
51 Cal.4th 547 (2011)
In re CURTIS F. PRICE on Habeas Corpus.
No. S069685.
Supreme Court of California.
February 14, 2011.
*549 Jan Nielsen Little, under appointment by the Supreme Court; Karen S. Sorensen; Robert L. McGlasson; Keker & Van Nest, Steven A. Hirsch, Asim M. Bhansali, Steven P. Ragland and Caitlin Bales for Petitioner Curtis F. Price.
Daniel E. Lungren, Bill Lockyer and Edmund G. Brown, Jr., Attorneys General, George Williamson, Robert R. Anderson and Dane R. Gillette, Chief Assistant Attorneys General, Ronald A. Bass and Gerald A. Engler, Assistant Attorneys General, Ronald E. Niver, Glenn R. Pruden, David H. Rose, Ronald S. Matthias, Joyce Blair and Peter E. Flores, Jr., Deputy Attorneys General, for Respondent State of California.

OPINION
KENNARD, Acting C. J. 
A jury convicted petitioner Curtis F. Price of the first degree murders (Pen. Code, § 187)[1] of Elizabeth Ann Hickey and Richard Barnes. As to the murder of Hickey, the jury made special circumstance findings of multiple murder (§ 190.2, subd. (a)(3)) and burglary murder (§ 190.2, subd. (a)(17)(G)), and it fixed the penalty at death. The trial court denied the automatic motion to modify penalty (§ 190.4, subd. (e)) and sentenced petitioner to death. On petitioner's automatic appeal, this court unanimously affirmed the judgment. (People v. Price (1991) 1 Cal.4th 324 [3 Cal.Rptr.2d 106, 821 P.2d 610].)
In a petition for a writ of habeas corpus, petitioner seeks relief from the judgment. He has alleged, among other things, that during the capital trial "the prosecutor in this case improperly tampered with a sitting juror by sending her alcoholic drinks and money, telling her to return a guilty verdict." We issued an order to show cause on this claim only. By limiting the order to show cause to this single claim, we made an implicit determination that petitioner failed to state a prima facie case as to the other claims alleged in the petition. (See In re Sassounian (1995) 9 Cal.4th 535, 547 [37 Cal.Rptr.2d 446, 887 P.2d 527].)
After the filing of respondent's return and petitioner's traverse, we determined that there were disputed questions of fact requiring an evidentiary hearing. We appointed as referee the Honorable W. Bruce Watson, a superior court judge in Humboldt County, and directed him to supervise discovery, take evidence, and make findings of fact on these questions:
"1. During [petitioner's] trial, did then Deputy Attorney General Ronald Bass and Geri Anne Johnson together patronize the Waterfront Cafe in *550 Eureka on an evening when [Juror Z.S.] was cooking at the restaurant and Robert McConkey was tending bar? If so, on approximately what date did this occur?
"2. While at the Waterfront Cafe, did Bass see or directly speak to [Juror Z.S.]? What, if anything, did he say to her?
"3. While at the Waterfront Cafe, did Bass ask McConkey to take any alcoholic drinks to [Juror Z.S.]? If so, did McConkey do so? If Bass did send drinks to [Juror Z.S.], did he know she was an alcoholic or had an alcohol problem?
"4. Did Bass give McConkey any money with the direction or request that it be conveyed to [Juror Z.S.]? If so, what amount of money?
"5. If Bass gave McConkey money for [Juror Z.S.], did McConkey give [Juror Z.S.] the money? Did [Juror Z.S.] accept it?
"6. If Bass gave McConkey money for [Juror Z.S.], did he ask McConkey to convey any message with the money? If so, what message?
"7. Did Bass direct, request or suggest that McConkey convey money to [Juror Z.S.] and tell her to vote guilty in [petitioner's] trial? If so, in what tone of voice did he do so? Did his tone, gestures and other surrounding circumstances suggest that he was serious or joking?
"8. If Bass directed, requested or suggested that McConkey convey money to [Juror Z.S.] and tell her to vote guilty, did he intend that McConkey follow that direction, request or suggestion?
"9. If Bass directed, requested or suggested that McConkey convey money to [Juror Z.S.] and tell her to vote guilty, did McConkey think that Bass actually wanted him to do so?
"10. If Bass directed, requested or suggested that McConkey convey money to [Juror Z.S.] and tell her to vote guilty, did McConkey do so?
"11. Did Johnson tell her husband, Worth Dikeman, about encountering [Juror Z.S.] while at the Waterfront Cafe with Bass? If so, what did she tell Dikeman?"
The referee held an evidentiary hearing over a one-week period during which he heard testimony from 11 witnesses, including Robert McConkey, Geraldine (Geri) Anne Johnson, and Ronald Bass. (Juror Z.S. had died in *551 1989.) The referee then prepared and submitted to this court an eight-page report stating his findings and conclusions. In brief, the referee found that during the guilt phase of petitioner's trial, Johnson and prosecutor Bass did patronize Cafe Waterfront in Eureka on an evening when McConkey and Juror Z.S. were working there. Bass and Johnson sat at the bar, where McConkey served them. Z.S. was cooking in the kitchen, but she came to the bar to give menus to Bass and Johnson. On seeing Z.S., Bass recognized her as a juror, held up his hands, and said he could not have any contact with her. Z.S. then returned to the kitchen. Bass and Johnson remained in the bar, where they had drinks and appetizers. When they finished, Bass paid the bill, which was around $60 to $70, in cash, including a tip in the range of $10 to $20. As he was doing this, Bass told McConkey, in a joking tone of voice, to "give this" or "split this" with Z.S. and "tell her to vote guilty." Bass, Johnson, and bartender McConkey all laughed at this remark, and McConkey understood it as a joke. Bass did not send any alcoholic drink to Z.S. Although McConkey split the tip with Z.S., this was normal practice at the restaurant, and McConkey did not convey any message from Bass to Z.S.
After considering the record of the evidentiary hearing and the referee's report, we conclude that petitioner's claim lacks merit and that the order to show cause should therefore be discharged and, by separate order, his petition for a writ of habeas corpus should be denied.

I. THE TRIAL EVIDENCE
The evidence supporting petitioner's conviction and sentence has been set forth in People v. Price, supra, 1 Cal.4th 324, and is summarized here.
Petitioner belonged to the Aryan Brotherhood, a prison gang. During the summer of 1982, the Aryan Brotherhood's leaders decided to retaliate against Steven Barnes, a prison inmate, for his testimony against Aryan Brotherhood members. Because prison authorities had placed Barnes in protective custody, the Aryan Brotherhood leaders decided to kill his father, Richard Barnes, and they selected petitioner to commit the murder. Petitioner agreed.
Petitioner was released from prison in September 1982. On January 23, 1983, while petitioner was staying in Eureka, in Humboldt County, Richard Moore's gun collection disappeared from his Eureka residence, apparently having been stolen in a burglary. One of the missing weapons was a.22-caliber handgun.
On February 13, 1983, the body of Richard Barnes was found in the bedroom of his house in Temple City, Los Angeles County. He had been killed by three bullets from a .22-caliber handgun that had been held against *552 the back of Barnes's head. The prosecution presented evidence that petitioner was driven to Barnes's house shortly before the murder and that afterwards he sent a note to an Aryan Brotherhood leader saying: "That's took care of. Everything went well."
Back in Eureka, on the morning of February 19, 1983, Berlie Petrie found the body of Elizabeth Ann Hickey, the stepdaughter of burglary victim Moore, in the residence Petrie and Hickey shared. Hickey had been beaten to death with a blunt instrument. Guns and other property belonging to Petrie and Hickey were missing. Some of these items were later found in petitioner's car, and many of the guns stolen from Moore, Petrie, and Hickey were found in a storage locker that petitioner had rented in Reno, Nevada.
At the penalty phase, the prosecution presented evidence that in May 1978, while incarcerated at San Quentin prison, petitioner had stabbed to death Leroy Banks, an African-American inmate, because Banks allegedly had acted disrespectfully to an Aryan Brotherhood gang member. The prosecution also presented evidence of other crimes petitioner had committed, including robbery, escape, and kidnapping.

II. THE REFERENCE HEARING: EVIDENCE AND FINDINGS
The evidence at the reference hearing amply supports the referee's findings that during the Cafe Waterfront incident prosecutor Ronald Bass did not speak to Juror Z.S. about petitioner's case, that he did not send alcoholic beverages or money to her, and that although he told bartender McConkey to give Z.S. money and "tell her to vote guilty," Bass intended and McConkey understood that this was merely a joke.

A. Testimony of Robert McConkey

One night during petitioner's trial, McConkey saw Ronald Bass and Geri Anne Johnson come into the Cafe Waterfront together. McConkey was working as a bartender and waiter; Juror Z.S. was working as a cook. McConkey had known Johnson for a few years as a regular customer of the restaurant. He knew that she was an attorney and that she was married to a deputy district attorney, Worth Dikeman. McConkey had not met Bass before. Petitioner's trial had been reported in the local newspaper and on television and radio, and customers in the Cafe Waterfront had talked about it. McConkey knew that Z.S. was a juror at petitioner's trial.
Bass and Johnson sat down at the bar; they "had a couple of martinis and ordered some appetizers." They stayed about an hour to an hour and a half. At some point, Bass and Johnson became aware that Z.S. was working in the *553 kitchen. Shortly before they left the restaurant, Bass paid the bill, which was around $60 to $70. Bass handed McConkey $10 or $20 as a tip and said, "Here, split this with [Z.S.] for a guilty verdict." The tip amount was appropriate for the food and drinks that had been ordered. Bass had a "big smile on his face," and McConkey had no doubt that he was joking. Bass and Johnson were both laughing. McConkey shared the tip with Z.S. because they routinely shared tips. McConkey may have told Z.S. about Bass's joking remark, but he was not sure that he did.
McConkey did not recall Bass "sharing any kind of drink with [Z.S.] in the kitchen"; indeed, he was "positive" this did not occur. Z.S. was not allowed to drink alcohol at the Cafe Waterfront, and McConkey did not remember ever seeing her do so while the restaurant was open for business. At one time, Z.S. had been in the habit of sitting at the Waterfront's bar and drinking "for a couple of hours" after work, but the owners stopped this practice immediately after McConkey began working there. It was McConkey's responsibility to see that Z.S. did not consume alcohol at the Waterfront.
McConkey described this incident to Gena Eichenberg, an attorney who was one of McConkey's friends. He did not recall telling Eichenberg that Ronald Bass ordered a drink for Z.S., that he (McConkey) delivered a drink to Z.S. in the kitchen, or that Z.S. drank alcohol that night. He did not recall telling petitioner's attorney that "Bass was having drinks sent back to [Z.S.] in the kitchen that evening."

B. Testimony of Geraldine Anne Johnson

During petitioner's trial and at the time of her testimony at the reference hearing, Geraldine Anne Johnson was married to Worth Dikeman, one of the prosecutors at petitioner's trial. Ronald Bass was Dikeman's coprosecutor at that trial. Johnson, an attorney, was the first woman partner in a Humboldt County law firm. One evening during petitioner's trial, she and Bass went to Cafe Waterfront for dinner and drinks after playing racquetball. They sat at the bar and ordered drinks from the bartender, Robert McConkey. When Z.S. approached with menus, Bass sprang up from his seat, went behind Johnson, held up his hands, and said something like "I can't talk to you. I've got to maintain propriety." Z.S. gave the menus to Johnson, suggested ordering crab cakes, and returned to the kitchen. Bass told Johnson that Z.S. was a juror in petitioner's trial.
Johnson and Bass each had two drinks and some food. After they had finished, McConkey brought them the check, which was around $25 or $26. Bass put two $20 bills on the bar, "leaned down fairly conspiratorially," and told McConkey to give one of the bills to Z.S. and "tell her to vote guilty." *554 Bass was smiling and they all laughed "[b]ecause it was clearly a joke." McConkey took the two $20 bills to the cash register, bringing back around $15 in change. Bass left an appropriate tip, then he and Johnson departed. They had been in the restaurant an hour and a half to two hours. To Johnson's knowledge, Bass did not send any drinks to Z.S. in the kitchen.
The next morning, Johnson told her husband, Worth Dikeman, everything that had happened at Cafe Waterfront. Before that evening, Johnson had never met Z.S., but afterward she saw her again at Cafe Waterfront and they waved hello to each other. They also met once in the courthouse. Johnson arrived for a hearing just after the jury in petitioner's case had been dismissed for the day. Z.S. saw Johnson and gave her a hug.

C. Testimony of Ronald Bass

Ronald Bass testified that he remembered very little about the Cafe Waterfront incident. He recalled playing racquetball with Geri Anne Johnson during petitioner's trial and going afterwards to a tavern for drinks and food, but he did not recall the tavern's name or location. He recalled that during petitioner's trial he was in a restaurant when he learned that a woman juror was working there as a cook or waitress, but he did not recall seeing the juror at that time. He did not remember ever sending money or drinks to a sitting juror or asking a juror, outside of the courtroom, to vote guilty. He would never do, and had never done, any of those things.

D. Other Testimony

In addition to McConkey, Johnson, and Bass, petitioner called as witnesses Gena Eichenberg, Sandra Michaels, Oscar Breiling, Rodney Emerson, and Peter Vodopals. Eichenberg and Michaels related prior statements by bartender Robert McConkey about the Cafe Waterfront incident. Oscar Breiling testified about prior untrue statements by Ronald Bass. Rodney Emerson, who is Juror Z.S.'s son, testified about his own criminal record. Peter Vodopals, a retired deputy public defender, testified that the judge who presided at petitioner's trial had asked him to represent Z.S. in a probation revocation matter. Respondent called as witnesses Worth Dikeman, Michael Phelan, and Virginia Bass. Their testimony primarily concerned Bass's character and reputation.
Gena Eichenberg testified that during the spring of 1995 she went to the Cafe Waterfront after work and chatted with bartender Robert McConkey, who said he had a "good lawyer story" for her. McConkey told her that during petitioner's trial, prosecutor Ronald Bass and Geri Anne Johnson had come to the Waterfront. At some point during that evening, Bass gave *555 McConkey $20 and told him to give it to Z.S. and "tell her to vote guilty." McConkey told Eichenberg that he did what Bass had asked him to do. Eichenberg knew that Z.S. had been a cook at the Waterfront and a juror in petitioner's trial.
The next day, Eichenberg reported this conversation to Karen Sorensen, one of petitioner's appellate attorneys. Some months later, in December 1995, Eichenberg asked McConkey to repeat the story to Robert McGlasson. McGlasson was another of petitioner's appellate attorneys, but Eichenberg told McConkey only that McGlasson was "an attorney from out of state." The conversation took place at a bar (not the Cafe Waterfront), and McGlasson bought drinks for himself and McConkey. McConkey told McGlasson "the same exact story" that he had previously told Eichenberg, this time adding that Bass had bought a drink, which McConkey took to Z.S. in the kitchen. A short time later, McGlasson returned to Eureka with an attorney named Sandra Michaels. Eichenberg introduced McGlasson and Michaels to McConkey, but she did not stay to hear their conversation.
Sandra Michaels testified that in 1996 petitioner's attorneys hired her to work on petitioner's case as an investigator. In that capacity, she interviewed bartender Robert McConkey about an incident at Cafe Waterfront involving a juror. The interview took place at "a dark small bar" in Eureka. On entering the bar with Robert McGlasson, she found McConkey sitting with Gena Eichenberg, who left after making introductions. McGlasson explained that he was one of petitioner's attorneys and that Michaels was also working on the case. McGlasson said they needed to talk to McConkey some more about the incident involving Juror Z.S. McConkey said that a prosecutor named Ron Bass and the wife of the other prosecutor at petitioner's trial sat at the Waterfront's bar and had drinks. At some point, Bass asked whether Juror Z.S. was working there that night. When McConkey answered yes, Bass gave him either a $10 or a $20 bill and said, "`Give this to [Z.S.] and tell her to vote guilty.'" McConkey said he then went back to the kitchen, gave the bill to Z.S., told her whom it was from, and relayed the message about voting guilty. But McConkey also told Michaels: "`I thought [Bass] was just kidding and didn't really mean for [Z.S.] to vote guilty.'" McConkey also said that Bass and the wife of the other prosecutor were sending back alcoholic drinks to Z.S. in the kitchen.
Oscar Breiling, a retired investigator for the California Department of Justice, testified that in April 1988 he telephoned Ronald Bass to ask him about a Department of Corrections and Rehabilitation investigator named James Hahn. During that conversation, Bass told Breiling that Hahn had perjured himself while testifying at petitioner's trial, that petitioner's case was almost lost as a result of Hahn's testimony, and that there was a strong *556 possibility that because of Hahn's testimony the conviction would be reversed on appeal. Breiling included this information in a memorandum to his superior, Hugh W. Allen, and he sent copies of the memorandum to Bass and Senior Assistant Attorney General John Gordnier, who was Bass's immediate supervisor.
At Gordnier's request, Breiling arranged a conference call with Bass, during which Bass denied ever telling Breiling that Hahn had perjured himself or that Hahn's testimony had jeopardized petitioner's conviction. Gordnier asked Breiling to prepare a "clarification memorandum" regarding this matter. Shortly after the conference call ended, Bass came to Breiling and said that on further reflection he did recall saying to Breiling that Hahn had committed perjury during petitioner's trial. Breiling asked Bass "to tape record his idea of what took place" so that Breiling could include it in the "clarification memorandum" to Gordnier.
A few days later, Breiling asked Bass when he was going to provide his taped recollection, and Bass said he hoped that in time Gordnier would just forget about it. Bass ultimately gave Breiling a written statement to the effect that, during the conference call with Gordnier, Bass had meant to say he did not remember making the statements to Breiling about Hahn, that upon reflection he was convinced he must have made those statements, that his use of the term "perjury" had been "unfortunate," and that he did not think petitioner's conviction would be reversed because of Hahn's testimony. Apart from this one incident, Breiling had no reason to doubt Bass's honesty.
Rodney Emerson testified that he is the son of Juror Z.S., who died in 1989. He described his criminal record and indicated he had been on felony probation at one time in Humboldt County. His mother drank alcohol but he was not aware of its being a problem.
Peter Vodopals testified that from 1977 to 2007 he was a deputy public defender in Humboldt County. The trial judge at petitioner's trial, Judge Buffington, asked him to help Juror Z.S. with a pending probation revocation arising from a guilty plea in January 1986 to driving under the influence.
Worth Dikeman, husband of Geraldine Anne Johnson and coprosecutor at petitioner's trial, testified that during the trial Johnson told him that she and Ronald Bass had gone for a drink at Cafe Waterfront, where Juror Z.S. worked, and that as Bass was paying the bill he jokingly told the bartender to tell Z.S. to vote guilty. From his wife's account of the incident, Dikeman had no doubt that Bass's remark had been a joke. Johnson did not tell Dikeman of any contact between Bass and Z.S. Dikeman did not discuss the incident with Bass.
*557 Michael Phelan, a retired Court of Appeal justice, testified that he had known Ronald Bass since 1970 when they both worked for the Contra Costa County District Attorney's Office. As a deputy district attorney, Bass had appeared before Phelan when Phelan was a superior court judge in Contra Costa County. Phelan was also acquainted with Bass's reputation in Moraga, California, where both Bass and Phelan lived. Bass's reputation for honesty, integrity, and truthfulness was outstanding.
Virginia Bass, Ronald Bass's younger sister and a lifelong resident of Eureka, testified that he is "one of the most honest people I have ever known" and that he has a good reputation for honesty in Eureka, the town where he grew up.

E. The Referee's Findings

In response to the first question asked by our order of reference (see p. 549, ante), the referee found that the parties agreed, and the testimony confirmed, that Ronald Bass and Geraldine Anne Johnson had together patronized Cafe Waterfront in Eureka on an evening when Juror Z.S. was cooking there and Robert McConkey was tending bar. The referee found that although the exact date was uncertain, this had occurred during the winter of 1985 to 1986, while petitioner's trial was in the guilt phase.
In response to our second question, the referee found that while at Cafe Waterfront, Bass saw and spoke to Z.S. when she brought menus to Bass and Johnson at the bar, and that, according to Johnson's testimony, Bass "held up his hands, moved away from [Z.S.], telling her he could not speak to her, he had to maintain propriety."
The referee found, in response to our third question, that while at Cafe Waterfront, Bass did not ask bartender McConkey to take any alcoholic drinks to Z.S. and McConkey did not do so. The referee explained that Johnson and Bass had testified that no drinks were sent and that McConkey testified he had no recollection of drinks being sent. Although drinks being sent was part of the "`good lawyer story'" that McConkey told to McGlasson and Michaels, he had not mentioned the sending of drinks when he first related the story to Eichenberg. The referee noted that at the hearing McConkey "was under oath ... and appeared to be testifying truthfully," and that Cafe Waterfront's owners had prohibited Z.S. from drinking there.
In response to our fourth question, the referee found that Bass gave McConkey $10 or $20 with a direction to give the money to or split it with Z.S., but also that the money was given as a tip and that the amount was appropriate to the bill, which McConkey had testified was in the range of $60 *558 to $70. The referee found, in response to our fifth question, that it was reasonable to assume that McConkey shared this tip money with Z.S., because he split tips with her in the normal course of business.
In response to our sixth, seventh, and eighth questions, the referee found that Bass did not give McConkey money "to specifically give to [Juror Z.S.] and convey a message," but the referee also found that as he paid the bill and left a tip Bass did say something to the effect of "give her this money and tell her to vote guilty." The referee found that Bass said this in a "joking" tone of voice and that "[t]he manner in which the comment was made, in a conspiratorial fashion with a stranger, the surrounding circumstances of alcohol consumption in a bar, and Mr. Bass having earlier stated to [Z.S.], `I cannot have contact with you,' suggests the intent of the remark was a joke." Thus, "[t]he evidence does not suggest or establish Mr. Bass intended Mr. McConkey follow his suggested statement."
In response to our ninth and 10th questions, the referee found that, as they had testified, both McConkey and Johnson believed that Bass's comment was a joke, and that, although McConkey shared the tip with Z.S., "there is no evidence Mr. McConkey conveyed the joke."
In response to our 11th question, the referee found that Johnson described the incident to her husband, Worth Dikeman, on the morning after it occurred. The referee noted, but did not resolve, the conflict in the testimony of Dikeman and Johnson as to whether Johnson told Dikeman that Bass had seen and spoken to Z.S.
The referee provided this summary of his findings: "On a late fall, winter evening in 1985, during the guilt phase of the trial, Deputy Attorney General Ronald Bass and [Geri Anne] Johnson, attorney and wife of Deputy District Attorney Worth Dikeman, after playing racquetball, went together to the Cafe Waterfront in Eureka. The Waterfront was not busy, the two patrons sat at the bar attended by Robert McConkey. Juror [Z.S.] was cooking in the kitchen. Mr. Bass had not been to the Waterfront before.
"The two ordered drinks, and were offered or inquired as to appetizers. At some point [Z.S.] came from the kitchen area bringing menus.
"Mr. Bass upon seeing [Z.S.] recognized her as a juror, held up his hands, and said in effect, I can't have contact with you, I have to maintain propriety. [Z.S.] left the menus, made a food recommendation, and returned to the kitchen.
"The two ordered and consumed appetizers and alcoholic drinks. The bill at the end of the evening was $60-$70.
*559 "As they were leaving and Mr. Bass [was] paying the bill, Mr. Bass said to Mr. McConkey in a joking, conspiratorial manner, `give this, or split this, money with [Z.S.], and tell her to vote guilty.' The three, Mr. Bass, Mr. McConkey, and Ms. Johnson, then laughed and Mr. Bass and Ms. Johnson left the cafe. The tip was in the range of $10-$20.
"The following morning Ms. Johnson related the encounter with [Z.S.] to Mr. Dikeman.
"Ten years later Mr. McConkey relates, possibly for the first time, his good lawyer story to Ms. Eichenberg. As Mr. McConkey later related the story to Mr. McGlasson and Ms. Michaels, added was Mr. Bass going to the Cafe and asking whether [Z.S.] was working, and ... sending ... drinks to her in the kitchen."

III. LEGAL PRINCIPLES
(1) "Because a petition for a writ of habeas corpus seeks to collaterally attack a presumptively final criminal judgment, the petitioner bears a heavy burden initially to plead sufficient grounds for relief, and then later to prove them." (People v. Duvall (1995) 9 Cal.4th 464, 474 [37 Cal.Rptr.2d 259, 886 P.2d 1252], original italics.) The petitioner "must prove, by a preponderance of the evidence, facts that establish a basis for relief on habeas corpus." (In re Visciotti (1996) 14 Cal.4th 325, 351 [58 Cal.Rptr.2d 801, 926 P.2d 987].)
In a proceeding on a petition for a writ of habeas corpus, this court independently reviews a referee's resolution of legal issues and mixed questions of law and fact. (In re Johnson (1998) 18 Cal.4th 447, 461 [75 Cal.Rptr.2d 878, 957 P.2d 299].) Because the referee observes the demeanor of testifying witnesses, and thus has an advantage in assessing their credibility, this court ordinarily gives great weight to the referee's findings on factual questions. (In re Avena (1996) 12 Cal.4th 694, 710 [49 Cal.Rptr.2d 413, 909 P.2d 1017].) "Deference to the referee is particularly appropriate on issues requiring resolution of testimonial conflicts and assessment of witnesses' credibility, because the referee has the opportunity to observe the witnesses' demeanor and manner of testifying." (In re Hamilton (1999) 20 Cal.4th 273, 296 [84 Cal.Rptr.2d 403, 975 P.2d 600]; accord, In re Lawley (2008) 42 Cal.4th 1231, 1241 [74 Cal.Rptr.3d 92, 179 P.3d 891].)
(2) A criminal defendant's constitutional right to due process of law includes a right to a trial by an impartial jury. (U.S. Const., 6th & 14th Amends.; Cal. Const., art. I, § 16; Irvin v. Dowd (1961) 366 U.S. 717 [6 L.Ed.2d 751, 722, 81 S.Ct. 1639]; In re Hamilton, supra, 20 Cal.4th 273, *560 293.) "In a criminal case, any private communication, contact, or tampering, directly or indirectly, with a juror during a trial about the matter pending before the jury is, for obvious reasons, deemed presumptively prejudicial ... [and] the burden rests heavily upon the Government to establish ... that such contact with the juror was harmless to the defendant." (Remmer v. United States (1954) 347 U.S. 227, 229 [98 L.Ed. 654, 74 S.Ct. 450]; see In re Hamilton, supra, at p. 295 ["a nonjuror's tampering contact or communication with a sitting juror ... usually raises a rebuttable `presumption' of prejudice"].) But "it is virtually impossible to shield jurors from every contact or influence that might theoretically affect their vote," and "due process does not require a new trial every time a juror has been placed in a potentially compromising situation." (Smith v. Phillips (1982) 455 U.S. 209, 217 [71 L.Ed.2d 78, 102 S.Ct. 940].) Rather, "[a]ny presumption of prejudice is rebutted, and the verdict will not be disturbed, if the entire record in the particular case, including the nature of the misconduct or other event, and the surrounding circumstances, indicates there is no reasonable probability of prejudice, i.e., no substantial likelihood that one or more jurors were actually biased against the defendant." (In re Hamilton, supra, at p. 296, original italics.) And "the touchstone of due process analysis in cases of alleged prosecutorial misconduct is the fairness of the trial, not the culpability of the prosecutor." (Smith v. Phillips, supra, at p. 219.)

IV. PETITIONER'S EXCEPTIONS TO THE REFEREE'S REPORT[2]
In his exceptions to the referee's report, petitioner urges us to reject certain of the referee's findings as unsupported by the evidence or as legally irrelevant, or on both grounds. Specifically, petitioner challenges the referee's findings that, during a visit to Cafe Waterfront in Eureka, Prosecutor Ronald Bass did not send alcoholic drinks to Juror Z.S., who was a cook at the cafe; that Bass did not give bartender McConkey money specifically to give to Juror Z.S.; that Bass used a joking tone when instructing McConkey to tell Z.S. to vote for a guilty verdict; that Bass did not intend for McConkey to follow that instruction; that McConkey understood it was a joke; and that McConkey did not convey to Juror Z.S. Bass's statement about voting for guilty. Alternatively, petitioner asks that we grant him additional discovery that the referee denied and that we defer our decision on this claim pending completion of that discovery and the submission of whatever additional evidence petitioner may obtain. As we explain, we reject petitioner's arguments.
As summarized above, the evidence presented at the reference hearing amply supports each of the referee's findings that petitioner challenges.
*561 Although Gena Eichenberg and Sandra Michaels testified that bartender McConkey told them that Prosecutor Bass sent drinks to Juror Z.S., Johnson testified that as far she knew this did not occur, Bass testified in substance that he would never have done such a thing, and bartender McConkey testified that he was "positive" this had not occurred and also that it was his responsibility to prevent Z.S. from drinking alcohol at Cafe Waterfront. The referee found that McConkey "appeared to be testifying truthfully" at the hearing and noted also that McConkey had not mentioned any sending of drinks the first time he related his "good lawyer story" to Eichenberg, thus suggesting that the sending of drinks was something that McConkey invented, when relating the story to McGlasson and Michaels, in an ill-considered attempt to enhance the story's entertainment value.
The referee's findings that prosecutor Bass did not give bartender McConkey money specifically to give to Juror Z.S., and that Bass's remarks on that subject were intended and understood to be a joke, are supported by the hearing testimony of McConkey, Johnson, and Bass. McConkey testified that while handing him $10 or $20 as a tip, Bass told him to "`split this with [Z.S.] for a guilty verdict.'" McConkey understood that Bass was merely joking because Bass and Johnson were both laughing and because the money that Bass handed him was just a normal amount to leave as a tip. Johnson testified that Bass, as he was putting two $20 bills on the bar, "leaned down fairly conspiratorially" and told McConkey to give one of the bills to Z.S. and "tell her to vote guilty." According to Johnson's testimony, they all laughed, and McConkey must have understood it was a joke because, instead of giving one of the bills to Z.S., McConkey took both of the bills to the cash register, deducted the amount owed for food and drink, and returned with the correct change. Bass testified, in substance, that although he did not recall exactly what happened that evening, he would never send money to a sitting juror for a guilty verdict.
The referee's finding that bartender McConkey did not convey to Juror Z.S. the statement by Bass about voting guilty is supported by McConkey's testimony, which the referee found credible, that he did not remember telling Z.S. about Bass's joking remark. It is true that McConkey had earlier testified that he thought he did tell Z.S. what Bass had said about sharing the tip, and that Gena Eichenberg and Sandra Michaels each testified that McConkey, when telling his "good lawyer story," had said that he had given Bass's message to Z.S. But the referee resolved this conflict in the evidence in favor of McConkey's later testimony that he did not remember telling Z.S. what Bass had said. Deferring to the referee on this point (see In re Lawley, supra, 42 Cal.4th 1231, 1241; In re Hamilton, supra, 20 Cal.4th 273, 296), we conclude that petitioner has not carried his burden of proving, by a preponderance of the evidence, that bartender McConkey told Juror Z.S. what Bass had said about wanting Z.S. to vote guilty in petitioner's trial.
*562 Petitioner argues that on this question the referee should have shifted the burden of proof to respondent (the Secretary of the Department of Corrections) "because the State's own wrongdoing had prevented petitioner from securing the testimony of the other eyewitness[Juror Z.S.]before she died." The "wrongdoing" to which petitioner refers is the failure of coprosecutors Ronald Bass and Worth Dikeman to tell the judge presiding at petitioner's trial about Bass's "improper juror contact" with Juror Z.S. But petitioner did not establish any "improper juror contact." The evidence at the reference hearing showed only that as Bass and Geri Anne Johnson were sitting in Cafe Waterfront, Z.S. emerged from the kitchen and approached them with menus. Bass jumped up from his bar stool, moved away from Z.S., and told her that he could not talk to her. Z.S. then made a food recommendation and returned to the kitchen. This brief and accidental meeting did not include any communication of significance. Because the only proven juror contact was not improper, there was no obligation to report it to the judge presiding at petitioner's trial, and thus no basis for shifting to respondent the burden of proof on the question whether bartender McConkey told Z.S. about Bass's joking remark.
In any event, even if we were to find that bartender McConkey did convey Bass's remark to Juror Z.S., the surrounding circumstances indicate there is no substantial likelihood that Z.S., as a result of this incident, was actually biased against petitioner. (See In re Hamilton, supra, 20 Cal.4th 273, 296.) Because McConkey understood that Bass was merely joking when he told McConkey to tell Z.S. to vote for a guilty verdict, Z.S. would have understood from McConkey that Bass made the statement in jest. And because Bass did not send any money or alcohol to Z.S., but merely left a normal tip for the food and beverages that had been ordered, there was no substantial likelihood that Z.S. would have viewed the incident as in any way significant, much less as an attempt to influence her vote. These circumstances are sufficient to rebut any presumption of prejudice that may have arisen from Bass's conduct during this incident.
Petitioner also asserts that this court should grant him discovery that the referee denied and should postpone its decision until that discovery has been completed. Among other things, petitioner seeks to depose the judge who presided at his capital trial, to review the handwritten notes made by Prosecutor Worth Dikeman during Juror Z.S.'s voir dire, and to inspect the probation records of Rodney Emerson (Juror Z.S.'s son). Apart from asserting that he expects the discovery "to yield evidence about what happened at the Waterfront Cafe," petitioner provides no reasoned argument and cites no authority to support a conclusion that the referee abused his discretion in denying the requested discovery. Because the requested discovery appears to have little if any relevance to our reference questions, we conclude that the referee did not abuse his discretion in denying the requested discovery.


*563 V. CONCLUSION AND DISPOSITION
(3) Giving great weight to the referee's credibility determinations, we adopt the referee's factual findings. Based on those findings, we conclude that petitioner has failed to prove by a preponderance of the evidence his claim that during his capital trial in Eureka, Prosecutor Ronald Bass, during a visit to a local restaurant, improperly tampered with Juror Z.S., a cook at the restaurant, by sending her alcoholic drinks and money, or by telling her, outside the courtroom, directly or indirectly, to vote for a guilty verdict.
Because our order to show cause and our reference order were limited to this claim, we do not here address any other claim set forth in the petition, which will be resolved by a separately filed order.
The order to show cause is discharged.
Baxter, J., Chin, J., Moreno, J., Corrigan, J., George, J.,[*] and Sills, J.,[] concurred.
NOTES
[1]  All further statutory references are to the Penal Code unless otherwise indicated.
[2]  Respondent does not take exception to any of the referee's findings.
[*]  Retired Chief Justice of California, assigned by the Chief Justice pursuant to article VI, section 6 of the California Constitution.
[]  Presiding Justice of the Court of Appeal, Fourth Appellate District, Division Three, assigned by the Chief Justice pursuant to article VI, section 6 of the California Constitution.
