be without legal necessity.” (Id. at p. 519.) Our decision in Stone became final two months before the jury declared its deadlock at defendant’s first trial. Citing People v. Chaney (1988) 202 Cal.App.3d 1109 [249 Cal.Rptr. 251] (Chaney), defendant argues the failure of the trial court in his first trial to inquire whether defendant’s jury could eliminate any of the charged offenses resulted in the mistrial lacking legal necessity. In Chaney, the Court of Appeal extended the rule in Stone as follows: “[E]vidence of an actual implied acquittal is unnecessary to take a declaration of mistrial outside the concept of legal necessity; it is enough if the trial court fails to afford the deadlocked jury with an opportunity to render a partial verdict of acquittal.” (Chaney, supra, 202 Cal.App.3d at p. 1122.) Under the facts of Chaney, the Court of Appeal’s statement that evidence of an actual implied acquittal is unnecessary to trigger the trial court’s duty under Stone to permit the jury to render a partial verdict was unnecessary to its holding. This is because in Chaney evidence of an actual implied acquittal was in fact presented on the record, albeit not as clearly as in Stone. In stating it was deadlocked on a murder charge, the Chaney jury informed the trial court “ ‘We have reached unanimity ... on several items. Where we are disagreeing is on the degree. . . . The division is on two close possibilities, and . . . it’s been this way just about from the first day of the deliberation.’ ” (Chaney, supra, 202 Cal.App.3d at p. 1113.) From this, the trial court in Chaney should have been aware the jury had eliminated some of the offenses; thus, the Court of Appeal’s statement that evidence of an actual implied acquittal is unnecessary to remove a declaration of mistrial from the concept of legal necessity was, arguably, dictum. In any event, we do not agree with the Chaney court’s extension of Stone, which must be understood in its context. The problem we addressed in Stone was the unfairness of forcing a defendant to stand trial a second time for a murder of which a jury clearly and unanimously agreed he was not guilty, simply for lack of an established procedure for the receipt of a partial verdict of acquittal. Thus, we held the trial court must afford a jury the opportunity to render a partial verdict of acquittal on a greater offense when it is deadlocked only on an uncharged lesser included offense. (Stone, supra, 31 Cal.3d at p. 519.) Absent some indication of deadlock only on an uncharged lesser included offense, the suggested procedures in Stone do not come into play. If the jury, in announcing apparent deadlock, gives such an indication, or if counsel so requests, the trial court, under Stone, should inquire further and determine whether any offenses can be eliminated. In the present case, the trial court conducted a sufficient inquiry before declaring a mistrial. Nothing in the jurors’ comments hinted they had agreed to acquit defendant of first degree murder and were in disagreement only on lesser included offenses. Moreover, neither the evidence in this case nor the defense proffered supports an inference of partial acquittal on a greater offense. We conclude the mistrial was a matter of legal necessity, and therefore reject defendant’s claim of double jeopardy. B. Faretta motion. Defendant argues the trial court erroneously denied him his constitutional right to self-representation, despite his repeated request to exercise that right at various points in the proceedings. He specifically asserts error in the denial of his request, four weeks into jury selection, to represent himself. His contention lacks merit. As noted, during the fourth week of trial, while the process of jury selection was still under way, the trial court heard defendant’s motion to proceed in propria persona. Defendant expressed concern with the progress of the investigation, contending he alone could attempt an inquiry of certain witnesses that would elicit the truth for the jury. The trial court noted trial counsel’s competence did not appear to be in question, and observed that the sort of investigation defendant appeared to contemplate would be infeasible given defendant’s custodial status. Concluding that a defendant has no right, after the commencement of trial, to relieve counsel and proceed in propria persona unless there is a showing that his present counsel is incompetent, the trial court denied the motion. As we have repeatedly held, although a defendant has a federal constitutional right to represent himself (Faretta v. California (1975) 422 U.S. 806 [45 L.Ed.2d 562, 95 S.Ct. 2525] (Faretta)), in order to invoke the right he must assert it within a reasonable time before the commencement of trial. (People v. Clark (1992) 3 Cal.4th 41, 98 [10 Cal.Rptr.2d 554, 833 P.2d 561]; People v. Burton (1989) 48 Cal.3d 843, 852 [258 Cal.Rptr. 184, 771 P.2d 1270]; see People v. Windham (1977) 19 Cal.3d 121, 128 [137 Cal.Rptr. 8, 560 P.2d 1187] (Windham).) A motion made after this time is addressed to the sound discretion of the trial court, which should consider such factors as the quality of counsel’s representation of the defendant, the defendant’s prior proclivity to substitute counsel, the reasons for the request, the length and stage of the proceedings, and the disruption or delay that might reasonably be expected to follow the granting of such a motion. (Windham, supra, 19 Cal.3d at p. 128.) Defendant complains the trial court both abused and failed to exercise its discretion, in that it improperly sought to condition his request on a showing of counsel’s incompetence and failed to consider the appointment of advisory counsel. To the contrary: Although in denying defendant’s Faretta motion the trial court relied heavily on the absence of any showing counsel was incompetent, the record reflects its explicit or implicit consideration of each of the other Windham factors. Furthermore, the trial court was aware of its power to appoint advisory counsel, but in its discretion elected not to do so. Defendant was not unconstitutionally denied his right to represent himself. C. Prosecutorial Misconduct. Defendant contends the prosecutor knowingly adduced perjured testimony by witness Kenny Mitchell and engaged in misconduct by arguing, in summation, that defendant bore the burden of raising a reasonable doubt as to his guilt. These prosecutorial actions, he contends, deprived him of a fair trial as guaranteed by the state and federal Constitutions. 1. Use of Perjured Testimony. A full understanding of defendant’s contentions requires that we set forth in some detail the circumstances under which Kenny Mitchell testified. On May 28, 1981, Mitchell, then in the Stanislaus County jail, gave Detective Ridenour a statement pertaining to the Marshall case. Mitchell was in custody on a parole violation and sought to avoid going back to prison. In return for the statement, Detective Ridenour agreed to appear before the parole board to recommend it not revoke Mitchell’s parole. Ridenour performed as agreed, and Mitchell was not ordered back to prison. At defendant’s first trial, the defense called Mitchell as a witness. Mitchell was then incarcerated in state prison on a burglary conviction. Mitchell refused to respond to questioning, claiming he did not want a “snitch jacket.” In lieu of Mitchell’s live testimony, a tape recording of his statement to Detective Ridenour was played to the jury and a transcript thereof was received in evidence. Defense counsel at the first trial argued Mitchell was the real killer and was lying about why he was unwilling to testify. The prosecutor argued the defense had wanted to use Mitchell to raise a reasonable doubt, in that the jury might believe Mitchell not only was present at the scene, but also committed the crimes. The prosecutor also pointed out that testimony by a police officer corroborated Mitchell’s statement the door to the Marshall residence was open on the morning of the offense. At defendant’s second trial, the defense again called Mitchell to testify. Mitchell invoked his Fifth Amendment rights and the trial court ruled he was unavailable under Evidence Code section 240. The defense then called Benson Neal as a witness. Neal testified Mitchell admitted having committed the murders. (See Evid. Code, § 1230 [hearsay exception for declaration against penal interest].) In its rebuttal case, the prosecution called Mitchell to the stand. Mitchell indicated he wished to testify and that nothing he said would tend to incriminate him. Mitchell’s testimony was generally consistent with the statement he had given Detective Ridenour: Mitchell had arrived at defendant’s residence around 10 or 11 a.m. on January 1, 1981, ostensibly to arrange a cocaine transaction, although in fact he intended to leave town with the money he hoped defendant would advance him. Mitchell parked his car around the block, and when he reached the driveway he heard a gunshot. Out of curiosity, he walked up to the porch of the house. At that point he heard another gunshot and the voice of a woman saying, “Oh, God, George, what are you doing this for?” The front door was open about 18 inches. Mitchell testified he saw defendant inside the house, wearing a white suit. Defendant appeared to be holding a black gun in his hand, and he was coming out of one room and going into a bedroom. Mitchell then left and drove to an Oak Street gambling shack. Several days later, the trial court interrupted the prosecutor’s closing argument to allow the defense to present two newly discovered witnesses, Thompson and Ward. The witnesses testified Mitchell had told one or the other of them that he (Mitchell) had not been at defendant’s house on January 1, 1981, and had seen nothing himself; that Annette May’s brother had given him the idea of testifying against defendant in order to get charges against him dropped, and that he had obtained such a deal and had learned about details of the killings from films and slides he had viewed at the prosecutor’s office. After Thompson and Ward testified, Mitchell was recalled to the stand. He acknowledged he knew Thompson and Ward and had discussed defendant’s case with both of them. He acknowledged he had told Thompson he was not really going to testify, but was merely “running a game” on the police. Mitchell denied the prosecutor had ever shown him any slides or pictures. Detective Ridenour briefly testified to deny having shown Mitchell any slides or videotapes. In closing argument, the prosecutor argued Mitchell had committed perjury on the stand. Defendant now contends the prosecutor’s use of perjured testimony requires reversal of his conviction. Due process is denied when a prosecutor knowingly uses perjured testimony to obtain a conviction. (Napue v. Illinois (1959) 360 U.S. 264, 269 [3 L.Ed.2d 1217, 1220-1221, 79 S.Ct. 1173]; In re Imbler (1963) 60 Cal.2d 554, 560 [35 Cal.Rptr. 293, 387 P.2d 6].) Originally, under the traditional rule, to obtain relief a defendant had to establish by a preponderance of the evidence that perjured testimony was adduced at his trial, that representatives of the state knew of its falsity, and that such testimony may have affected the outcome of the trial. (In re Imbler, supra, 60 Cal.2d at p. 560; cf. § 1473, subd. (b) [writ of habeas corpus available when substantially material false evidence was presented at trial]; see People v. Gordon (1973) 10 Cal.3d 460, 473, fn. 7 [110 Cal.Rptr. 906, 516 P.2d 298] [when alleged perjury appears from the record, same test applies on appeal as in habeas corpus proceedings].) Under the current rule, a showing that the false testimony was perjurious, or that the prosecution knew of its falsity, is no longer necessary. (In re Hall (1981) 30 Cal.3d 408, 424 [179 Cal.Rptr. 223, 637 P.2d 690]; In re Wright (1978) 78 Cal.App.3d 788, 809, fn. 5 [144 Cal.Rptr. 535].) Defendant argues it was incumbent on the prosecutor, having acknowledged in closing argument that Mitchell had lied on the stand, to move to strike his testimony. In the absence of such a motion, defendant contends, his conviction must be reversed because Mitchell’s testimony was surely false and just as surely material. We conclude that, under the peculiar facts of this case, the presentation of Mitchell’s testimony, although apparently false and certainly material, does not require reversal. As the Attorney General points out, it was initially the defense that sought to call Mitchell as a witness. Their aim in doing so was obvious: to place Mitchell at the scene of the offense and thereby to support defendant’s claim that, notwithstanding the self-exculpating particulars of Mitchell’s testimony, he—not defendant—was in fact the perpetrator. The prosecution too had its purpose in calling Mitchell: to rebut the testimony of Benson Neal that Mitchell had admitted responsibility for the killings. Mitchell’s testimony thus supported certain aspects of both the defense and the prosecution, and enabled counsel for both sides to argue certain inferences beneficial to their respective positions. The falseness of Mitchell’s testimony was not concealed from the jury: As described above, in closing argument the prosecutor repeatedly declared in no uncertain terms that Mitchell had lied on the stand. Both defense counsel and the prosecutor were able to and did argue to the jury concerning the precise nature of Mitchell’s lies. Defendant never moved to strike Mitchell’s testimony; indeed, given its utility in his defense of third party culpability, defendant probably would have opposed any such motion had the prosecution made it. We conclude defendant waived his claim that his conviction was based on false testimony by failing to raise it at trial when the falseness of Mitchell’s testimony was well known to him, and the claim lacks merit in any event. Defendant’s aim at trial—to use Mitchell’s testimony to establish a possible defense—cannot be reconciled with his present argument the testimony should not have been used at all. Defense counsel’s evident tactical purpose in acquiescing in the presentation of Mitchell’s testimony bars defendant’s related claim of ineffective assistance of counsel. Defendant also contends the prosecutor, in denying Mitchell was at defendant’s house, improperly implied there was additional evidence known to him but unavailable to the jury, thereby making himself an unsworn, un-cross-examined witness. (See People v. Bolton (1979) 23 Cal.3d 208, 213 [152 Cal.Rptr. 141, 589 P.2d 396].) We disagree. In context, the prosecutor’s argument was merely fair comment on the evidence. 2. Misstatement of Law on Burden of Proof Defendant argues the prosecutor engaged in misconduct by misstating the applicable law in suggesting to the jury, in closing argument, that it was incumbent on defendant to raise a reasonable doubt concerning his guilt, and to do so not just by providing evidence he was not the killer, but by affirmatively showing who the killer was. Defendant notes it is improper for the prosecutor to misstate the law generally (People v. Bell (1989) 49 Cal.3d 502, 538 [262 Cal.Rptr. 1, 778 P.2d 129]), and particularly to attempt to absolve the prosecution from its prima facie obligation to overcome reasonable doubt on all elements (People v. Gonzalez (1990) 51 Cal.3d 1179, 1215 [275 Cal.Rptr. 729, 800 P.2d 1159]). This, defendant contends, is what the prosecutor did in arguing the defense wanted Kenny Mitchell’s testimony in the record, despite the falsity of his story, because “They had to come up with another possible suspect to create in your minds that reasonable doubt that they want you to have when you enter that jury deliberation room.” Defendant concedes his trial counsel failed to object to these remarks, but urges he should be excused from the usual consequences of such failure (see People v. Gonzalez, supra, 51 Cal.3d at p. 1215 [waiver of error by failure to object]) because counsel thereby rendered ineffective assistance of counsel. In the context of the whole argument and the instructions, we see no reasonable likelihood (see People v. Berryman (1993) 6 Cal.4th 1048, 1072 [25 Cal.Rptr.2d 867, 864 P.2d 40]) the jury construed the prosecutor’s remarks as placing on defendant the burden of establishing a reasonable doubt as to his guilt. When the prosecutor made the challenged comment, he had just finished reviewing the evidence presented in the prosecution’s case-in-chief, with the evident aim of demonstrating he had succeeded in proving defendant guilty beyond a reasonable doubt. As in People v. Gonzalez, supra, 51 Cal.3d at page 1215, the prosecutor then could legitimately argue that in order persuasively to cast doubt on the prosecution’s case, the defense of third party culpability would need to identify a possible perpetrator. Accordingly, defendant fails to establish either misconduct or, it follows, ineffective assistance of counsel. (See Strickland v. Washington, supra, 466 U.S. at pp. 691-692 [80 L.Ed.2d at pp. 695-697, 104 S.Ct. 2052].) D. Admission of Photographic Evidence. Defendant contends the trial court erred in admitting, over his objection, photographs depicting the waterbed as it was reconstructed in October 1982. The reconstruction was designed to show that on the day of the crimes Annette May could, as she testified, have looked through a crack in the headboard of the waterbed and identified defendant. The trial court held a hearing, outside the presence of the jury, to determine whether the prosecution had met its burden of showing that the reconstructed waterbed, as depicted in the photographs, was set up in the same manner as on January 1, 1981, and that the conditions in the bedroom were substantially similar to those prevailing on that date. (Evid. Code, § 403.) The trial court ruled there was sufficient evidence from which the jury could find the foundational facts and, accordingly, admitted the photographs. Defendant contends the trial court erred in so ruling. Evidence Code section 403, subdivision (a), provides in pertinent part as follows: “The proponent of the proffered evidence has the burden of producing evidence as to the existence of the preliminary fact, and the proffered evidence is inadmissible unless the court finds that there is evidence sufficient to sustain a finding of the existence of the preliminary fact, when: [^] (1) The relevance of the proffered evidence depends on the existence of the preliminary fact . . . .” The trial court viewed its function as being “to establish whether or not there is any sufficient evidence that could possibly support a finding that the foundational fact exists,” and concluded in the affirmative. Defendant argues the trial court employed an erroneous standard, and that even applying that standard, admission of the photographs was an abuse of discretion. The proper standard is that of preponderance of the evidence. In other words, the trial court must determine whether the evidence is sufficient to permit the jury to find the preliminary fact true by a preponderance of the evidence (People v. Simon (1986) 184 Cal.App.3d 125, 134 [228 Cal.Rptr. 855]), even if the court personally would disagree (People v. Pic’l (1981) 114 Cal.App.3d 824, 860 [171 Cal.Rptr. 106], disapproved on other grounds in People v. Kimble (1988) 44 Cal.3d 480, 498 [244 Cal.Rptr. 148, 749 P.2d 803]). In the present case, the trial court’s paraphrase of Evidence Code section 403 enables us confidently to conclude it understood its obligation under that statute. Further, we are persuaded the court’s ruling was no abuse of discretion. The evidence was ample from which the jury could determine the photographs depicted the waterbed under conditions substantially similar to those prevailing at the time of the offense. Detective Ridenour testified he set up the waterbed in the bedroom, using indentations in the carpet to position it. The photographs were taken around noon, on October 28,1982, using a flash with no lights on in the room, under bright and clear weather conditions. Thus, the reconstruction took place near the same time of day, under similar lighting conditions (barring the camera flash) as prevailed at the time of the offense, although weather conditions evidently were not identical. Furthermore, Annette May identified the photographs as depicting what she saw through the headboard crack at the time of the offenses, and the prosecution introduced a photograph taken on the day of the offense, showing a crack between the waterbed headboard and the base of the waterbed. Thus, the jury could directly compare the reconstruction photographs with those initially taken at the scene of the offense. Even, however, were we to conclude the trial court abused its discretion in admitting the reconstruction photographs, we would hold reversal to be unwarranted, as we are unpersuaded, in light of the other evidence bearing on May’s identification of defendant, a reasonable probability exists the photographs affected the outcome. (People v. Watson (1956) 46 Cal.2d 818, 836 [299 P.2d 243].) In a related claim, defendant argues the trial court erred in failing to instruct the jury, sua sponte, to disregard the reconstruction photographs unless it found the conditions represented in the photographs to be substantially similar to those prevailing at the time of the offense. Evidence Code section 403, subdivision (c)(1), however, provides that if the court admits the evidence, it “[m]ay, and on request shall, instruct the jury to determine whether the preliminary fact exists and to disregard the proffered evidence unless the jury finds that the preliminary fact does exist.” The statute clearly does not contemplate a sua sponte duty to instruct, and we see no abuse of discretion in the court’s failure to do so. The jury was aware the waterbed had been taken down and reconstructed, and that it might not have been put back together exactly as it had originally been set up. Defense counsel presented testimony designed to prove there was no visible crack, and argued the jury should disregard the reconstruction photographs. We see no possibility the jury could have misunderstood its obligation to assess the relevancy of the reconstruction photographs. E. Witness May. 1. Court Questioning. Annette May’s testimony revealed certain intellectual limitations and difficulties in expressing herself. During her cross-examination, she stated she did not know the meaning of the terms “perjury” and “under oath” and did not know what happens if a witness fails to tell the truth under oath. The prosecutor suggested the court voir dire May on her understanding of her duty to tell the truth. Defense counsel joined in the suggestion, and requested voir dire be conducted outside the presence of the jury. The court did not respond to defense counsel’s request, but proceeded immediately to voir dire the witness without excusing the jury. Although May exhibited confusion over some of the terms the court used, she acknowledged her understanding that upon being sworn by the clerk, the law required her to tell the truth and that a witness who lies under oath can be punished. The court denied the motion to disqualify May under Evidence Code section 701. On appeal, defendant acknowledges the trial court did not err in denying the motion to disqualify May. He urges, however, the trial court abused its discretion in failing to voir dire May outside the presence of the jury. Its failure to do so, he contends, surrounded May’s testimony with an undeserved aura of credibility. As defendant implicitly concedes, whether to conduct voir dire outside the presence of the jury was a matter within the trial court’s discretion. (Evid. Code, § 402, subd. (b) [the court “may” determine the admissibility of evidence outside the jury’s presence, but in criminal cases the admissibility of a confession or admission by defendant “shall” be determined outside the jury’s presence on any party’s request].) Defendant fails to persuade us the trial court abused its discretion in not doing so in this instance. We see no possibility the jury might have understood the trial court’s ruling that May was competent as a witness as placing on her “a mantle of judicial approval,” nor any way in which the defense might have been hindered in attacking her credibility. To avoid this very possibility, the trial court admonished the jury that a ruling that certain evidence was admissible in no way implied an endorsement of the witness’s credibility or the weight to be given the testimony. Those matters, the court emphasized, were reserved to the jury. 2. Denial of Psychiatric Examination. Out of the jury’s presence, defense counsel, having unsuccessfully sought a mistrial on the ground that Annette May was incompetent as a witness, moved for an order requiring May to submit to a psychiatric or psychological examination to determine her competency. The trial court denied the motion, expressing its belief a psychiatrist or psychologist could not add anything to what had been accomplished in May’s cross-examination. Defendant concedes the trial court may very well have been justified in denying the motion, but argues we cannot presume from the silent record that the trial court took “appropriate factors” into account in doing so. We find no error in either the trial court’s ruling on the motion or the manner in which it was made. The use of psychiatric testimony to impeach a witness is generally disfavored. (In re Darrell T. (1979) 90 Cal.App.3d 325, 335 [153 Cal.Rptr. 261]; see § 1112 [prohibiting compulsory psychiatric or psychological examination to assess credibility of victim or witness in sexual offense prosecution].) The fact a witness makes inconsistent and exaggerated statements does not compel a different conclusion. (People v. Knox (1979) 95 Cal.App.3d 420, 431 [157 Cal.Rptr. 238].) Defendant fails to enumerate any “appropriate factors” the trial court failed to consider, and we see none on this record. F. Refusal to Permit Rebuttal. Defendant contends the trial court erred in refusing to allow him to call a witness, Irdee Williams, on surrebuttal. After both sides had rested and the prosecutor had begun his guilt phase summation, the trial court allowed defense counsel to reopen in order to present two witnesses (Charles Thompson and Albert Ward) to impeach Kenny Mitchell. Defense counsel then sought permission to present the testimony of Williams, making an offer of proof she would testify that she had lived in the Black community of Modesto for a number of years; that at times relevant to the offenses she was engaged in the sale of new and used clothing; and that in mid-December 1980 she possessed about 150 three-piece white suits, of which she sold about 50 to the Black community and of which 8 were stolen from her in the period preceding Christmas. Defense counsel argued Williams’s evidence would show the prevalence of white suits within the concentrated Black community of Modesto, which in turn would enable him to argue to the jury “the likelihood that it might have been anyone wearing a white suit within that community who entered the home at Locust Street that morning.” The trial judge refused to permit the testimony, stating he did not consider the evidence of sufficient probative value to justify admitting it after the evidence had been, for practical purposes, closed and argument had commenced. Defendant contends the trial court’s ruling denied him his constitutional right to present evidence relevant to his defense theory, and as such constituted an abuse of discretion. (Washington v. Texas (1967) 388 U.S. 14, 19 [18 L.Ed.2d 1019, 1023, 87 S.Ct. 1920]; People v. Burrell-Hart (1987) 192 Cal.App.3d 593, 599 [237 Cal.Rptr. 654].) Although a criminal defendant is constitutionally entitled to present all relevant evidence of significant probative value in his favor, this does not mean the court must allow an unlimited inquiry into collateral matters; the proffered evidence must have more than slight relevancy. (People v. Jennings (1991) 53 Cal.3d 334, 372 [279 Cal.Rptr. 780, 807 P.2d 1009]; People v. Babbitt (1988) 45 Cal.3d 660, 684 [248 Cal.Rptr. 69, 755 P.2d 253].) We review for abuse of discretion a trial court’s ruling on a motion to reopen a criminal case to permit the introduction of additional evidence. (§ 1094; People v. Rodriguez (1984) 152 Cal.App.3d 289, 294-295 [199 Cal.Rptr. 433] [factors an appellate court will consider in reviewing the trial court’s determination include the stage the proceedings had reached when the motion was made, the diligence shown by the moving party in discovering the new evidence, the prospect the jury would accord it undue emphasis, and the significance of the evidence].) We find no constitutional error or abuse of discretion in the trial court’s refusal to permit defendant to present Williams’s testimony. The prosecutor had already begun his summation, and Williams’s testimony would have increased the disruption already occasioned by the appearance of witnesses Thompson and Ward. While it does not appear defendant failed to exercise reasonable diligence in discovering the witness, that the jury would have accorded her testimony much weight seems very unlikely, because its relevance, in our view, was slight. The primary evidence against defendant, Annette May’s identification of him shortly after the shootings, did not hinge on the uniqueness of his white suit. That others in the Black community in Modesto owned white suits did not undermine May’s testimony. Accordingly, we cannot say the trial court erred in declining to reopen the case to permit Williams to testify. G. Refusal to Declare Mistrial. The prosecution tried to establish a motive for the killings through the testimony of Alvin Green. Green had met defendant while defendant and Green’s wife were employed at Gallo Glass Company, and Green worked for defendant at the disco as a security guard and substitute disc jockey for several months until December 1980. On December 31, 1980, Green testified, he spoke with defendant at the disco. Defendant told him he and Cynthia were not getting along, that they were having problems and might be separating. Green elaborated that defendant told him “he was an ex-felon and that so far as the business wise it was in his wife’s name and that if she left him, he would lose everything and that he would see her dead before he lost everything.” Immediately after this testimony the trial court dismissed the jury and allowed defense counsel to voir dire the witness. Green indicated he had discussed his testimony with the prosecutor the preceding night, and the prosecutor did not caution him to avoid mentioning in court that defendant was an ex-felon. Defense counsel objected to both the appearance of prosecutorial misconduct and the introduction of what he claimed was a highly inflammatory and inadmissible statement, and moved for a mistrial. The prosecutor admitted Green had related the “ex-felon” statement to him the previous evening, but contended Green had not told him defendant made the statement during the December 31,1980, conversation in the disco. Had he understood that to have been the case, the prosecutor stated, he would have instructed Green not to mention it in court. The trial court found the evidence did not support a finding the prosecutor had deliberately “set this matter up for the purpose of prejudicing the defendant’s case and that any failure to warn the witness not to mention this was inadvertent.” The trial court eventually denied the motion for mistrial. Under the impression defendant was not, in fact, an ex-felon, the trial court tentatively expressed the view the jury should be instructed defendant was not an ex-felon. Later, still unsure about the nature of defendant’s prior conviction, the trial court expressed an inclination to admonish the jury to consider the ex-felon statement only on the question of motive, if it accorded the statement any weight at all. Defense counsel agreed to submit a draft admonition to the court, but failed to do so. Later, defense counsel acknowledged he had never submitted an admonition because he “couldn’t write one that didn’t do more damage than it cured.” Ultimately, the court granted defense counsel’s motion to strike from the record Green’s ex-felon testimony, and to give no admonition to the jury. The court, however, never actually struck the testimony, which therefore remained in the record for the jury to consider. Defendant now contends his conviction must be reversed because the trial court erred in refusing to grant a mistrial. Defendant argues mistrial was required because (1) Green’s ex-felon statement was extraordinarily prejudicial; (2) the prosecutor knew or should have known Green would make the statement, yet consciously decided not to caution him; and (3) the trial court’s failure to follow through with its stated intention to strike the ex-felon testimony meant the damage was never undone. To the extent the second of defendant’s arguments implies the prosecutor engaged in misconduct, the record refutes it. As the trial court noted, “[Green’s ex-felon statement] was not presented to me in advance and that was not a matter of design by the District Attorney’s office, nor was it done with any knowledge that the witness was going to respond in the particular way that he did respond, and . . . [defense counsel] has indicated while we were off the record that he feels that [the prosecutor] acted in complete good faith in that matter.” Absent any strong contrary evidence in the record, we will not second-guess the trial court’s determination of the prosecutor’s bona Tides. Although finding no prosecutorial bad faith, the trial court concluded that, had the opportunity existed to rule in advance on the admissibility of the ex-felon statement, exclusion would have been appropriate. This conclusion was not an abuse of discretion. The trial court could reasonably find, as it did, that the potential prejudice from the statement outweighed its relevance on the issue of motive. (Evid. Code, § 352.) The question, then, is whether the trial court’s inadvertent failure to strike the “ex-felon” statement relates back, as it were, to the denial of the mistrial motion or, in other words, whether the denial of the mistrial motion can be said to have been conditioned on striking the statement, so that the failure of the condition vitiated the ruling. Nothing in the trial court’s comments suggests it intended the striking of the statement as the sine qua non of its ruling on the mistrial motion. Reviewing the court’s denial of the motion for abuse of discretion, we are unable to conclude the court committed reversible error. True, the solution most agreeable to the defense—striking the ex-felon statement—was not effectuated. Nevertheless, at no time during the subsequent progress of the trial was the jury’s attention recalled to the statement, whether by an (undesired) admonishment, argument of counsel, or otherwise. Moreover, to the extent it supported a theory of motive, Green’s testimony was amply rebutted by evidence showing that most of the property owned by defendant and his wife was in both their names, not, as Green suggested, in Cynthia’s alone. And because defendant had, in fact, been convicted of a felony, the jury was not told a damaging falsehood about defendant’s criminal record. Accordingly, while to strike the statement, as the trial court intended to do, would arguably have been better, we are unable to say its remaining in the record was so prejudicial as to require reversal. H. Refusal to Order Discovery of Witnesses’ Correctional Records. Defendant argues the trial court erred in denying his request for discovery of Department of Corrections records pertaining to prosecution witnesses in general and Gary Brady in particular. We first discuss contentions relating to Brady. Brady testified on direct examination that, while they were both in custody in the Stanislaus County jail, defendant admitted his guilt to Brady. Defense counsel then moved for discovery of Brady’s Department of Corrections file, stating he had been informed Brady had once been committed to Patton State Hospital after a section 1368 competency hearing, and the file was needed to cross-examine Brady effectively as to his mental competency. The trial court denied the motion, commenting Brady had indeed been committed to Patton State Hospital, had escaped, and had been wounded and apprehended in Arkansas. Defense counsel argued the file might contain psychiatric evaluations and other evidence casting light on Brady’s mental capacity to tell the truth. The trial court denied the motion on the basis the material sought was privileged. It acknowledged, however, that if defense counsel furnished some authority to the contrary, the appropriate course would be to conduct an in camera review of the file to determine specific questions of relevancy and privilege. Defense counsel did not renew his discovery motion, but cross-examined Brady extensively on his prior criminal history, his involvement in unrelated crimes, his history of testifying against other defendants in return for favorable treatment