
25 P.3d 717 (2001)
200 Ariz. 229
STATE of Arizona, Appellee,
v.
Scott Douglas NORDSTROM, Appellant.
No. CR-98-0278-AP.
Supreme Court of Arizona, En Banc.
June 21, 2001.
*724 Janet Napolitano, The Attorney General, by Kent E. Cattani, Chief Counsel, Capital Litigation Section, Phoenix, and Bruce M. Ferg, Assistant Attorney General, Tucson, Attorneys for the State of Arizona.
Law Office of David Alan Darby, by David Alan Darby, Tucson, Attorneys for Nordstrom.

OPINION
McGREGOR, Justice.

I. FACTS AND PROCEDURAL HISTORY

A. Moon Smoke Shop
¶ 1 On May 30, 1996, shortly after six p.m., four employees were working at the Moon Smoke Shop in Tucson, Arizona. Noel Engles and Steven Vetter stood behind a counter, facing away from the front door, training a new employee, Mark Naiman. The fourth employee, Thomas Hardman, sat in a chair near the back of the store's main room. The employees heard a buzzer indicating the front door had been opened, followed immediately by a gunshot and someone shouting at them to get down. Before dropping to the ground, Engles saw a man with a cowboy hat, glasses, and a mustache, carrying a gun. Engles also noticed another person moving around. As Engles, Vetter, and Naiman crouched behind the counter, they heard and saw someone run toward the back room of the store. The other person approached the counter where Engles, Vetter, and Naiman were crouched, demanding that they open the register and waving his gun, a semi-automatic pistol, over their heads. Naiman opened a nearby register. Their assailant responded by demanding that he open the other register. As Naiman moved toward that register, he heard the robber begin firing shots toward Engles and Vetter, who were still crouched on the floor. Two bullets *725 struck Vetter, one in the face and one in the arm. While these shots were being fired, Engles heard more gunshots and someone in the back room shouting to "get out." When the assailant in the front room began shooting, Naiman glanced back over his shoulder and then fled without opening the second register. Naiman described the shooter as about 5'10", with brownish-blond, shoulder-length hair and a handlebar mustache, wearing a black cowboy hat, sunglasses, jeans, and a dark blue or black striped cowboy shirt. Naiman ran out the front door toward the grocery store and called the police.
¶ 2 After the shooting ceased, Engles left the store through the back door. On his way out, he saw a man he did not recognize lying at the front of the store and Hardman on the floor in the store's back room. Engles ran out the back door and along the rear of the strip mall, yelling for help. As he was running, he saw a light blue pickup truck driving along the back of the strip mall. Although he told police on the scene that he saw two people in the truck, at trial he testified that he was not sure about the number of people in the truck. He also stated that the two people he was sure he saw were seated far apart, one in the driver's position and the other up against the passenger window, and that none of the people in the truck wore a cowboy hat.
¶ 3 Vetter left shortly after Engles did, using the back door. On his way out of the store, he saw the body of a person he did not know on the floor at the front of the store, and Hardman's body lying face down in the back room. The man that neither Engles nor Vetter recognized was Clarence O'Dell, who died of a 9 mm gunshot wound to the head. The shot that killed O'Dell was fired from less than two feet away, and would have incapacitated him immediately.
¶ 4 Thomas Hardman was dead when Engels and Vetter found him in the back room. Two shots from a .380 hit him, one shot fired from several inches away, the other from two to four feet away. One shot would have been immediately disabling and lethal, the other would not necessarily have been fatal or caused unconsciousness. Hardman was found lying face down, but the medical examiner could not determine whether he was shot before or after falling.

B. Firefighters' Union Hall
¶ 5 The Firefighters' Union Hall in Tucson is a firefighters' social club that allows nonfirefighters to join as associate members. The front door to the Hall remains locked, and members gain admittance by inserting a key card into a slot. Members who forget their key cards and non-members can request admittance by ringing a buzzer. The bartender can open the door using a switch at the bar, although patrons often respond themselves by opening the door.
¶ 6 At about nine p.m. on the evening of June 13, 1996, four people were in the bar area at the Firefighters' Hall: the bartender, Carol Lynn Noel, and three customers, Arthur Bell, his wife Judy Bell, and Maribeth Munn. When Munn's partner arrived at the Hall at about nine-thirty p.m., he found all four dead from gunshot wounds. Munn, who still sat on her stool at the bar, had been killed by a 9 mm gunshot fired from a distance of six inches to two-and-a-half feet. Mr. Bell was also still seated at the bar, dead as a result of a 9 mm gunshot to the head. Mr. Bell had a bruise and cut on his face that were inflicted within twenty-four hours of his death. Mrs. Bell was lying on the floor next to a barstool, dead from a 9 mm gunshot to the head. The investigating officers found shell casings on the bar, as well as nicks in the bar, consistent with the gunshots having been fired while Munn and the Bells had their heads resting on the bar. The medical examiner also testified that the gunshot wounds of Munn and Mr. Bell were consistent with this scenario, particularly those of Munn, who was killed by a bullet that also passed through her upper arm.
¶ 7 Noel was found dead behind the bar, lying face down. She had been shot twice with a .380, once in the head and once in the back. Both shots were fired from a distance of approximately three feet. She died as a result of the head wound. The shot to her back would neither have killed her nor caused her to lose consciousness. Noel also had a large laceration on her face, the result of blunt force impact such as that from a fist *726 or a shoe. The wound would have bled significantly, and some of Noel's blood was found in the back room of the bar, on and around the safe, which she could not open.

C. Evidence at Trial
¶ 8 Scott Nordstrom was tried in superior court on twelve counts: six counts of first-degree murder as to Clarence O'Dell, Thomas Hardman, Maribeth Munn, Carol Lynn Noel, Arthur Bell, and Judy Bell; one count of attempted first-degree murder as to Steven Vetter; three counts of armed robbery as to Steven Vetter, Mark Naiman, and Noel Engles; and two counts of burglary in the first degree of the Moon Smoke Shop and the Firefighters' Hall. His trial lasted twenty-three days between October 22 and December 2, 1997, and involved the testimony of sixty-eight witnesses. Robert Jones was tried separately as the other participant in these crimes.[1]
¶ 9 The State relied primarily on the testimony of three witnesses: Carla Whitlock, an eyewitness from the Moon Smoke Shop, who identified the defendant as the last of three men she saw run out of the shop on the night of the robbery; David Nordstrom, the defendant's brother, who claimed to have been the driver at the Moon Smoke Shop and to have heard from the defendant about what happened at the Firefighters' Hall; and Michael Kapp, who claimed that the defendant had solicited him to rob the Firefighters' Hall two years earlier.
¶ 10 The defense presented primarily two types of evidence: evidence suggesting that David Nordstrom had perpetrated the crimes and implicated his brother to protect himself, and alibi evidence for May 30, the day of the Moon Smoke Shop robbery. At the time of these crimes, David was participating in a home arrest program that had allowed his early release from prison. Although the State originally charged David with crimes related to both locations, it dropped all charges related to the Firefighters' Hall crimes when electronic monitoring records showed that David had not violated his curfew on June 13.[2] In an attempt to demonstrate that David could have perpetrated the Firefighters' Hall murders, the defense presented testimony from David's parole officer that revealed problems with parole record-keeping and from witnesses who claimed either that they had seen David out after curfew or had heard him say that he could get curfew extensions whenever he wanted. The defense also presented testimony about David's substance abuse and reputation for dishonesty. The State countered this evidence, in part, with testimony by the parole department supervisor and results from a field test demonstrating that the electronic monitoring system could not be mechanically defeated.
¶ 11 The defendant presented alibi evidence in an attempt to prove that, during the afternoon and evening of May 30, he called friends in Pennsylvania to arrange for the return of some personal items, went to the store with his girlfriend and her son, went to look at a dog that his girlfriend was considering adopting, went to the park for a barbecue, and then called Pennsylvania again. The defendant's girlfriend, her son, and the two owners of the dog testified about the meeting. The defense used their testimony, that of other relatives and friends, and work and telephone records in its attempt to narrow the possible dates for the dog viewing to May 30. The State attempted to impeach these witnesses, several of whom had met to determine the date of the dog viewing, suggesting that while the defendant had indeed gone with his girlfriend and her son to look at a dog, he had not done so on May 30. The defense presented no alibi evidence for June 13.
¶ 12 The jury unanimously convicted the defendant of felony murder on all six counts. The jury also unanimously convicted him of *727 premeditated murder with respect to Thomas Hardman and Carol Lynn Noel, and two members of the jury also found him guilty of premeditated murder with respect to Clarence O'Dell, Maribeth Munn, Arthur Bell, and Judy Bell.
¶ 13 Following a sentencing hearing, the trial judge found three statutory aggravators (F.1, F.5, and F.8), no statutory mitigators, and three non-statutory mitigators (employment history, caring family, and no prior serious felony convictions). The judge sentenced the defendant to death, and the court clerk filed this automatic appeal pursuant to Arizona Rule of Criminal Procedure 31.2.b. We exercise jurisdiction under Arizona Constitution Article 6, Section 5.3, and affirm the defendant's convictions and sentences.

II. TRIAL ISSUES

A. Change of Venue
¶ 14 Defendant sought a change of venue several months before trial. The trial court found that he had not made a sufficient showing of bias on the part of the public due to media coverage and denied the motion, indicating that the defense could later renew its motion if appropriate. In considering a motion for change of venue, the court is concerned with the effect of pretrial publicity, rather than its quantity. State v. Jones, 197 Ariz. 290, 307 ¶ 44, 4 P.3d 345, 362 ¶ 44 (2000) (citing State v. Greenawalt, 128 Ariz. 150, 162, 624 P.2d 828, 840 (1981) and State v. Murray, 184 Ariz. 9, 26, 906 P.2d 542, 559 (1995)). We will not overturn a trial court's ruling on a motion for change of venue due to prejudicial pretrial publicity absent an abuse of discretion and prejudice to the defendant. Murray, 184 Ariz. at 26, 906 P.2d at 559.

1. Presumed Prejudice
¶ 15 To obtain a change of venue, a defendant must show "pretrial publicity so outrageous that it promises to turn the trial into a mockery of justice or a mere formality." State v. Bible, 175 Ariz. 549, 563, 858 P.2d 1152, 1166 (1993). This is a heavy burden, infrequently met. 175 Ariz. at 564, 858 P.2d at 1167. The court must disregard the results of voir dire in this inquiry and reach its own conclusion based on the totality of the circumstances. 175 Ariz. at 565, 858 P.2d at 1168. In considering a motion for change of venue, the court considers the effect of pretrial publicity, rather than its quantity, and first examines whether the publicity created a presumption of prejudice. Jones, 197 Ariz. at 307 ¶ 44, 4 P.3d at 362 ¶ 44 (citing Greenawalt, 128 Ariz. at 162, 624 P.2d at 840 and Murray, 184 Ariz. at 26, 906 P.2d at 559). Presumed prejudice exists only when publicity is so unfair, pervasive, and prejudicial that the court cannot give credibility to the jurors' attestations, during voir dire, that they could decide fairly. Bible, 175 Ariz. at 565, 858 P.2d at 1168. We have been reluctant to presume prejudice if publicity was primarily factual and non-inflammatory or if the publicity did not occur close in time to the trial. See Jones, 197 Ariz. at 307 ¶ 45, 4 P.3d at 362 ¶ 45; Bible, 175 Ariz. at 563-64, 858 P.2d at 1166-67; State v. Befford, 157 Ariz. 37, 39, 754 P.2d 1141, 1143 (1988).
¶ 16 The facts here indicate that the trial court did not abuse its discretion in failing to find presumed prejudice sufficient to require a change of venue. The proffered newspaper articles and newscast excerpts were not particularly inflammatory or biased. Most described the place and time of the murders and listed the names of the victims. Few addressed the manner in which the murders were committed, with the exception of isolated comments about their "brutal" nature. Some of the articles discussed the effect of the murders on the families and friends of the victims. The most emotionally stirring of these accounts, however, as well as most of the police statements about the brutal nature of the crime, appeared soon after the time of the murders, some fifteen to sixteen months before the trial.
¶ 17 The more troubling publicity took place near the time of the defendant's arrest in February, eight months before trial. The Tucson Police Department initially arrested the defendant and his brother David Nordstrom for the murders. Newspaper and television accounts of the brothers' arrest discussed their prior criminal records, their histories of drug and alcohol abuse, and their negative reputations in the community. *728 Some accounts included speculation about the reason their mother left her position as a bartender at the Firefighters' Hall. Others reported comments by Firefighters' Hall members asserting that they believed the Nordstrom brothers could have committed the murders and resembled the police sketches. Some of the information in these newspaper accounts was erroneous, and some of it was inadmissible at trial. Cf. Bible, 175 Ariz. at 564, 858 P.2d at 1167. However, this publicity occurred many months before trial, and the parties presented much of the information in this group of articles as evidence at trial. Based on the information before it, the trial judge acted within his discretion in refusing to presume prejudice.[3]

2. Actual Prejudice
¶ 18 To determine whether actual prejudice sufficient to justify a change of venue existed, we examine the effect of the publicity on the jurors' objectivity. State v. Murray, 184 Ariz. 9, 26, 906 P.2d 542, 559 (1995). A defendant "must show that the jurors have formed preconceived notions concerning the defendant's guilt and that they cannot lay those notions aside." State v. Chaney, 141 Ariz. 295, 302, 686 P.2d 1265, 1272 (1984). This defendant has not made such a showing.
¶ 19 The trial judge took several steps to discover and excuse potential jurors with preconceived notions of guilt. Prospective jurors answered a questionnaire that probed their exposure to media coverage of the case and the extent to which they could lay that information aside in rendering a verdict; the court removed thirty-seven of the two hundred prospective jurors because of their responses.[4] After removing these jurors, the trial judge again questioned the remaining jurors about their ability to be fair, given the information they may have gained from the media. No juror's response required his or her removal.[5] During his instruction of the selected jury, the trial judge emphasized that the jurors must carefully avoid all media accounts of the trial. To ensure that the jurors did not inadvertently disobey the admonition, the judge instructed them to entirely avoid radio or television news broadcasts on any topic. The trial judge reminded the jurors of this admonition at breaks in the trial, and repeated it in detail on later occasions. The defendant has failed to show that the trial court abused its discretion.

B. Testimony of Identification Witness
¶ 20 Carla Whitlock appeared as one of the State's three primary witnesses. According to her testimony, she parked her car in front of the Moon Smoke Shop shortly after six p.m. on May 30, 1996. As she pulled into a parking space, she saw three men run out of the store in fairly rapid succession. The first man ran in the direction of the shopping center. The next two men ran the opposite direction, around the back of the building. Whitlock testified that, while she did not pay much attention to the first two men, her suspicion and attention grew with each successive exit. Hence, she paid more attention to the third man to leave the shop. That man paused in the doorway of the shop and looked toward the shopping center, the direction in which the first man had run. He then turned back toward the direction in which the second man had run. As his head turned, he saw Whitlock looking at him and stopped to look back at her. They stared at each other for less than a minute. The man then ran around the back of the building.
¶ 21 Whitlock worked with a sketch artist to produce a drawing of the third man, provided *729 a description of him, and participated in numerous photo lineups. She noted the similarity of some photos in the lineups to the man she had seen, but did not identify anyone. In the late fall of 1996, when she saw news photos of two men the police suspected of being the robbers, she called the investigating officers to tell them that neither of the men they suspected was the man she had seen.
¶ 22 After the defendant was arrested, the police showed Whitlock a photo spread that included the defendant and his brother, David Nordstrom. She did not identify anyone in that lineup. Network news programs shortly thereafter showed the arraignment of the defendant and his brother. Within the next two days, Whitlock called the investigating officer to say that the defendant was the third man she saw. She said she recognized him because he looked into the camera in the same way that he had looked at her on the day of the robbery. She claimed to have seen a news segment in which the defendant, dressed in an orange jumpsuit, was standing in a hallway and turned to face the camera. After reviewing all the news broadcasts about the defendant's arraignment, however, the parties stipulated that none of those broadcasts showed the defendant standing in a hallway and turning to face the camera.
¶ 23 The defendant challenges the admissibility of Whitlock's identification testimony as impermissibly tainted and unreliable. The due process clause of the Fourteenth Amendment requires that pretrial identifications be conducted in a fundamentally fair manner to secure the defendant's right to a fair trial. Stovall v. Denno, 388 U.S. 293, 297-98, 87 S.Ct. 1967, 18 L.Ed.2d 1199 (1967). In cases in which a witness's pre-trial identification is problematic, the likelihood of misidentification raises due process concerns. Neil v. Biggers, 409 U.S. 188, 198, 93 S.Ct. 375, 34 L.Ed.2d 401 (1972). To establish that the admission of identification testimony violated his due process rights, a defendant must show "that the circumstances surrounding the pretrial identification `created a substantial likelihood of irreparable misidentification' " and that the state was "sufficient[ly] responsible[ ] for the suggestive pretrial identification to trigger due process protection." State v. Williams, 166 Ariz. 132, 137, 800 P.2d 1240, 1245 (1987) (quoting Simmons v. United States, 390 U.S. 377, 384, 88 S.Ct. 967, 19 L.Ed.2d 1247 (1968)).
¶ 24 In this case, however, the media, rather than the State, allegedly tainted Whitlock's identification of the defendant. Because the state action requirement of the Fourteenth Amendment therefore cannot be established, due process analysis is inapposite. Shelley v. Kraemer, 334 U.S. 1, 13, 68 S.Ct. 836, 92 L.Ed. 1161 (1948).
¶ 25 Recognizing that shortcoming in his argument, the defendant argues that our opinion in State v. Atwood, 171 Ariz. 576, 832 P.2d 593 (1992), suggests that we require a Biggers analysis even absent an allegation that state action tainted an identification. Some statements in Atwood indeed suggest that the Biggers analysis applies even to private suggestive identification procedures. 171 Ariz. at 602-03, 832 P.2d at 619-20. To the extent that Atwood permits that conclusion, we disapprove it. Only identification evidence allegedly tainted by state action must meet the reliability standard articulated in Biggers. Whitlock's identification, therefore, was not subject to a Biggers analysis.
¶ 26 Our conclusion does not mean that due process concerns can never be implicated in the absence of state action. As we recognized in Williams, "it is conceivable that the due process clause prohibits identification testimony that falls below some minimal threshold of reliability when the defendant's right or ability to bring the testimony's weaknesses to the jury's attention is somehow restricted," even though state action is not present. Williams, 166 Ariz. at 138, 800 P.2d at 1246. That concern arises when evidence lacking in foundation reaches the jury under circumstances that do not afford a defendant an opportunity to point out its weaknesses.[6] The admission *730 of Whitlock's testimony, however, does not raise the concern referred to in Williams. The defendant thoroughly cross-examined Whitlock, pointing out inconsistencies between her description and the defendant's appearance, noting factors that might have made it difficult for her to observe and remember, and introducing a stipulation that the news broadcast as she described it did not exist. In addition, the defendant presented the conflicting testimony of Whitlock's husband, testimony about the defendant's significant weight loss between the summer of 1996 and his arraignment in 1997, and expert testimony about reliability problems associated with eyewitness accounts.
¶ 27 Moreover, Whitlock's testimony was sufficiently reliable to meet threshold requirements. Although Whitlock's description of the third man she saw leave the Moon Smoke Shop differs significantly from the defendant's physical appearance at the time of the crime, she stated that she was focused on the man's face, was largely unable to see his body because he was standing behind a door, and that she is not good at estimating height and weight. In addition, an eyewitness identification expert testified to the tendency of witnesses, particularly females, to not notice facial hair. Whitlock testified to her certainty that the defendant is the man she saw, her unobstructed view of the third man under good conditions for a sufficient period of time, and her degree of attention, which she described as high but not inhibited by excessive fear or anxiety. Whitlock's identification testimony, therefore, meets the threshold standard of minimum reliability articulated in Williams. Any weakness in her testimony goes to its weight and credibility, both matters for the jury to consider. The trial court did not abuse its discretion in admitting her identification testimony.

C. Limitation of Expert Testimony
¶ 28 The defendant challenges the trial court's limitation of the testimony of three of its expert witnesses: Dr. Thomas MacSpeiden, an expert on eyewitness testimony; Dr. Phillip Kanof, an expert on the neuroscience and pharmacology of drug abuse; and Jeanne Boylan, a facial identification specialist.
¶ 29 The court can admit relevant expert testimony that meets four criteria: the expert is qualified, the subject is a proper subject of expert testimony, the opinion conforms to an appropriately scientific explanatory theory, and the unfair prejudicial effect does not outweigh the probative value. State v. Chapple, 135 Ariz. 281, 291, 660 P.2d 1208, 1218 (1983). We review rulings on evidentiary issues for abuse of discretion. State v. Atwood, 171 Ariz. 576, 634, 832 P.2d 593, 651 (1992).

1. Dr. MacSpeiden
¶ 30 Dr. MacSpeiden testified at length about the various factors that affect the ability of an eyewitness to observe, the effects of time on the reliability of eyewitness memory, and the accuracy of eyewitness identification. Dr. MacSpeiden also described a number of features of eyewitness identification that bore directly on this case: no correlation exists between certainty and accuracy, "squinting eyes" are not a distinctive feature of the type the human brain uses to process information about the human face, people have a remarkable ability to remember that they have seen a face before but an ability to remember where they have seen that face no greater than chance, anxious people exhibit an impaired ability to observe and overestimate duration, and post-event information such as a lineup or a statement of certainty that the right person has been apprehended can influence the content of memory. The trial court, however, precluded Dr. MacSpeiden from expressing any opinion about the accuracy of Whitlock's eyewitness testimony and from addressing the specifics of this case.
¶ 31 This court first permitted expert testimony about eyewitness observation in State v. Chapple, 135 Ariz. 281, 296-97, 660 P.2d 1208, 1223-24 (1983). As the Chapple court emphasized, that testimony was appropriate because it was "limited to an exposition of the factors affecting reliability ... and no attempt was made to have the witness render opinions on the actual credibility or accuracy of the identification witnesses." Chapple, *731 135 Ariz. at 295, 660 P.2d at 1222. We specifically cautioned that expert witnesses should not be allowed to give their opinion of the accuracy or credibility of a particular witness. Chapple, 135 Ariz. at 297, 660 P.2d at 1224; see also State v. Lindsey, 149 Ariz. 472, 475, 720 P.2d 73, 76 (1986); State v. Via, 146 Ariz. 108, 123, 704 P.2d 238, 253 (1985). Applying those principles, we conclude the trial court appropriately limited Dr. MacSpeiden's testimony.

2. Dr. Kanof
¶ 32 The trial court allowed Dr. Kanof to testify about the effects of methamphetamine usage on perception and memory, but prohibited him from discussing any tendency of methamphetamine users to be violent, paranoid, or aggressive. The defense sought to introduce additional testimony about the violent tendencies of methamphetamine users, as well as information that David Nordstrom had used methamphetamine some time between June 11 and June 15, 1996, to bolster its argument that David was the perpetrator of the Firefighters' Hall crimes. Character evidence may not be introduced to show that a person acted in conformity with that character on a particular occasion. Ariz. R. Evid. 404(a); State v. Watkins, 126 Ariz. 293, 299, 614 P.2d 835, 841 (1980). In this case, the proposed testimony from Dr. Kanof, which the trial court prohibited, constitutes impermissible character evidence. The court did not abuse its discretion in excluding this testimony.

3. Jeanne Boylan
¶ 33 Jeanne Boylan, a facial identification expert and sketch artist, worked with Carla Whitlock to prepare a sketch of the third man to exit the Moon Smoke Shop after the robbery. At trial, she testified about how Whitlock described the third man, about Whitlock's demeanor during their conversation, and about Whitlock's satisfaction with the resulting drawing. Defense counsel attempted to ask Boylan whether, in her expert opinion, the defendant's appearance as shown in a family picture taken near the time of the murders was consistent with the description that Whitlock gave of the third man to leave the shop, particularly to the extent that Whitlock described the man as "slim." The trial judge disallowed this opinion testimony, but permitted the defense to elicit testimony about how Whitlock herself explained what she meant by "slim" during her interaction with Boylan.
¶ 34 We permit expert testimony when it assists the jury "to understand the evidence or to determine a fact in issue." Chapple, 135 Ariz. at 292, 660 P.2d at 1219. To determine whether expert testimony is proper on a particular subject, the court considers whether the subject is one of common knowledge about which the jury can form an opinion as well as can the witness. Id. Boylan's prohibited testimony falls outside the bounds of expert testimony. Boylan was no more qualified than the jurors to determine what Whitlock meant when she described the third man as "slim" or to compare Whitlock's description to the defendant's appearance. The trial court did not abuse its discretion in restricting Boylan's testimony.
D. Refusal to Admit Impeachment Evidence Against David Nordstrom
¶ 35 David Nordstrom, the defendant's brother, was the most important of the State's three major witnesses. He testified that, on May 30, 1996, he accompanied the defendant and Robert Jones to the Moon Smoke Shop, which Jones suggested they rob. When David told Jones he did not want to participate, Jones told him to wait in the truck. David stayed in the truck, which Jones parked behind the shop, while Jones and the defendant ran around the front, armed with 9 mm and .380 semi-automatic handguns, respectively. David heard shots, and then saw Jones and the defendant come running back to the truck. As David drove out of the shopping center, Jones and the defendant told him that they had each shot a person. Jones, the defendant, and David split the money acquired in the robbery.
¶ 36 David also testified that on June 13, 1996, the defendant asked him to meet with some people. David refused because of his home arrest curfew. Late that night, Jones came to David's house, woke him up, and told *732 him about the Firefighters' Hall murders. The next morning, the defendant told David about the murders, including that he had stolen Arthur Bell's wallet and that he had kicked the bartender when she was unable to open the safe in the back room. David also testified that he went with the defendant and Jones to ponds outside Tucson, where they disposed of the guns used in the robberies, and that he accompanied the defendant to another desert location that the defendant checked to make sure no evidence remained of Arthur Bell's wallet, which he had burned at that location.
¶ 37 The defense thoroughly impeached David with inconsistencies and lies in the series of statements he made to the police, with his early attempts to avoid implicating himself or his brother in these crimes, with his multiple prior felony convictions and parole violations, with an uncharged robbery that he had committed with Jones before the defendant was released from prison, with the potential impact of his frequent drug and alcohol use on his memory, and with the plea bargain pursuant to which he was testifying. In addition, the defense presented evidence that David could have committed the Firefighters' Hall murders because even though he was on electronic monitoring and the murders were committed after his curfew, he could have received an unrecorded curfew extension. The defense alleges error in the trial court's refusal to allow David's impeachment with five additional facts: an arrest for false information to a police officer in 1988, a 1989 forgery conviction, an alleged assault, positive drug tests while on probation in 1992-93, and his manipulation of curfews while on probation in 1992-93.
¶ 38 The defendant waived error as to the first three items, which the defense never offered as impeachment. Rather, the defense requested that the court order David to answer questions about these allegations during a deposition. The trial court denied the motion but noted that the defense could ask David about these matters during cross-examination. The trial court never precluded the defense from doing so, and the defense made no attempt to do so.
¶ 39 The two remaining items of potential impeachment, which relate to David's conduct during a previous probation in 1992-93, involve areas that the trial court precluded the defense from addressing during cross-examination. The trial court based its decision on the remoteness of these matters and the amount of evidence introduced about David's misconduct during his more recent probationary period. The trial court did not abuse its discretion in finding that these remote matters constituted an unnecessary use of the court's time. Moreover, any error was harmless given the thoroughness with which David was impeached.

E. Letter Found in Defendant's Home
¶ 40 After arresting David Nordstrom and taking a statement from him in which he implicated the defendant, the police obtained and executed a search warrant for the defendant's home. During their search, they found an unmailed letter from the defendant to Robert Jones, who at the time was incarcerated in Phoenix awaiting trial on unrelated capital charges.[7] The trial court admitted the letter after one of the officers who conducted the search provided a foundation and the parties stipulated that the defendant had written the letter. The State argued that the letter established two matters: the relationship between the defendant and Jones and the defendant's belief that one who commits a robbery should kill all the witnesses.
*733 ¶ 41 The defendant objected to the letter on four grounds: that the search warrant under which the police found it was constitutionally invalid under Franks v. Delaware, 438 U.S. 154, 98 S.Ct. 2674, 57 L.Ed.2d 667 (1978); that the police failed to comply with the statutory and constitutional requirement that they knock and announce their presence before executing that search warrant; that the letter should have been suppressed as more prejudicial than probative; and that the court should have given a limiting instruction with regard to the letter. We address each of these challenges.

1. Sufficiency of Affidavit
¶ 42 In Franks, the Supreme Court held that a search pursuant to a warrant obtained by false statements can violate the Fourth Amendment. 438 U.S. at 155-56, 98 S.Ct. 2674. A trial court must suppress evidence seized pursuant to a warrant if a defendant proves, by a preponderance of the evidence, that the affiant knowingly, intentionally, or with reckless disregard for the truth made a false statement to obtain the warrant and that the false statement was necessary to a finding of probable cause. Id.; State v. Spreitz, 190 Ariz. 129, 145, 945 P.2d 1260, 1276 (1997).
¶ 43 After conducting a Franks hearing, the trial court found that the police officer who had sworn out the affidavit for this warrant did not knowingly, intentionally, or recklessly include false statements or make omissions. We review a trial court's finding on this issue for clear error. State v. Buccini, 167 Ariz. 550, 554, 810 P.2d 178, 182 (1991).
¶ 44 Some of the information the defense alleges the officer should have added was not correct, based on the information that the police officer had at the time of the affidavit.[8] Other information that the defense would have added to this affidavit was not significant to the finding of probable cause, and its omission was therefore not misleading.[9] Including an assertion that "[t]he Informant stated that in the past, Scott Nordstrom had discussed robbing the Fire Hall," without indicating that the informant's knowledge of such discussions was secondhand, raises the most troubling question. With regard to this statement, however, the police officer's testimony supports the conclusion that he did not intend to mislead the issuing judge or even entertain "serious doubts about the truth of the affidavit" in this regard. State v. Carter, 145 Ariz. 101, 109, 700 P.2d 488, 496 (1985) (defining the standard for reckless disregard for the truth). In addition, David Nordstrom's statements to police corroborated information received from the confidential informant. See Illinois v. Gates, 462 U.S. 213, 242, 103 S.Ct. 2317, 76 L.Ed.2d 527 (1983) (noting the value of corroboration of details of an informant's tip). We conclude that the trial court did not commit clear error in finding that the police officer was not recklessly, knowingly, or intentionally deceitful in failing to include the information that the defense offered in its redrafting of the search warrant affidavit. The Franks inquiry ends here.

2. Knock and Announce Requirement
¶ 45 Absent exigent circumstances, the Fourth Amendment requires police officers to knock and announce their presence before entering a home to serve a search warrant. Wilson v. Arkansas, 514 U.S. 927, 934, 115 S.Ct. 1914, 131 L.Ed.2d 976 (1995). Arizona Revised Statutes (A.R.S.) section 13-3916 codifies this constitutional requirement: "An officer may break *734 into a building ... to execute the warrant when ... [a]fter notice of the officer's authority and purpose, the officer receives no response within a reasonable time ... [or] the officer is refused admittance." A.R.S. § 13-3916.B.1 and .2 (2001). If an officer violates this requirement, evidence obtained in the search is inadmissible. State v. Brady, 105 Ariz. 592, 594, 469 P.2d 77, 79 (1970).
¶ 46 At the time the police served this warrant, Arizona's statute did not contain an exception for exigent circumstances. Our courts, however, had read in that exception, and the legislature has since added it to the statute. A.R.S. § 13-3916.B.4 (2001). In State v. Bates, we held that, while the statute dictated that police officers must wait a "reasonable time" before forcing entry, what constitutes a reasonable amount of time depends on the circumstances of each case. 120 Ariz. 561, 562, 587 P.2d 747, 748 (1978). In Bates, we cautioned against blanket rules, such as allowing police to force entry almost immediately in all drug cases simply because of the easily disposable nature of drugs. Instead, we require that substantial evidence in a particular case support the finding of exigency justifying forcible entry. Bates, 120 Ariz. at 563, 587 P.2d at 749; see also State v. Mendoza, 104 Ariz. 395, 400, 454 P.2d 140, 145 (1969). To this point, we have addressed the availability of an exigent circumstances exception only in cases in which the exigency at issue involves the potential destruction of evidence. Bates, 120 Ariz. at 563, 587 P.2d at 749. Federal courts and the Arizona Court of Appeals have held that a risk to officers also can constitute an exigent circumstance, and have applied the exception in cases in which police officers reasonably suspected a defendant of a particularly violent crime, had reason to believe that the defendant was armed, or had reason to believe that the defendant might be aware of the police plan so as to arm himself or plan a response. Richards v. Wisconsin, 520 U.S. 385, 394, 117 S.Ct. 1416, 137 L.Ed.2d 615(1997); Wilson v. Arkansas, 514 U.S. 927, 936, 115 S.Ct. 1914, 131 L.Ed.2d 976 (1995); United States v. Reilly, 224 F.3d 986, 991 (9th Cir.2000); Thompson v. Mahre, 110 F.3d 716, 723 (9th Cir.1997); State v. Piller, 129 Ariz. 93, 96, 628 P.2d 976, 979 (App.1981). We are persuaded by their reasoning, and hold that danger to officers can constitute an exigent circumstance that may justify forcible entry shortly after the officers knock and announce their presence.
¶ 47 We turn then to whether the circumstances surrounding the execution of this warrant justified these officers' forcible entry only a few seconds after knocking and announcing their presence. For a rapid forcible entry to be justified, the officers must do more than presume that some negative consequence will result from waiting. They must possess substantial knowledge that causes them to believe that waiting would be dangerous, futile, or lead to the destruction of evidence. Here, the police were entering the defendant's home to arrest and search a person suspected of having killed six unresisting victims on two separate occasions. Knowing that officers had served a search warrant at the home of the defendant's brother and father only a few hours before, and that friends and family of the defendant present at the earlier search could have notified the defendant, the police reasonably could believe that the defendant expected them and might have prepared to resist. Although the police also possessed information that the defendant had disposed of the particular firearms used in the robberies and that the defendant was recovering from a serious stabbing injury, neither of these circumstances would have prevented the defendant from acquiring additional firearms or reacting violently to the arrival of the police. The trial court did not abuse its discretion in denying the defense motion to suppress.
3. Motion to Preclude Use of the Letter at Trial
¶ 48 The State sought to admit the defendant's letter to Jones for two reasons: to show the relationship between Jones and the defendant and to provide evidence that the defendant believed that one who robs should kill all witnesses. The defense objected, arguing that the letter is irrelevant, hearsay, and unfairly prejudicial.
¶ 49 We agree with the trial court that the letter provides evidence of the relationship *735 between Jones, alleged to be the other participant in these crimes, and the defendant. The defendant placed their relationship at issue. As part of the defendant's argument that David Nordstrom actually committed these crimes, defense counsel questioned witnesses who knew Jones, the defendant, and David about who had introduced them to Jones and the frequency with which they saw Jones with David or with the defendant. Through this questioning, the defense attempted to argue that David, as a closer friend of Jones, was more likely than the defendant to have been Jones' collaborator in these crimes. Evidence showing that the defendant corresponded with Jones in prison, offered to do favors for him, and kept Jones abreast of his medical condition relates to the relationship between the defendant and Jones, and therefore meets the definition of relevance: evidence that makes a fact in issue more or less probable. Ariz. R. Evid. 401. The letter is not hearsay, because the State offered the letter not for the truth of its statements but for the fact of the correspondence and because the letter, offered against the defendant, is his own statement. Ariz. R. Evid. 801.
¶ 50 Whether the letter is relevant to the defendant's beliefs about eliminating witnesses presents a closer question. The State's interpretation of the letter is weak at best; the defendant could have been referring to any number of things when he expressed his anger at Jones for "not taking care of things the way we talked about." The State's proposed speculation about the letter's meaning raises concern about the letter's unfairly prejudicial effect or tendency to confuse the jury. See Ariz.R.Evid. 403. The vagueness of the letter, however, also allowed the defendant to argue his own interpretation of it, which tended to offset the State's weak argument. We conclude that any prejudice that resulted is minimal, particularly when weighed against the letter's probative value on the important issue of the defendant's relationship with Jones. We conclude, therefore, that the trial court did not abuse its discretion in admitting the letter.

4. Failure to Give Limiting Instruction
¶ 51 The defendant also alleges the trial court erred by failing to give a limiting instruction regarding the letter. On multiple occasions, the trial court invited defense counsel to fashion a limiting instruction, but counsel did not do so, stating that they were unable to formulate an instruction that addressed their concerns. A limiting instruction would have been appropriate under Rule 105, which provides that when evidence is admissible for a limited purpose, the court should so instruct the jury. However, the trial court does not err in failing to give a limiting instruction if trial counsel does not properly request an instruction. State v. Hyde, 186 Ariz. 252, 278, 921 P.2d 655, 681 (1996); State v. Atwood, 171 Ariz. 576, 629, 832 P.2d 593, 646 (1992); State v. Mincey, 141 Ariz. 425, 434, 687 P.2d 1180, 1189 (1984). We find no error.

F. Testimony of Michael Kapp
¶ 52 Michael Kapp testified that the defendant tried to convince him to rob the Firefighters' Hall during the summer of 1994. The defendant ostensibly told Kapp that his mother formerly tended bar at the Firefighters' Hall and that the safe in the back was always kept open. The defendant suggested that they rob the bar on a Monday morning, when business was light but the safe would have the money from the busy weekend. Kapp testified that he and the defendant went to the Firefighters' Hall so that the defendant could try to gain admittance to the hall, in preparation for the actual robbery. Kapp also testified that the defendant said they would have to kill anyone who knew him and was present during the robbery.
¶ 53 The defense impeached Kapp with his prior felony convictions, the plea agreement pursuant to which he was testifying, and allegations that he had been dealing drugs in prison and was testifying in order to get out before other prisoners hurt him for taking their money and not giving them drugs. The defendant asserts the trial court erred in admitting Kapp's testimony about being solicited to assist in the robbery and in precluding certain impeachment evidence.
*736 1. Motion to Preclude
¶ 54 Four provisions of the rules of evidence govern admission of prior bad act evidence: Rule 404(b) requires that the evidence be admitted for a proper purpose, Rule 402 requires that the evidence be relevant, Rule 403 requires that the danger of unfair prejudice not outweigh probative value, and Rule 105 requires that the judge give an appropriate limiting instruction upon request. State v. Terrazas, 189 Ariz. 580, 583, 944 P.2d 1194, 1197 (1997). The profferer of prior bad act evidence must establish by clear and convincing evidence that the defendant committed the prior bad act. Terrazas, 189 Ariz. at 582, 944 P.2d at 1196. Of course, the evidence must comply with other relevant evidentiary rules.
¶ 55 The defendant's statements to Michael Kapp about robbing the Firefighters' Hall, which the defendant attacks as hearsay, qualify as admissions of a party, which are non-hearsay under Rule 801(d)(2)(A). Michael Kapp's statements to the defendant about robbing the Firefighters' Hall constitute admissions of a party under Rule 801(d)(2)(E), which defines as non-hearsay admissions the statements of a co-conspirator of a party in the course of the conspiracy. No hearsay problems arise from this testimony.
¶ 56 The defendant also argues that Rule 404(b) bars Kapp's statements. The State first asserts that Rule 404(b) does not apply to this evidence because the bad acts at issue are intrinsic to the charged crimes, rather than separate, extrinsic acts to which Rule 404(b) applies. We agree that intrinsic evidence is admissible absent Rule 404(b) analysis. State v. Dickens, 187 Ariz. 1, 18 n. 7, 926 P.2d 468, 485 n. 7 (1996). Other act evidence is intrinsic when "evidence of the other act and evidence of the crime charged are `inextricably intertwined' or both acts are part of a `single criminal episode' or the other acts were `necessary preliminaries' to the crime charged." Id. The defendant's alleged solicitation of Kapp meets none of those criteria. The defendant solicited Kapp, not the person with whom he ultimately committed the crime, two years before the crime, and discussed carrying out the crime at a notably different time of the day and week than the time at which the crime actually occurred. The intrinsic evidence at issue in Dickensthe defendant's theft of the gun used in the murders and robberiesrevealed acts that were a necessary preliminary to the crime charged, whereas the defendant's alleged solicitation of Michael Kapp two years earlier did not.
¶ 57 Kapp's testimony therefore is subject to Rule 404(b), and the State had to satisfy the Terrazas requirement that the other act be established "by clear and convincing evidence that the prior bad acts were committed and that the defendant committed the acts." Terrazas, 189 Ariz. at 582, 944 P.2d at 1196 (emphasis omitted). At trial, the State offered more than Kapp's allegations that the defendant solicited his participation in robbing the Firefighters' Hall. The State also presented corroborating testimony from Firefighters' Hall employees that the defendant's mother did work at the bar and that, at the time she worked there, the money in the safe was accessible to the bartenders. In addition, the State presented testimony that the defendant and Michael Kapp lived and socialized together during the summer of 1994, as Kapp testified. This evidence satisfied the Terrazas standard.

2. Attempted Impeachment
¶ 58 The trial court precluded the defense from impeaching Michael Kapp with allegations that he threatened his sister-inlaw Tina Kapp about testifying in this case and with his post-testimony arrest for theft and drug possession. The trial court precluded both lines of inquiry.
¶ 59 Tina's testimony at the hearing suggested that Michael's threats involved not her testimony in this case, but rather her alimony dispute with Michael's brother and her revelation to Michael's mother that Michael had been dealing drugs. The trial court did not abuse its discretion in precluding this testimony.
¶ 60 The defendant also argues that Michael Kapp's arrest, two days after testifying in this case, for drug and theft charges, is *737 relevant because during his testimony he denied dealing drugs in prison. The defense argues that the arrest relates to his credibility because the arrest shows that he must have been dealing drugs in prison because, without a background of dealing, he could not have become a drug dealer in only two days. However, Michael Kapp's prison sentence resulted from drug charges, and he had been released from prison for more than the two days after testifying as a result of his bargain with the State. The possibility that he returned to drug dealing upon release but had not dealt in prison, and the collateral issues that would have been raised in establishing otherwise, make any testimony on this issue of minimal impeachment value and likely to confuse the jury.
¶ 61 The defense also argues that Kapp's arrest is relevant to the motive to lie created by his deal with the State. However, Kapp's testimony two days before his arrest could not have been motivated by events that occurred days later. The trial court did not err in excluding the profferred impeachment evidence.

G. Parking Lot Assault as Prior Bad Act

1. Denial of Motion to Preclude
¶ 62 Prior to trial, the State filed a disclosure of bad acts, announcing it intended to present evidence that on the night of the Firefighters' Hall murders, the defendant and Jones, using black semi-automatic pistols, pistol-whipped two men in the parking lot of an apartment complex. According to the State, the defendant and Jones pistol-whipped these two men because they believed one of them to be Larry Kapp, brother of witness Michael Kapp. The defendant allegedly wanted to confront Larry about implicating David Nordstrom in a theft, and he received information about where to find Larry from Larry's wife, Tina, who was engaged in a custody dispute and wanted the defendant to tell Larry to stay away from her. The State asserted that Tina Kapp would testify to the solicitation of this attack as well as to a telephone conversation in which the defendant told her that he had pistol-whipped the wrong people.
¶ 63 The State sought to admit this evidence under Arizona Rule of Evidence 404(b) to show identity, as well as to tell the "complete story" of what happened on the night of the Firefighters' Hall murders. The trial court ruled that the State could show that the defendant and Jones had contact in the parking lot with two people on the night of the murders while in possession of semiautomatic handguns, but forbade any mention of violence or of solicitation by Tina Kapp.
¶ 64 Prior to trial, the parties stipulated to a description of the incident, which was read into the record following the testimony of David Nordstrom.[10] They stipulated that, between two and four hours before the Firefighters' Hall murders, the defendant and at least one other person were in the parking lot of an apartment complex in possession of black 9 mm handguns.[11]
¶ 65 The defendant now argues that this information served only to prove the defendant's bad character and was therefore improperly admitted under Rule 404(b). The fact that the defendant and another man matching the description of Robert Jones were together, in possession of weapons of the type used in the Firefighters' Hall murders, a few hours before those murders, tends to show that the defendant, and not someone else, was involved with Jones in the Firefighters' Hall murders later that evening. Evidence of identity and opportunity *738 is relevant to determining a defendant's guilt and is explicitly permitted by Arizona Rule of Evidence 404(b). The trial court adequately protected against any unfair prejudice by limiting admissibility to only those facts necessary to establish that the defendant was armed with the type of weapon used in the charged offenses and in the company of the other alleged perpetrator. In addition, the trial court instructed the jury to limit its use of the stipulation to the question of the defendant's opportunity to commit the crimes charged. The trial court did not abuse its discretion in admitting this evidence subject to these protective limitations and instructions.
2. Denial of Mistrial Due to Testimony About the Incident
¶ 66 Appearing as a witness for the defense, Tina Kapp testified to her belief that her husband Larry provided State's witness Michael Kapp drugs that he sold to other prisoners. During cross-examination, the State questioned Tina Kapp about her conversations with the defendant concerning her husband. She testified that during the summer of 1996, she went to the defendant's home and left her pager number with the defendant's girlfriend. The defendant contacted her, and she gave him information about where he could find her husband to "have some contact" with him. Later that same evening, the defendant told her that he "had contact" with the wrong people.
¶ 67 Following this testimony, the defense moved for a mistrial, arguing that the State's line of questioning had suggested the solicitation of violent contact that the trial court had explicitly forbidden the State from introducing. The trial court denied the motion for mistrial. We review this decision for abuse of discretion. State v. Adamson, 136 Ariz. 250, 263, 665 P.2d 972, 985 (1983).
¶ 68 A declaration of mistrial is the most dramatic remedy for trial error and is appropriate only when justice will be thwarted if the current jury is allowed to consider the case. Id. Although the State's use of the words "doing him" with respect to the defendant's contact with Larry Kapp could have been understood by the jury as suggesting violent contact,[12] in the overall context of the examination, and given the prosecutor's immediate correction of his words, the trial judge's finding that the jury would not have gleaned that meaning from the testimony is not unreasonable. The trial judge did not abuse his discretion in denying the motion for mistrial.

H. Refusal to Grant a Continuance
¶ 69 Two days before the trial began, the State disclosed the results of its test of an electronic bracelet monitoring system similar to the one used by David Nordstrom at the time of the Firefighters' Hall murders. Over the previous weekend, the State's attorney, the police, and the parole department conducted a test using the telephones at the house at which David lived at the time of the murders. They made various physical attempts to defeat the system, such as unplugging the unit from the wall and cutting the bracelet, and the electronic monitoring computer recorded each attempt. The testers were unable to defeat the system and leave no record of the transgression. The defendant challenged this evidence on two grounds: that the test was inadmissible under Bledsoe and that the late disclosure of the test required that the court exclude the results or grant a continuance.
¶ 70 In Bledsoe, a wrongful death suit based on a cyclist's collision with an access gate, the court of appeals held that a purported replication of the accident introduced by the plaintiff was improperly admitted because it was not sufficiently similar to the underlying event. Bledsoe v. Salt River Valley Water Users' Ass'n, 179 Ariz. 469, 471, 880 P.2d 689, 691 (App.1994). However, the reenactment in Bledsoe had several reliability problems not present here. There, the plaintiff's attorney conducted an "experiment" under conditions markedly dissimilar *739 from those surrounding the accident. In addition, the attorney first presented his experiment during the plaintiff's rebuttal argument, which left the defendant without opportunity to question, counter, or impeach the "evidence." In this case, the State tested an electronic monitoring system similar to that in use with David and used similar telephone equipment in the same location. In addition, the defense had ample opportunity to question the methodology and the meaning of the results. We find no error based upon Bledsoe.
¶ 71 The defendant also argues that the State's late disclosure of the test results required that the judge preclude the evidence or grant a continuance. We agree that it would have been far preferable for the State to conduct its test earlier. However, in determining whether to preclude evidence disclosed late in the process, the court considers "how vital the precluded [evidence] is to the proponent's case, whether the opposing party will be surprised and prejudiced by the [evidence], whether the discovery violation was motivated by bad faith or willfulness, and any other relevant circumstances." State v. Fisher, 141 Ariz. 227, 246, 686 P.2d 750, 769 (1984). We will not disturb the trial court's decision absent a showing of abuse of discretion and a showing of prejudice. Id.; State v. Williams, 144 Ariz. 433, 441, 698 P.2d 678, 686 (1985).
¶ 72 The defendant established no bad faith on the part of the State, which disclosed the test results as soon as they were known. In addition, the defendant could hardly have been surprised that the State conducted the test. The defendant was well aware that the accuracy of electronic monitoring was at issue in the case; his own theory of David's role as perpetrator of the crimes made the issue important. Indeed, the test results were presented at trial during the cross-examination of defense witnesses and in the testimony of rebuttal witnesses, rather than during the State's case in chief. The defendant could have anticipated that the State would attempt to prove that David could not have been the perpetrator because of his electronic monitoring. Cf. Fisher, 141 Ariz. at 247, 686 P.2d at 770. In addition, the defense was able to cross-examine the witnesses who participated in the test about foundational issues, including the accuracy of the test and the similarity of the test conditions to David Nordstrom's monitoring situation. Most importantly, the test did not affect the defense's strongest argument with regard to electronic monitoring: that David was able to commit the Firefighters' Hall crimes without any curfew violation being recorded because he was able to get a curfew extension that was not recorded in his file. The defense presented multiple witnesses who testified that David had been able to get curfew extensions or that he had told them he could get extensions by lying, and the testimony of David's parole officer made clear to the jury that an extension could have been granted without being reflected in the parole department's records. The trial court did not abuse its discretion.

I. Preclusion of Impeachment of Rebecca Matthews
¶ 73 The State called Rebecca Matthews, supervisor of the home arrest program at the time David Nordstrom was on home arrest, to rebut testimony by David Nordstrom's parole officer. The parole officer's testimony indicated that the electronic monitoring system, while not susceptible to physical tampering, could be defeated by acquiring an extension of curfew that was not recorded in the individual's file. Matthews testified about a test of the electronic monitoring system, how the system responds to and documents attempts at physical tampering, and the ways in which parole officers are instructed to document the schedules of prisoners in the home arrest system.
¶ 74 The defense sought to cross-examine Matthews about a legal action pending against the Department of Corrections. The complaint, filed by surviving victims and family members of the Moon Smoke Shop and Firefighters' Hall murders, alleged that the department failed to adequately supervise Jones and the Nordstrom brothers, all of whom were on parole at the time of these crimes. The fact of the lawsuit and the nature of the parties' claims were admitted into evidence. The defense argued that Matthews' *740 knowledge of the pending lawsuit was relevant to any bias or motive to fabricate that she might have. However, in a pre-trial interview, Matthews had denied any knowledge of the lawsuit. On this basis, the trial court forbade the defendant from cross-examining her on this issue. The trial court explained that, because a witness cannot be biased about something of which she has no knowledge, no legitimate reason justified this line of questioning. The court also noted that Matthews did not have a direct role in the preparation of David Nordstrom's parole documents.[13]
¶ 75 We agree with the defendant that the trial judge should have permitted the defense to ask Matthews whether she was aware of the lawsuit.[14] The questions sought testimony relevant to evaluating the credibility of this witness. Any error, however, was harmless. Nothing suggests that Matthews in fact had knowledge of the action, the defense introduced into evidence proof of the existence and nature of the suit, and the defense demonstrated that electronic monitoring records were unreliable. In view of those factors, the error did not affect the outcome of the trial.

J. Preclusion of Keith Thomas' Opinion Testimony
¶ 76 Keith Thomas testified to his opinion that David Nordstrom was not trustworthy or honest when he was drinking heavily or using drugs. The defense also sought to solicit Thomas' opinion that David had propensities for violence, being hot-tempered, and taking advantage of friends. The credibility of a witness may be attacked using opinion evidence only with respect to the witness's character for truthfulness or untruthfulness. Ariz. R. Evid. 608. The trial court did not abuse its discretion in disallowing this testimony.

K. Admission of Sherry Ford's Testimony
¶ 77 Christopher Lee, a friend of David Nordstrom, Robert Jones, and the defendant, testified as a witness for the defense. Lee testified that David and Jones were close friends; that he was with them on multiple occasions while they drank, used drugs, and socialized in violation of their parole; and that David had bragged about being able to get curfew extensions by lying to his parole officer. Lee also testified that one evening he had been with Jones in Jones' truck while the defendant and/or David Nordstrom followed them in the defendant's truck. Sometime between five and seven-thirty p.m., Jones left Lee at the Rainbow Bar, where he drank heavily while waiting for Jones to return. While he waited at the bar, which is located near the Firefighters' Hall, he heard gunshots and sirens. He went out into the parking lot, along with his ex-girlfriend Sherry Ford and bartender Carolyn Wood, to see what was happening. They could not determine the source of the noise and returned to the bar. Jones came back to the bar and picked him up between one and two hours later. Jones seemed agitated, and either David or Scott Nordstrom was in the truck. Lee testified that he believed the person in the truck was David because they dropped that person off at David's house. Lee testified that the night in question could have been the night of the Firefighters' Hall murders.
¶ 78 The State originally interviewed Lee after learning of a letter he had written to his girlfriend in which he worried that David Nordstrom and Jones had tried to set him up for the Firefighters' Hall murders. At the time, Lee was in prison, and the State did not disclose his existence as a potential witness out of fear that he would be in danger when it became known that he was testifying. The State believed that Lee would be released in the late spring or early summer of 1997, and intended to disclose him at that *741 time. When it became clear that Lee would not be released, the State disclosed him to the defense. However, by that point Carolyn Wood, a witness who allegedly could have corroborated Lee's tale about the gunshots and the parking lot as well as about Jones' appearance with David in the truck, had died unexpectedly. Wood had given a statement to the police, but that statement did not mention going into the parking lot after hearing shots and sirens, although it did mention seeing someone in Jones' truck on some occasion. As a remedy for the disclosure violation, the trial court allowed a redacted version of Wood's statement to be read into evidence at trial.
¶ 79 On appeal, the defendant challenges the trial court's decision to allow Sherry Ford to rebut Lee's testimony about going out into the parking lot of the Rainbow Bar in response to gunshots and sirens. Ford testified that she had not seen Lee at the Rainbow Bar at all in the summer of 1996, and that she certainly had not gone into the parking lot with him in response to shots and sirens. The defense argues that because Wood was unavailable to corroborate Lee's testimony, Ford should not have been allowed to impeach Lee's testimony.
¶ 80 We review the trial court's decision to allow rebuttal testimony and its choice of sanctions for discovery violations for abuse of discretion. State v. Talmadge, 196 Ariz. 436, 439 ¶ 12, 999 P.2d 192, 195 ¶ 12 (2000); State v. Dumaine, 162 Ariz. 392, 406, 783 P.2d 1184, 1198 (1989). In the case of discovery violations involving exculpatory evidence, we examine whether the previously undisclosed information would have created a reasonable doubt had it been presented to the jury. Dumaine, 162 Ariz. at 405, 783 P.2d at 1197. In this case, any impact on the jury is doubtful. In addition to the fact that we cannot know the exact nature of Wood's testimony, the State impeached Lee extensively, and his rehabilitation seems unlikely. The State revealed Lee's prior felony convictions and inconsistent statements to the police, as well as his repeated admissions that his heavy drug and alcohol use rendered his memory, at best, "fuzzy." Wood herself might have been subject to impeachment as a drug dealer.[15] Ford's testimony rebutting Lee was impeached by her admitted strong dislike of Lee and their continuing custody dispute over their son. Any corroboration that Wood might have offered would likely have made little difference. We find no reversible error in the trial court's decision to let Ford testify to rebut Lee.

L. Jury Instructions

1. Second Degree Murder
¶ 81 The defendant argues that the trial court's failure, sua sponte, to instruct the jury on second-degree murder requires reversal. Because the defendant did not request a second-degree murder instruction at trial or object to the absence of one, we review this issue for fundamental error only. State v. Dickens, 187 Ariz. 1, 22-23, 926 P.2d 468, 489-90 (1996). A sentence of death may not be imposed if the jury was not permitted to consider a lesser-included, non-capital offense and the evidence would have supported such a verdict. Beck v. Alabama, 447 U.S. 625, 627, 100 S.Ct. 2382, 65 L.Ed.2d 392 (1980). The goal of this rule is to ensure that the jury does not choose to convict the defendant of a death-eligible offense because it faces an all-or-nothing choice between that verdict and innocence. Spaziano v. Florida, 468 U.S. 447, 455, 104 S.Ct. 3154, 82 L.Ed.2d 340 (1984). Failure to instruct on all lesser-included offenses supported by the evidence constitutes fundamental error and requires reversal. State v. Schad, 163 Ariz. 411, 417, 788 P.2d 1162, 1168 (1989).
¶ 82 In Arizona, second-degree murder is a lesser-included offense of first-degree murder, but felony murder has no lesser-included offense. State v. Atwood, 171 Ariz. 576, 629, 832 P.2d 593, 646 (1992). The jury convicted the defendant of felony murder with regard to all six victims.[16] A Beck *742 analysis therefore is unnecessary. Cf. Randall v. State, 716 So.2d 584, 590 (Miss. 1998); Orbe v. Commonwealth, 258 Va. 390, 519 S.E.2d 808, 813 (1999). Moreover, the evidence at trial did not support a second-degree murder verdict. No reversible error occurred.

2. Prior or Inconsistent Statements
¶ 83 The trial court refused a defense instruction that would have told the jurors that they could consider prior inconsistent statements both with regard to the credibility of a witness's testimony at trial and as substantive evidence of the truth of the witness's prior statements. We previously have held that a trial court does not err by denying such an instruction when the trial judge has no reason to believe that the jury would improperly limit its consideration of prior inconsistent statements and when the judge instructed the jury about evaluating the credibility of witnesses. State v. Walden, 183 Ariz. 595, 614, 905 P.2d 974, 993 (1995). In addition, the defendant has failed to explain how he was prejudiced as a result of the trial court's ruling, and indeed has failed to present any argument as to why we should reverse for failure to include the proposed language. Cf. State v. Bolton, 182 Ariz. 290, 298, 896 P.2d 830, 838 (1995). We find no error here.

3. "Bad Character"
¶ 84 The judge instructed the jury as follows about character evidence:
Evidence that Scott Nordstrom possessed what appeared, according to a witness, [sic] a 9 millimeter handgun between 5:00 p.m. and 7:30 p.m. on June 13, 1996 has been admitted in this case. You must not consider this evidence to prove the defendant is a person of bad character or that the defendant acted in conformity with that bad character. You may, however, consider the evidence only as it relates to the defendant's opportunity to commit the crimes charged on June 13, 1996.
The defense asserts that including the word "bad" in the instruction unduly emphasized the character of the defendant and prejudiced him by doing so. However, this otherwise standard character evidence instruction correctly instructs as to the use of character evidence. Courts do not presume that jurors betray the court's trust and ignore their instructions. State v. Trujillo, 120 Ariz. 527, 531, 587 P.2d 246, 250 (1978); cf. Estelle v. McGuire, 502 U.S. 62, 75, 112 S.Ct. 475, 116 L.Ed.2d 385 (1991) (finding a similar instruction on character evidence not erroneous). The trial court did not err in giving this instruction.

4. Reasonable Doubt
¶ 85 The trial court instructed the jury using the standard instruction on reasonable doubt from the Revised Arizona Jury Instructions (RAJI). The trial judge refused the defendant's request to give the additional paragraph of reasonable doubt instructions recommended by the committee that drafted the RAJI. We have approved giving only the standard instruction on reasonable doubt on multiple occasions. State v. Van Adams, 194 Ariz. 408, 418 ¶ 30, 984 P.2d 16, 26 ¶ 30 (1999); State v. Portillo, 182 Ariz. 592, 596, 898 P.2d 970, 974 (1995). The trial court did not err.

M. Denial of Rule 24 Petition

1. Jurisdictional Issue
¶ 86 The defendant was convicted on December 2, 1997, and sentenced on May 18, 1998. Pursuant to Arizona Rule of Criminal Procedure 31.2.b, the clerk of the court filed a notice of automatic appeal of the sentence of death on May 18, 1998. On July 1, 1998, the defendant filed a motion to vacate the judgment on grounds of newly discovered evidence pursuant to Rule 24.2.a.2. The trial court denied this motion on September 25, 1998, and the defendant did not appeal the denial at that time.
¶ 87 In the defendant's opening brief in the automatic appeal, filed with this court on February 24, 2000, counsel included a challenge to the trial court's denial of the Rule 24.2 motion. In response, the State questioned whether the Rule 24.2 issue was properly before this court, and both parties filed memoranda addressing the issue. We postponed *743 resolution of the jurisdictional issue until this discussion on the merits.
¶ 88 Rule 31.3, which addresses judgments and sentences, requires that all appeals be filed within twenty days of the entry of judgment and sentence. Although Rule 31.3 does not address the time frame in which appeals of post-conviction orders must occur, the court of appeals applied this time limit to all appeals, including those of a Rule 24.2 denial. State v. Wynn, 114 Ariz. 561, 563, 562 P.2d 734, 736 (App.1977). The defendant argues that the special rule requiring automatic appeal of capital convictions carves out an exception for the denial of Rule 24.2 motions in capital cases, and contends that Rule 24.2 denials are included in the automatic appeal. See Ariz.R.Crim.P. 31.2.b. While we do not agree with the defendant's interpretation of this rule, the parties have fully briefed and argued the order denying the Rule 24.2 motion. In the interests of justice and judicial efficiency, we therefore suspend the time to appeal, and address the merits of the defendant's Rule 24.2 argument. See Ariz.R.Crim.P. 31.20 (authorizing the court to suspend the requirements of any section of Rule 31 in exceptional circumstances).

2. Merits of the Petition
¶ 89 The newly discovered evidence on which the defendant's Rule 24.2 motion relies consists of: (1) allegations that David Nordstrom falsely alleged that someone tried to kidnap his family members and attempted to arrange a scam whereby a fellow inmate named Buddy Carson would assault David, who then could sue the prison for negligence; (2) Zachary Jones' claim that David had made statements indicating he was the perpetrator of these crimes; and (3) David's statements to another inmate about leaving no witnesses in committing a crime. To warrant post-conviction relief based on newly discovered evidence, the material must meet five requirements: the evidence must be newly discovered, the motion must show due diligence, the evidence must not be merely cumulative or impeaching, the evidence must be material, and the evidence must be likely to change the verdict if it were introduced at trial. State v. Serna, 167 Ariz. 373, 374, 807 P.2d 1109, 1110 (1991). David Nordstrom's alleged deceitful acts and statement about killing witnesses are purely impeachment matters, insufficient under Rule 24.2. Zachary Jones' statements were not merely impeachment matters. However, Zachary had refused, on Fifth Amendment grounds, to testify to this alleged conversation at the trial of Robert Jones for these crimes, and, according to his attorney, would do so again if a new trial were ordered.
¶ 90 We review the trial court's decision to deny a Rule 24.2 motion for abuse of discretion. Serna, 167 Ariz. at 374, 807 P.2d at 1110. Here, the proffered new evidence would be either cumulative impeachment or unavailable for presentation at trial, and therefore unlikely to affect the verdict if presented at trial. Cf. State v. Jeffers, 135 Ariz. 404, 426, 661 P.2d 1105, 1127 (1983). The trial court did not abuse its discretion in denying the motion for post-conviction relief.
¶ 91 In his reply brief and at oral argument, however, the defendant alleged that Buddy Carson would testify not only to David Nordstrom's attempted fake kidnaping and sham negligence suit but also that David told him a version of the Moon Smoke Shop robbery that did not match his testimony at trial. Specifically, according to a police report of an interview conducted after the jury's verdict in defendant's trial, Carson told the investigating officers that David told him that Michael Kapp was originally a co-conspirator in the Moon Smoke Shop robbery, that the defendant excluded Kapp at the last minute, and that David went into the shop with the defendant and Jones but ran out scared when they began shooting. This information was not presented to the trial court in the defendant's Rule 24.2 motion, and we cannot determine from the record before us whether this evidence is newly discovered. We therefore affirm the trial court's denial of the Rule 24.2 motion without prejudice to the defendant's right to raise appropriate issues concerning his actual innocence, ineffective assistance of counsel, or newly discovered evidence in Rule 32 proceedings.
*744 N. Refusal to Grant Second Counsel for Purposes of Appeal
¶ 92 The defendant's appellate counsel moved in the trial court for the appointment of second counsel for purposes of the appeal. The trial judge refused this request because the requested individual had represented the defendant at trial, was not qualified under the rules, and was not on the county contract attorney list. The defendant alleges no prejudice as a result of this denial, but rather cites the comments to Arizona Rule of Criminal Procedure 6.8 as well as the American Bar Association and National Legal Aid and Defender Association guidelines as support for his argument that second counsel should be appointed in all capital appeals. Where neither prejudice nor a violation of the rules has taken place, we find no reversible error. See State v. Lee, 189 Ariz. 590, 601, 944 P.2d 1204, 1215 (1997).

III. SENTENCING ARGUMENTS AND ANALYSIS
¶ 93 The defendant has not challenged the appropriateness of his death sentence. Even absent such a challenge, we independently consider the aggravating and mitigating circumstances found by the trial judge to determine whether the death penalty is appropriate. A.R.S. § 13-703.01.A (2001).
¶ 94 The jury convicted the defendant of both felony and premeditated first-degree murder with respect to two victims, Thomas Hardman and Carol Lynn Noel, and of felony murder only with respect to Clarence O'Dell, Maribeth Munn, Arthur Bell, and Judy Bell. The death penalty may not be imposed for felony murder convictions unless the defendant was a major participant in the underlying felony and acted with reckless disregard for human life. Tison v. Arizona, 481 U.S. 137, 158, 107 S.Ct. 1676, 95 L.Ed.2d 127 (1987); Enmund v. Florida, 458 U.S. 782, 797, 102 S.Ct. 3368, 73 L.Ed.2d 1140 (1982). The trial court found, and we agree, that the defendant was a major participant in the armed robberies of both the Moon Smoke Shop and the Firefighters' Hall. We further agree that he must have anticipated that lethal force would or might have been used, particularly in the latter incident, given that he had used lethal force in the commission of the first crimes. The trial court correctly concluded that the requirements of Enmund and Tison were met in this case.
¶ 95 With respect to each of the six victims, the trial court found the State had proved three aggravating factors beyond a reasonable doubt: the defendant had been convicted of another offense for which a sentence of life imprisonment or death may be imposed (A.R.S. section 13-703.F.1), the defendant committed the offense for pecuniary gain (F.5), and the defendant has been convicted of one or more other homicides during the commission of the offense (F.8). In the appeal of Robert Jones, convicted for committing these offenses with the defendant, we upheld the trial court's findings of F.1 or F.8[17] and F.5 with respect to these same crimes. State v. Jones, 197 Ariz. 290, 309-11 ¶¶ 54-66, 4 P.3d 345, 364-66 ¶¶ 54-66 (2000).
¶ 96 Although the State argued the F.6 aggravator, that the murders were committed in an especially heinous, cruel, or depraved manner, the trial court did not find this factor proven beyond a reasonable doubt given the rapidity of the crimes and the amount of speculation that would be necessary to such a finding.
¶ 97 The trial court found that the defendant did not prove any of the statutory mitigators by a preponderance of the evidence. The defense offered six non-statutory mitigators that the trial court found it did not prove by a preponderance of the evidence: difficult childhood and family background, residual *745 doubt, mental health issues, artistic talent, that defendant was a follower, and successful adjustment to prison. The court found that the defense did prove two nonstatutory mitigators by a preponderance of the evidence: employment history and caring parent and family relationships. In addition, the trial court found that the defense proved the non-statutory mitigating factor of no prior convictions for serious offenses, but found this factor devoid of mitigation in light of the defendant's conviction for multiple murders on different occasions.
¶ 98 Given the strength of the aggravating factors and the minimal value of the mitigating factors, we independently conclude that the sentence of death is appropriate.

IV. CONCLUSION
¶ 99 For the foregoing reasons, we affirm the defendant's convictions and sentences.
CONCURRING: THOMAS A. ZLAKET, Chief Justice, CHARLES E. JONES, Vice Chief Justice, STANLEY G. FELDMAN, Justice, FREDERICK J. MARTONE, Justice.
NOTES
[1]  Jones matched the description of the hatted assailant in the front room of the Moon Smoke Shop, and his truck was consistent with Engles' description of the truck he saw driving away after the robbery. We upheld Jones' convictions and death sentence in State v. Jones, 197 Ariz. 290, 4 P.3d 345 (2000).
[2]  The Firefighters' Hall robbery took place between nine and nine-thirty p.m., after David's curfew began, while the Moon Smoke Shop robbery was committed shortly after six p.m., before his curfew began.
[3]  The defense moved for a change of venue on April 18, 1997, and submitted newspaper articles and newscast clips from before that time. Defense counsel did not provide any supplemental evidence of media coverage that might have occurred after that time.
[4]  At the beginning of jury selection, defense counsel mentioned that, if a significant number of juror questionnaires revealed bias, he would renew his motion for change of venue. However, when the juror questionnaires were returned to the court and analyzed, the defense attorney did not renew that motion.
[5]  The trial judge questioned the jurors again on the first day of trial and dismissed a juror who inadvertently heard a news account about the case during the weekend between selection and trial.
[6]  This situation should not arise, given the trial judge's ability to exclude evidence that fails to meet evidentiary standards. Ariz. R. Evid. 104, 901; State v. Lavers, 168 Ariz. 376, 386, 814 P.2d 333, 343 (1991).
[7]  The full text of the letter reads as follows: Red

What type of bird does not fly? A red bird! You ass hole. You sure fucked things up for your self. Im still pissed off at you for not taking care things, the way we talked about!
Now instead your counting brick's in your 4' by 9' cell, waiting for them to do what you should have done! ....
On another note I looked in to that cross you wanted. The only thing is you didn't tell me what you wanted it in.? Your oppsians are 14K-silver-nickel? Im going to get my last surgery the end of this month. Ill keep you informed.
On your truck, I havent havent went to look for it, my sititation does not allow me at the moment. david Red's said he has looked for it. but to no avail. Ill help you out as soon as I can. That should be in 3 or 4 month's. hang in there bro Ill do what I can.
[8]  For instance, the police officer possessed conflicting information about the stature of the defendant and of the suspect, rather than the markedly dissimilar descriptions suggested by the defendant's redrafted affidavit. The police officer also stated that he did not hear David "slip" and confess to shooting people, a statement the defendant thought should have been included in the affidavit. In addition, the police officer appropriately did not include information about David's requests for money in exchange for information because David provided the information used in the affidavit before requesting payment.
[9]  David's statement that he "had nothing to lose," the incremental nature of his confession, and the inability of witnesses to identify the defendant from a photo spread that included pictures taken at an unknown time, fall into this category.
[10]  In his opening brief, the defendant suggests that he was coerced into making this stipulation, when he would have preferred to present evidence that he was not one of the assailants that night. In our scrutiny of the record, we have found no indication of coercion. To the contrary, the trial court merely suggested that a stipulation would be an efficient way of dealing with this information and was careful to reiterate that the decision to enter into a stipulation was entirely up to the parties.
[11]  The Firefighters' Hall murders were committed with two semi-automatic handguns: a 9 mm and a .380. A witness at trial testified that 9 mm and .380 semi-automatic handguns look remarkably similar and are often mistaken for each other by people who do not have experience with both types of guns.
[12]  The relevant exchange was:

Q (by State's attorney): And you had a conversation with Scott Nordstrom?
A (by Tina Kapp): Yes.
Q: And about doing him, having some contact with Larry; correct?
A: Yes.
[13]  Matthews did supervise David's parole officer, had access to his records, and actively participated in the test of the electronic monitoring system's susceptibility to tampering.
[14]  The State argues that this line of questioning would have been impermissible as impeachment by innuendo. Cross-examiners may not impeach by implying the existence or non-existence of facts they are not prepared to prove. State v. Hines, 130 Ariz. 68, 71, 633 P.2d 1384, 1387 (1981). In this case, existence of the lawsuit was not questioned.
[15]  The record does not make clear whether Wood had been convicted of drug charges, and thus whether she could have been impeached with these allegations.
[16]  For two of the victims, the jury convicted the defendant of premeditated first-degree murder as well.
[17]  In Jones' appeal, we found error in the trial court's possible "double counting" of the murders to find both the F.1 and F.8 factors. Jones, 197 Ariz. at 311 ¶ 65, 4 P.3d at 366 ¶ 65. We noted that, while it is "mathematically possible to satisfy both the F.1 and F.8 factors in this case without ever counting a single murder twice," because we could not determine whether the trial judge actually did so, we could not use both the F.1 and F.8 factors. Id. The trial judge in this case also did not make clear that the aggravator analysis complied with the prohibition on double-counting. Therefore, although the trial court in this case found both F.1 and F.8, we can factor only one of those findings into our independent consideration.
