After his first trial ended in a mistrial,1 the defendant was convicted of the murders in the first degree of Jay Schlosser and Heather Buchanan, on the theories of deliberate premeditation, extreme atrocity or cruelty, and felony-murder.2 He appealed from his convictions and from the denial of his post-conviction motions for a new trial and for postconviction discovery. The defendant argues that the trial judge erred in the *309admission and exclusion of certain evidence; the prosecutor erred in failing to disclose material evidence and in exceeding the proper scope of closing argument; and the judge erred in denying the postconviction motions. He also seeks relief pursuant to G. L. c. 278, § 33E. Because we conclude that none of the defendant’s claims of error requires reversal of his convictions, and discern no reason to exercise our power under G. L. c. 278, § 33E, we affirm his convictions and the denial of his postconviction motions.
Facts. We recite the essential facts the jury could have found, reserving certain details for our discussion of the issues.
The defendant and two critical witnesses who testified at trial for the Commonwealth, John Sweeney and Kevin Trundley, all sold cocaine and knew each other. In addition, the defendant was familiar with, and had access to, firearms, including guns that had ammunition “clip[s],” and had been seen wearing gloves and using “WD-40,” a spray lubricant, to clean a gun and to coat bullets. The defendant believed that by coating bullets with WD-40 no fingerprints would be detected. He carried a gym bag with him that always contained duct tape and the lubricant. The defendant was acquainted with the victims, who were boy friend and girl friend.
Sometime in 1985 or 1986, the defendant gave John Sweeney money to invest in a business, the purpose of which was to search for sunken Spanish “treasure ships” off the coast of the Bahamas. The approximately $25,000 to $35,000 the defendant gave Sweeney came from the defendant, his father, and some of the defendant’s friends. The treasure hunting operation turned out to be a scam, and the money was lost.3 Sweeney told the defendant that he would get his money back. As of the time of the murders, Sweeney had not reimbursed the defendant.
The defendant was angry about losing his money and blamed Sweeney. At trial, witnesses testified to several incidents involving the defendant that occurred after the defendant learned about the scam. One witness saw the defendant at Sweeney’s mother’s house. The defendant was sitting on a couch firing a gun through an open sliding glass door. He was aiming at an insignia on one of Sweeney’s shirts that was hanging outside on a clothesline. *310The defendant told the witness that he did not want Sweeney “to have a nice shirt to go out in” that night. The gun the defendant was using was a gun “like the cops carry” with a clip on the end, either a Luger or a .22 caliber.
A couple of months before the murders, the defendant told Sweeney that he was upset that Sweeney seemed to have money to go out and stated, “John are you going to pay back my money? If you don’t, I am going to kill you. You know what I am capable of.” After this conversation, Sweeney began giving the defendant cocaine. Moreover, Sweeney also moved at least twice, and ended up living with Schlosser in Westwood. Buchanan sometimes stayed there with Schlosser. Schlosser also sold drugs and was Sweeney’s business partner. Schlosser kept cocaine and money hidden in his bedroom, behind a panel used to access certain plumbing pipes.
At around this time, the defendant also became aware that Sweeney and Schlosser were going to use cash from their cocaine sales to invest in a real estate deal. Schlosser informed the defendant that he had a lot of cash in his house. The defendant was upset and later told Kevin Trundley, “I’m going to get my money.” The defendant and Trundley, with whom the defendant was living, attempted, unsuccessfully, to find out where Sweeney lived.
When, at some point, Sweeney left a receipt that contained his Westwood address at Trundley’s apartment, Trundley gave it to the defendant. Trundley, the defendant, and their respective girl friends drove to Westwood approximately two weeks before the murders and stopped near Schlosser’s house. The defendant stated that the location of the house would make it “an easy hit.” He later told Trundley that he and a “guy” and “girl” would commit the robbery sometime between 8 and 11 p.m. on an evening when it was raining, so that anyone in Schlosser’s neighborhood would be watching television and have their windows closed. The defendant told Trundley that, if Schlosser’s door was locked, the girl would pretend that her vehicle had broken down to gain access to the house.
On the evening of June 25,1987, which was rainy, the defendant told Trundley that the robbery would happen that night. The defendant told Trundley that he was going to get his money and *311some cocaine and that he would give Trundley some of the cocaine. Trundley was afraid that if Sweeney, a former serviceman, was at the house when the robbery occurred, something violent would happen. Therefore, at approximately 7:30 p.m., Trundley telephoned Schlosser’s house and asked Schlosser if he could speak to Sweeney. Trundley convinced Sweeney to come to his apartment, where there were three women who had come to Trundley’s to buy cocaine, but who stayed to drink and use cocaine. Sweeney arrived, in his vehicle, at approximately 8:30 p.m.
At approximately 11 p.m., Sweeney and one of the women left Trundley’s for Schlosser’s, so that they could obtain more cocaine. When they arrived, Sweeney left the woman in his vehicle and went into Schlosser’s house. He entered through an open sliding glass door that led into the kitchen. He saw an antique gun that belonged to Schlosser (and usually kept in a closet) on the kitchen table. After calling out to Schlosser, Sweeney entered the living room and saw the victims’ bodies on the couch, bound in duct tape.
The woman Sweeney was with did not hear any noise while he was in the house. Sweeney came out of the house quickly, seemingly upset, but he did not inform the woman what he had found. Instead, on the drive back to Trundley’s, Sweeney stopped so that the woman could use a restroom, and while alone, he telephoned Trundley and told him that the three women would have to leave as soon as Sweeney arrived. After the women left, Sweeney told Trundley that the victims were dead. He and Trundley left, in Sweeney’s vehicle, and headed toward Cape Cod. On the drive they discussed what they should do. Sweeney’s concern was that police would think he had killed the victims or that his drug dealing would be discovered.
Later that night, Sweeney called an agent from the Federal Bureau of Investigation (FBI) with whom he was familiar because of the investigation into the treasure hunting scam. Ultimately, Sweeney, Trundley, and the FBI agent went to the Westwood police department to tell them about the murders. Police tested Sweeney’s hands for blood, finding none.4
When Westwood police arrived at Schlosser’s house, they *312noticed the gun on the kitchen table and the two victims dead on the couch. Each was bound with duct tape about the ankles, knees, eyes, and hands. Although Buchanan’s mouth had duct tape over it, Schlosser’s mouth did not. However, a piece of duct tape was found in an ashtray on the coffee table next to the couch. The wall panel where Schlosser had hidden his money and cocaine was open (and empty) and an open dresser drawer in the bedroom contained a large bag of cocaine.
A day or so after the murders, Trundley’s girl friend drove the defendant to where Sweeney and Trundley were staying in Bourne. On the way, the pair stopped, and the defendant went behind a bathhouse holding a crumpled paper bag. He returned to the car without it. Moreover, while the pair were conversing, the defendant told her that something had gone wrong and that he had to talk to Trundley. When he was alone with the defendant, Trundley asked him why he had killed the victims. The defendant stated that the victims recognized him.* **5 He then told Trundley to be “cool” and keep his “mouth shut.”
Also within days after the murders, an angry defendant showed up at the house of one of Sweeney’s friends looking for Sweeney. The defendant stated that he had lost money and that he would get his money back “one way or the other.”
Sometime in the fall of 1987, Trundley again spoke to the defendant about the murders. The defendant related that he and two accomplices, see note 2, supra, had entered Schlosser’s house through a sliding glass door and that Schlosser had retrieved his gun from a hallway closet. The defendant wrestled it out of Schlosser’s hands, and “they” beat Schlosser. They bound Schlosser with duct tape. The defendant spoke only to Schlosser and not to Buchanan. Schlosser said that no one needed to get hurt and that he would give the defendant what he wanted. As the trio was about to leave the house, the defendant said, “I got us into this and I’ll get us out.” The defendant stated, “I’m a gentleman, ladies first,” and shot Buchanan twice. He stated that he *313then shot Schlosser once.6 The defendant told Trundley that he deliberately left some cocaine behind so it would look like a drug deal and that the police would not care about the death of a drug dealer. The defendant also told Tmndley that he did not get much money. He gave Trundley a bag of cocaine. Sometime later, the defendant revealed to Trundley that the people who aided him in the murders were a brother and sister. See note 2, supra.
There was no physical evidence tying the defendant to the murders. At Schlosser’s house, police found cartridge casings and spent projectiles that corresponded to the number of bullets used to kill the victims. The murder weapon, most likely a nine millimeter semiautomatic pistol, was never found.
The defendant did not testify. He called one witness, an individual who served as an attorney for, and (eventually) became the president of, the defunct treasure-hunting business. The witness stated that the defendant was always friendly to him after he learned that the venture was a scam and that many people were upset at losing the money they had invested.
Through cross-examination of the Commonwealth’s witnesses, the defense asserted three main defenses. The first was that there was an inadequate police investigation, especially in gathering forensic evidence from Schlosser’s house and pursuing leads to other witnesses or suspects. The second was that Sweeney and Trundley, perhaps in collusion with at least one other person, killed Schlosser and were lying and trying to blame the murders on the defendant. Sweeney admitted that he was a former Green Beret, owned firearms, had training in the use of automatic weapons, and was an expert marksman. Trial counsel highlighted the weaknesses in Sweeney’s and Trundley’s stories about what had happened, and elicited from the pair that they had lied to police during the investigation. The third defense was that there were other people involved in the drug trade who may have been targeting Sweeney; for example, once Sweeney had telephoned Trundley from Florida, claiming that he was being held hostage and that his thumbs would be cut off if he was not sent several thousand dollars.
*314Discussion. The issues the defendant raises in his direct appeal are, save two, the same issues he raised in his motion for a new trial. He also argues that it was error for the motion judge, who also was the trial judge, to deny his postconviction motions in her written memorandum of decision and order.
1. Inadequate police investigation evidence. At trial, counsel sought to introduce evidence of an inadequate police investigation. The evidence, contained mostly in police reports, was that there may have been other individuals, with whom Sweeney or Schlosser were involved as part of their drug activity in Florida, who may have had a motive for murder. His proffer was as follows. On June 26, 1987, Westwood police received a “national broadcast” from police in Stuart, Florida, sent out to law enforcement asking “any agency having information on an execution-style murder involving two persons, (poss[ibly] male and female), tied to chairs that occurred within the past week” to contact a Stuart detective. Detective John Nash of the Westwood police learned (apparently by telephoning the police in Stuart) that “silver duct tape and shot in [the] head is a trademark” of Colombians in the Florida drug world. The defendant also proffered that police officials learned from various sources, including Stuart police, reports of interviews with individuals associated with Schlosser, a message from the FBI agent who helped Sweeney on the night of the murders, and Schlosser’s telephone records, that, in essence, Schlosser had ties to the Florida drug world.7
At trial, the judge allowed the Commonwealth’s motion to exclude evidence of unknown third-party culprits as speculative and remote.8 The judge stated in her decision:
*315“Specifically, [trial counsel] wanted to introduce evidence of the victims’ and Sweeney’s connections to the Colombian drug trade. The [judge] ruled that during the cross-examination [a detective] could be asked about an investigation into Sweeney’s dealings in Florida and any potential enemies he made. Sweeney did not recall any involvement with Colombians during his appearance at trial, while Trundley mentioned traveling with a Colombian named ‘Carlos’ on a trip to New York to pick up cocaine. Additionally, the [judge] specifically remarked that [the defendant] was not precluded from questioning the sufficiency of the police investigation . . . .”
The judge also told the defendant that he could call Andrew De-Caro, the individual allegedly involved with Schlosser in the New York drug deal that “went bad,” but that “[t]he defendant elected not to call DeCaro . . . .” These findings are fully supported in the record.
On cross-examination trial counsel asked Nash whether he had interviewed a number of the individuals whose names arose through the course of the police investigation, as well as whether the detective recalled being told that someone was taking “pot shots” at and “chasing” Sweeney. Nash testified that he had no recollection of the “pot shots” allegation, and either did not recall the specifics of his interviews with certain individuals, did not recall the individual at all, or did not interview the individual personally.9
The defendant argues, as he did in his motion for a new trial, that it was error for the judge to exclude such evidence and that he was deprived of his Federal and State constitutional and statutory right to question the adequacy of the police investigation. He contends that he should have been able to introduce hearsay about third-party culprits from the police investigation because he was not offering it for the truth of the matter.
*316In Commonwealth v. Silva-Santiago, 453 Mass. 782, 800 (2009), this court explained the differences between third-party culprit and inadequate police investigation defenses, stating that the two “are sometimes offered simultaneously and often confused with each other, but ... are logically (and legally) distinct.” Under the so-called Bowden defense, a defendant has the right to challenge the adequacy of a police investigation and may use information concerning third-party culprits to question whether the police took reasonable steps to investigate the crime. Commonwealth v. Bowden, 379 Mass. 472, 486 (1980). Because the information is not offered for the truth of the matter, it is not hearsay. Commonwealth v. Silva-Santiago, supra at 802. However, the information is admissible only if police learned of the information during their investigation. Id. at 803. In the Silva-Santiago case, we concluded that a trial judge must, therefore, “conduct a voir dire hearing to determine whether the third-party culprit information had been furnished to the police, and whether the probative weight of the Bowden evidence exceeded the risk of unfair prejudice to the Commonwealth from diverting the jury’s attention to collateral matters.” Id. If the information is admitted, the Commonwealth may offer evidence explaining why the police did not follow that line of investigation. Id. at 803 n.25.
Here, the judge did not prevent the defendant from challenging the adequacy of the police investigation, but limited the scope of questioning to exclude certain hearsay. The parties have not pointed to a request for a voir dire of police officials anywhere in the record. Although the defendant argues that he should have been allowed to raise certain issues with police officials, the specifics of what he wanted to raise are presented in the form of quotes from trial counsel’s argument to the judge when the parties were discussing what the defendant would be allowed to ask, i.e., before the actual cross-examination of certain police officers. The defendant fails to address the fact that almost all of what he contends he wanted to raise was, in fact, asked of Detective Nash (i.e., whether the police had interviewed Mark Alvord, Jose Loriedo, and another individual from New York named Foreman). The sole issue he was not allowed to explore was whether there was a police investigation of “other homicides that may have happened in Florida that may have happened in *317the drug world.” In his brief, in his new trial motion, and in the affidavit trial counsel submitted in support of the defendant’s new trial motion, the defendant does not specifically state what it is from the hearsay that he was prevented from introducing that would have helped his defense, especially in light of the detective’s lack of memory. He also does not address the reason trial counsel used the hearsay contained in various reports only once to attempt, albeit unsuccessfully, to refresh the detective’s memory after he claimed that he could not recall interviewing certain individuals. Counsel also chose not to call Andrew DeCaro to bolster his defense that the police inadequately investigated potential third-party culprits who may have been after Schlosser. Moreover, counsel asked no questions about the adequacy of the police investigation of a State trooper who testified to the defendant’s interview with police, even though the defendant argues that he should have been able to do so.
Although the judge held a nonevidentiary hearing concerning the evidentiary issue, she did not hold the requisite voir dire of police officials.10 The information the defendant sought to introduce came from police files; thus, it is undisputed that the police were aware of the third-party culprit information. But the judge did not determine whether the probative value outweighed the risk of unfair prejudice to the Commonwealth, and thus abused her discretion.11 Commonwealth v. Silva-Santiago, supra at 804 (without voir dire for Bowden defense, court must determine whether judge abused discretion).
Because the defendant objected to the exclusion of the evidence, and because there was no voir dire, we must look at the record to determine whether the defendant was prejudiced. Id. *318“An error is nonprejudicial only ‘[i]f ... the conviction is sure that the error did not influence the jury, or had but slight effect.’ ” Commonwealth v. Flebotte, 417 Mass. 348, 353 (1994), quoting Commonwealth v. Peruzzi, 15 Mass. App. Ct. 437, 445 (1983).
We conclude that, in the specific circumstances of this case, the hearsay that was excluded from the cross-examination of the detective could not have prejudiced the defendant. The defendant’s proffer did not demonstrate that the probative value of the excluded evidence outweighed the risk of unfair prejudice. The inquiry from Stuart, Florida, police concerned the deaths of two individuals in Florida, not Massachusetts, and those individuals were tied to chairs; the statement that binding a victim in duct tape and shooting the victim in the head was the hallmark of Colombian drug dealers in Florida is of remote relevance, as other murders have involved the use of duct tape, or the shooting of a victim in the head12; and, in any event, there is no evidence that any of the people from Florida mentioned in the reports were from Colombia. In addition, none of the witnesses was able to connect Schlosser to Colombians from Florida, see note 9, supra, and trial counsel chose not to call the one witness who had the potential to connect Schlosser to a conflict concerning a drug deal. See Commonwealth v. Silva-Santiago, supra at 804-805 & n.27 (no abuse of discretion where defendant’s proffer inadequate). Cf. Commonwealth v. Phinney, 446 Mass. 155, 161-162, 166 (2006) (grant of new trial affirmed where defendant denied right to question police investigation of third-party neighbor whose wife observed suspicious behavior at time of murder).
2. Jail house informant testimony. The Commonwealth called two witnesses, Dean Lindstrom and Mark Condon, who testified to incriminating statements the defendant made to them while they were incarcerated with the defendant in 1996 and 2002, respectively.
Lindstrom testified that he had no agreement with the Commonwealth or police in exchange for his testimony. On cross-examination, trial counsel elicited that Lindstrom had an exten*319sive criminal history, including convictions of murder in the second degree, armed assault, and armed robbery; that he suffered from mental illness in the 1980’s and 1990’s that included auditory and visual hallucinations; that he had a history of being a police informant; that, when he came forward to tell police what the defendant said to him, he was trying to get transferred to a prison in another State; and that he hoped his testimony would be noticed by the parole board when he became eligible for parole in three years.
Condon testified that he also had no agreement with the Commonwealth or police. On cross-examination, trial counsel elicited Condon’s criminal history and aliases and established that, after being housed with the defendant, he was transferred to a maximum security prison from which he contacted the State police. Condon testified that, due to his transfer, the defendant spoke to him because he could pass a message from the defendant to James Rakes. See note 2, supra.
The defendant argues, as he did in his motion for discovery and request for an evidentiary hearing, that the prosecution did not disclose all relevant information concerning all relevant details of cooperation agreements between Lindstrom and the Commonwealth. He also argues that it is not clear whether Condon’s placement was deliberate, thus making him an instrument of law enforcement.
The defendant points to nothing in the record to support his assertions. Trial counsel’s affidavit does not assert that he failed to receive discovery. Moreover, in his affidavit submitted with the Commonwealth’s opposition to the defendant’s motion, the prosecutor averred that he had turned over all information that he had about the two witnesses to trial counsel, that he had no agreement with Lindstrom, and that Condon’s placement in the house of correction with the defendant was entirely coincidental. The judge credited these averments. As she stated in her decision, Lindstrom testified that he had been a police informant in the past, but that he was, at the time of trial, incarcerated in Florida, and that he made no agreement with the Commonwealth concerning his testimony at the defendant’s trial. She also stated that Condon’s placement with the defendant was entirely coincidental. Furthermore, she found that, throughout the trial and “currently,” the criminal history of both had been available from the bureau *320of probation. There was no error in denying the defendant’s motion for a new trial and an evidentiary hearing or the motion for further discovery on these matters.
3. State trooper’s observations. In 1988, the defendant spoke to a State trooper about the murders. In the report prepared after the interview, the trooper stated that the defendant was given his Miranda rights and was asked a number of questions. In sum, the defendant stated that he had no idea who killed the victims. He denied knowing the victims or anyone else in West-wood, or that Sweeney lived with the victims. He also denied that he sold cocaine, or carried duct tape or a gun. At one point during the interview, as a ruse, the trooper gestured to some tape recordings he had with him in the interview room, and stated to the defendant, “I think you did kill them. You know who is going to sink you? No one but yourself because we have you on tape saying that you killed [the victims].” The defendant did not say anything, but the trooper noticed that the defendant was staring at the floor, with his chin and legs twitching. The trooper further stated in his report that, after he urged the defendant to tell him what happened in Westwood, and after he told the defendant that he had witnesses who had seen the defendant with duct tape in his gym bag, the defendant said, twice, “I know nothing.” The interview ended after the trooper asked the defendant if he would take a polygraph test, and the defendant replied, “I don’t think I’ll answer any more questions.” The trooper and Detective Nash then drove the defendant back to the South Boston section of Boston.
The defendant filed a motion in limine to prevent the trooper from testifying that the interview ended when the defendant invoked his right to remain silent, or from testifying about the defendant’s demeanor when the trooper said that he thought that the defendant had killed the victims. The judge allowed the motion only as to how the interview with the defendant ended. On the first day of trial, counsel argued that it was “impermissible” for the jury to hear that the trooper told the defendant about the tape recordings. He also requested that the judge exclude the defendant’s statement, “I know nothing,” so that the jury “would be left with [the defendant’s] denial . . . that he used duct tape [and] possessed a gun.”
The judge ruled that, although the trooper would be allowed *321to testify about his observations of the defendant’s demeanor, he could not reference tape recordings or the defendant’s statement that he knew nothing. Thus, when the trooper testified to his observation of the defendant’s demeanor, it immediately followed his testimony that the defendant was asked whether he killed the victims.13
On appeal, the defendant argues that he was denied his due process rights when the evidence was admitted in this fashion because the trooper did not mention that, before the defendant’s demeanor changed, the trooper had just accused the defendant of murder and told him that there were tape recordings. Thus, he contends, the jury were left with the impression that the demeanor was a direct result of the trooper’s question concerning whether the defendant had killed the victims, i.e., an implied admission or consciousness of guilt. He further argues that the testimony was particularly prejudicial because the trooper was the Commonwealth’s last witness. Trial counsel did not cross-examine the trooper to put the defendant’s demeanor in context.
The Commonwealth argues that, because the defendant had waived his Miranda rights, observations of his demeanor were admissible. We need not address whether it was admissible because, even assuming that it was error to allow the trooper’s observation of the defendant’s demeanor, we agree with the judge that any error was nonprejudicial and does not warrant a new trial. As the judge stated in her memorandum of decision, “demeanor testimony was only a small fraction of the substantial quantity *322of evidence presented by the Commonwealth supporting its theory of [the defendant’s] involvement in the murders. Thus the impact . . . was de minimis . . . .” See Commonwealth v. Braley, 449 Mass. 316, 326 (2007) (where other evidence overwhelming, cumulative evidence nonprejudicial); Commonwealth v. Flebotte, 417 Mass. 348, 353 (1994) (error nonprejudicial where court “is sure that the error did not influence the jury or had but very slight effect”).
4. Evidence of the defendant’s bad acts. The defendant argues, as he did in his motion for a new trial, that it was error to admit evidence of his shooting at Sweeney’s shirt and of his access to, and familiarity with, guns and bullets, particularly where, he alleges, none of the weapons he was seen with was similar to the murder weapon. Concerning evidence of the defendant’s coating bullets with a lubricant, he argues that the testimony left the jury with the impression that he was cleaning them just before the murder occurred. There was no error.
Because of its highly prejudicial nature, “the prosecution may not introduce evidence that a defendant previously has misbehaved, indictably or not, for purposes of showing his bad character or propensity to commit the crime charged.” Commonwealth v. Mullane, 445 Mass. 702, 708 (2006), quoting Commonwealth v. Helfant, 398 Mass. 214, 224 (1986). However, such evidence may be admitted if it is relevant “to show a common scheme, pattern of operation, absence of accident or mistake, identity, intent, or motive.” Commonwealth v. Mullane, supra at 708-709. It also may be admitted to show that the defendant has the means to commit the crime. See Commonwealth v. Anderson, 448 Mass. 548, 560 (2007).
At trial, the defendant opposed the Commonwealth’s motion in limine to introduce evidence of the defendant’s access to, and knowledge of, firearms and bullets.14 We agree with the judge that this evidence fell within a proper exception to the prohibition of bad acts evidence. Where the evidence was used for this proper purpose, whether or not the defendant was seen cleaning the bullet before or after the murder is immaterial. See Com*323monwealth v. Otsuki, 411 Mass. 218, 235-236 & n.12 (1991). Moreover, the judge instructed the jury that the evidence was only to show that the defendant had some familiarity with firearms and not that he was a bad person. Commonwealth v. Auclair, 444 Mass. 348, 360 (2005) (jury presumed to follow judge’s instructions).
At trial, the defendant objected to the testimony about his shooting at one of Sweeney’s shirts. The witness further testified that he was “not one hundred per cent positive” exactly when the incident happened, but that it was “probably months not years” before the murders. The defendant argues, as he did in his motion for a new trial, that the testimony was improperly admitted and especially prejudicial, not only because it was evidence of bad acts, but also because it was remote and “as likely” that the incident occurred before the scam as after. The evidence was allowed to show the defendant’s state of mind and motive. Commonwealth v. Mullane, supra at 709. Evidence relevant to motive is admissible where its probative value is not substantially outweighed by its prejudicial effect, is connected to the facts, and is not too remote in time. Commonwealth v. Butler, 445 Mass. 568, 574-575 & n.6 (2005). The judge did not err in concluding that this evidence, which demonstrated the defendant’s anger against Sweeney, outweighed any possible prejudice or that, if the witness’s assertion that the incident occurred months before the murder was believed, the event was not too remote in time from the murders. Moreover, the judge gave the jury a limiting instruction to the effect that they could use the evidence only as to the defendant’s motive and state of mind and not to his character. See Commonwealth v. Auclair, supra.
Although he does not raise it in his direct appeal, in his motion for a new trial, the defendant also argued that evidence of his lack of gainful employment also was improperly admitted as bad act evidence. There was no error.
The witness who testified that the defendant was shooting at one of Sweeney’s shirts also testified that the defendant carried duct tape with him, either in his car or in a gym bag. The witness saw the defendant use duct tape to tape his ankles while he was playing basketball. On cross-examination, trial counsel elicited that duct tape was very common and that the witness himself *324used it. On redirect examination, over a defense objection, the prosecutor elicited that the witness used duct tape in connection with his work as a construction foreman. When the prosecutor asked whether the witness knew the type of work the defendant was doing, he responded that he had “never known [the defendant] really to have a job.”
As the judge stated in her decision, this evidence was properly admitted for two reasons. The Commonwealth had the right to rebut any “adverse testimony or inferences developed during cross-examination.” Commonwealth v. Arriaga, 438 Mass. 556, 577 (2003), quoting Commonwealth v. Marrero, 427 Mass. 65, 69 (1998). In addition, trial counsel opened the door to discussing duct tape, thus permitting the Commonwealth to inquire about the witness’s reasons for having it and whether the defendant may have worked in a similar field with reason to possess it.
5. Testimony of Joanne Sullivan. At trial, the Commonwealth called Joanne Sullivan as a witness. She had testified before the grand jury, inter alia, that she had seen the defendant with a gun more than once and that the first time she saw the defendant with a gun, it was in a black bag. At trial, Sullivan appeared only after she was threatened with arrest; police drove her to the court. Immediately prior to Sullivan’s testimony, the prosecutor stated to the judge that he expected that he was “going to have problems with her” and that he may “be asking to treat her as a hostile witness.”
During her testimony, Sullivan claimed gaps in her memory, and the judge allowed the Commonwealth to treat her as a hostile witness. Sullivan testified that, at the time she testified before the grand jury, she did not recall anything from a statement she apparently gave to police “twenty years ago” because she “did a lot of drugs.” She stated that, because she could not recall, a detective told her everything she had told police twenty years earlier and told Sullivan, “Just say what you said twenty years ago.” At trial she further testified to knowing one of the defendant’s accomplices and remembered that the defendant had been at her house in 1987. However, when asked about other statements she made in her grand jury testimony, including questions concerning the defendant’s possession of guns, Sullivan stated that she did not recall. Showing her a transcript of her grand jury testimony did not refresh her memory.
*325The defendant argues, as he did in his motion for a new trial, that the prosecutor failed to disclose to the defense “exculpatory evidence” that Sullivan had no independent recollection of her involvement with the defendant; that it was reversible error for the judge to allow the prosecutor to ask Sullivan leading questions, particularly after she testified that she had been coached before her grand jury testimony; and that the prosecutor knowingly presented unreliable and inaccurate information to the grand jury, which remained unknown to the defense until trial.
In the affidavit he submitted with the Commonwealth’s opposition to the defendant’s motion for a new trial, the prosecutor averred, “Prior to Ms. Sullivan’s testimony at trial, I was not aware that she intended to claim that she lacked any memory of her prior testimony, or that she intended to claim that her grand jury testimony was the result of prompting by the police rather than her independent memory.” The judge found the prosecutor’s affidavit credible. We accept a motion judge’s finding of credibility. Commonwealth v. Thomas, 399 Mass. 165, 167 (1987) (motion judge’s discretion to determine credibility of affidavit, especially if judge also presided at trial). There is no error where the prosecutor did not know about potentially exculpatory information. See Commonwealth v. Caillot, 454 Mass. 245, 262-263 (2009), citing Brady v. Maryland, 373 U.S. 83, 87 (1963) (no Brady violation where prosecutor had no knowledge of intentional suppression of exculpatory evidence).15
The defendant argues that the prosecutor impaired the integrity of the grand jury. He claims that Sullivan’s testimony before the *326grand jury was false because it was coached. To establish that the integrity of grand jury proceedings was so impaired as to warrant dismissal of the indictment, a defendant must demonstrate that the prosecutor knowingly introduced false or deceptive evidence before the grand jury, that the false or deceptive evidence was significant in the view of the grand jury, and that the evidence was presented with the intention of obtaining an indictment. Commonwealth v. Drumgold, 423 Mass. 230, 235 (1996), quoting Commonwealth v. Mayfield, 398 Mass. 615, 621-622 (1986).
In her decision, the judge found that nothing in the record besides Sullivan’s testimony at trial supports the conclusion that her grand jury testimony was false. Implicit in this finding is a determination that the prosecutor’s affidavit, where he averred that he “had no reason to believe that Ms. Sullivan’s [grand jury] testimony would vary in any way from that contained in the reports available to me,” was credible. Leaving aside these two issues, however, the defendant cannot meet his burden to show that the grand jury proceedings were impaired because the judge also found that “[s]everal grand jury witnesses testified that [the defendant] used and sold cocaine, used and owned firearms, and often carried a black gym bag.” In light of this finding, which the defendant does not contest, we agree with the judge that Sullivan’s testimony before the grand jury was cumulative of the testimony of other witnesses, and therefore could not have been significant to the grand jury. See Commonwealth v. Mayfield, supra at 626 n.9, citing United States v. Udziela, 671 F.2d 995, 1001 (7th Cir.), cert. denied, 457 U.S. 1135 (1982) (“If perjured testimony is presented, generally an indictment may be challenged successfully only if there was no other evidence before the grand jury sufficient to support the indictment”). There was no substantial likelihood of a miscarriage of justice.
The defendant further contends that it was error to allow the prosecutor to treat Sullivan as a hostile witness and ask her leading questions based on her grand jury testimony. He contends that all the jury heard were the prosecutor’s leading questions, not Sullivan’s denials.
The “decision whether to allow leading questions [is] left for the most part to the wisdom and discretion of the trial judge.” Commonwealth v. Flynn, 362 Mass. 455, 467 (1972), quoting *327Guiffre v. Carapezza, 298 Mass. 458, 460 (1937). It is not improper to allow leading questions where a witness’s testimony is evasive, ambiguous, or inconsistent. See Commonwealth v. Sineiro, 432 Mass. 735, 743-744 (2000), and cases cited; Commonwealth v. Carrion, 370 Mass. 408, 411 (1976). Moreover, prior inconsistent statements of a witness are admissible, provided that the witness can be effectively cross-examined concerning the accuracy of the statement and the statement itself was not coerced or a mere confirmation or denial of an allegation by the interrogator. See Commonwealth v. Daye, 393 Mass. 55, 75 (1984), as modified by Commonwealth v. Cong Duc Le, 444 Mass. 431, 432-433 & n.3 (2005).
In her decision, the judge stated that, although some of Sullivan’s statements may have been denials or confirmation of the statements by the prosecutor, she did testify consistently with at least some of her grand jury testimony. We agree with the judge that, in any event, “even if the prosecutor’s leading questions were overdone, Sullivan’s testimony alone was not crucial to the prosecution’s case [because] it was cumulative,” and that her “trial performance” of changing many of her answers “itself contradicts any assertion that her testimony was of paramount importance, as it is unlikely that the jury gave the testimony great weight.” See Commonwealth v. Murphy, 442 Mass. 485, 499 (2004) (court gives “special deference to the decisions of a judge who was, as here, the trial judge”).
The defendant’s contention, in a postargument letter, that this case is similar to Commonwealth v. Stewart, 454 Mass. 527 (2009), is unavailing. In the Stewart case, the witness, who refused to be sworn, answered, “No comment,” to a series of leading questions, based on that witness’s statement to police and his grand jury testimony. The questions posed “put forth the Commonwealth’s entire theory of how the murder was committed,” information that the court concluded was “highly prejudicial.” Id. at 528, 530. The court stated that the problem in the case was “with the questions themselves and with the ambiguity of the ‘no comment’ responses; and the jury were not instructed to ignore the responses.” Id. at 532. In determining that the errors were not harmless, the court concluded that the questions “went to the heart of the case [and] were not cumulative; [and] there was no other evidence concerning how the murder occurred.” Id. at 534. *328Here, Sullivan’s testimony did not go to the heart of the case and was cumulative, and there was other evidence of how the murders occurred.
6. Delayed disclosure of statement attributed to defendant. At trial, Trundley testified during direct examination that he had a conversation with the defendant in which he told the defendant that certain individuals with whom he had business dealings owed him money. The defendant objected to Trundley’s testimony at that point. At a sidebar conference, the prosecutor made a proffer that Trundley would testify that he told the defendant about a person who owed Trundley money, that the person had said “he was going to come and get [Trundley],” and that the defendant responded that he “would take care of it” and “get” James Rakes (see note 2, supra) to take care of the person. It was the first time the statement had been disclosed to the defendant. Acknowledging the delayed disclosure, the prosecutor did not seek to introduce the statement, nor was it admitted.
Admission of undisclosed statements subject to a discovery agreement is reversible error only if the defendant makes a “showing that [he] was significantly prejudiced at trial by the [nondisclosure,” or if he shows “how a new trial would substantially cure any error.” Commonwealth v. Bregoli, 431 Mass. 265, 270 (2000), quoting Commonwealth v. Cundriff, 382 Mass. 137, 150 (1980), cert. denied, 451 U.S. 973 (1981).
The defendant argues, as he did in his motion for a new trial, that he was prejudiced by the delayed disclosure of the statement he allegedly made to Trundley. Here, although the late-disclosed statement was not admitted, the defendant contends that he was nonetheless prejudiced because the jury could have inferred from the direction of the line of questioning, in the context of other evidence introduced at trial (e.g., the defendant’s possession and use of firearms, his previous incarceration, his use and dealing of drugs, and his reputation for violence) that the defendant was a bad character who would use force to collect money for a fee. This argument is unavailing. No reasonable inference could have been drawn from Trundley’s testimony that he told the defendant some people with whom he had become involved in a business deal owed him money, that might have logically led to the jury’s concluding that Trundley spoke to the defendant because the *329defendant was violent and would “take care of [the debt owed to Trundley].” The defendant has not shown that he was significantly prejudiced at trial by the Commonwealth’s late disclosure of the statement, nor has he shown how a new trial would substantially cure any error.
7. Late disclosure of documents. The defendant was convicted in this case after his second trial. See note 1, supra. During his first trial, the Commonwealth produced previously undisclosed documents, including police reports, witness statements, telephone records, and other related documents. The defendant’s motion for a mistrial was granted. On appeal, the defendant argues that the judge erred in denying his posttrial motion for an evidentiary hearing on his motion for a new trial. The defendant sought the evidentiary hearing to develop a predicate factual basis as to why the delayed disclosure occurred at his first trial. There was no error.
Where a defendant is prejudiced by a prosecutor’s failure to disclose properly exculpatory, material evidence, the relief typically granted is a mistrial followed by a new trial. Commonwealth v. Lam Hue To, 391 Mass. 301, 310 (1984). Here, the defendant can demonstrate no prejudice to his defense at his second trial where a mistrial was granted following the delayed disclosure during his first trial. The judge correctly concluded that, in the absence of any showing that the late-disclosed evidence prejudiced his defense, or that any of the evidence served an exculpatory purpose that was somehow thwarted by the late disclosure, the defendant was not entitled to any relief beyond the mistrial granted during his first trial.16
8. Prosecutor’s closing argument. During his closing argument the prosecutor stated, “What you see in this picture here didn’t come from the. national news that you see every night. It’s not a picture that was taken in some foreign country. It was taken at Westwood, Massachusetts, about a [ten to fifteen] minute drive *330from here.” He further stated, “[T]he Commonwealth has the burden to prove the case beyond a reasonable doubt. . .. It is no magical thing. Every case that you see on TV that is a criminal case, the Commonwealth has that burden.” In addition, the prosecutor stated, “Many witnesses have taken the stand and they told you that they were scared. It took many, many years for some of them to decide to say what they were going to say, but they did. They came to the grand jury at the end of 2001 and the end of 2002 when they testified.”
The defendant timely objected to each of the statements and moved for a curative instruction. The judge denied the motion, stating that the argument was fair. In her instructions, the judge told the jury that they should not use any concept of law they held from television, personal experience, or reading; that they could not be swayed by sympathy for the victims or prejudice against the defendant; and that they had to make a decision solely on the evidence and not based on any opening or closing arguments, which are not evidence.
The defendant argues, as he did in his motion for a new trial, that the first two remarks impermissibly played to the sympathy and emotions of the jury. In particular, the defendant claims that the first remark referred to the news reports about the wars in Iraq and Afghanistan that were ongoing during the trial. He also argues that the last statement was not supported by evidence. In evaluating alleged errors in closing argument, statements are considered in the context of the entire argument and in light of the judge’s instructions to the jury and the evidence at trial. Commonwealth v. Freeman, 430 Mass. 111, 118 (1999), quoting Commonwealth v. Passley, 428 Mass. 832, 835 (1999). There was no error.
In closing argument, counsel “may argue from the evidence and may argue fair inferences that might be drawn from the evidence.” Commonwealth v. Murchison, 418 Mass. 58, 59-60 (1994), citing Commonwealth v. Earltop, 372 Mass. 199, 205 (1977) (Hennessey, C.J., concurring). Counsel also may call on the experience and common knowledge of the jury. Commonwealth v. Silva, 388 Mass. 495, 508 (1983), and cases cited. Moreover, “[i]t is proper for counsel to use analogy, example and hypothesis as an aid to effective and aggressive argument.” Id., *331quoting Leone v. Doran, 363 Mass. 1, 18, modified on other grounds, 363 Mass. 886 (1973). It is not error for a prosecutor to state that it took courage for witnesses to testify. Commonwealth v. Pina, 430 Mass. 266, 269-270 (1999).
Here, the judge properly concluded that the first two remarks, referencing United States involvement in foreign conflicts and how criminal cases are portrayed on television, “were brief utterances that were within the common knowledge of the jury”; that the reference to the portrayal of crimes on television “was also a use of [permissible] analogy to better communicate the Commonwealth’s standard of proof”; and that, when considered in light of the prosecutor’s entire closing argument, the statement did not impermissibly play on the jury’s emotions or fears. See Commonwealth v. Kozec, 399 Mass. 514, 517 & n.5 (1987), and cases cited (prosecutor’s closing may not play on juror sympathy or emotion). The cases on which the defendant relies to support his argument are easily distinguishable. See Commonwealth v. Graziano, 368 Mass. 325, 332 (1975) (reversible error where prosecutor’s closing appealed to “popular ethnic stereotypes”); Commonwealth v. Ward, 28 Mass. App. Ct. 292, 294 (1990) (reversible error where prosecutor “sounded a persistent theme that the jury had a duty to confront crime in the streets bravely and to avenge the wrong done to the victim”).
The judge also did not err in concluding that the prosecutor’s statement that it took courage for the witnesses to testify was proper, as it was a reasonable inference from the evidence. For example, both Sweeney and Trundley testified that they were afraid of the defendant.
Pursuant to our plenary review of the record, we note that the prosecutor did misstate part of the evidence in his closing argument, but there was no objection to the misstatement. In recounting part of Tmndley’s testimony, the prosecutor accurately stated that one of the victims, Jay Schlosser, told the defendant that no one needed to get hurt. The prosecutor went on to say that Schlosser said, “I can go to the bank tomorrow and take some money out and give it to you guys.” Trundley testified, however, that Schlosser told the defendant that “he would give whatever they wanted to them.” Although the prosecutor’s comment communicated the essence of Schlosser’s statement, i.e., that he was *332trying to placate the defendant, the latter statement is not supported by Trundley’s testimony at trial. Considering this comment in light of the totality of the prosecutor’s argument and the judge’s instructions, we conclude that there was no substantial likelihood of a miscarriage of justice. See generally Commonwealth v. Anderson, 445 Mass. 195, 202 (2005) (issue whether victim said “Please, please” or “Police, police” irrelevant where words were cry for help).
9. Denial of the defendant’s postconviction motions. The defendant argues that the judge erred in denying the postconviction motions for a new trial, for an evidentiary hearing, and for discovery. All but one of the issues the defendant raised in his motions have been addressed, so we turn to that one issue, raised by the defendant in his motion for a new trial.
In his motion, the defendant contended that, where the murders took place in 1987, but the indictments did not issue until 2002, the prosecution used a strategy of delay to gain a tactical advantage resulting in prejudice to the defendant. “In order to be entitled to dismissal of the indictments due to a preindictment delay, the defendant must demonstrate that he suffered substantial actual prejudice to his defense, and that the delay was intentionally or recklessly caused by the government.” Commonwealth v. George, 430 Mass. 276, 281 (1999), and cases cited. The defendant’s burden is a “heavy one,” and “[gjeneral or conclusory allegations on such issues are insufficient for the drastic remedy of dismissal.” Commonwealth v. Best, 381 Mass. 472, 484 (1980), and cases cited.
The judge credited the prosecutor’s statement in his affidavit that the government was awaiting Trundley’s cooperation, which did not materialize until 2001. The prosecutor further averred that Trundley indicated that he was fearful that he would be killed; that Trundley “could have asserted his Fifth Amendment rights and refused to testify” where there was sufficient evidence to charge him as a coconspirator or joint venturer; and that without Trundley’s testimony, the prosecutor believed that the Commonwealth would not have sufficient evidence to persuade the jury of the defendant’s guilt beyond a reasonable doubt. The judge’s conclusion that the defendant had not “asserted that he has suffered any specific prejudice” and that he “fail[ed] to *333assert any prejudicial facts” is supported in the record. The judge did not err in concluding that the defendant failed to meet his burden, or in denying his request for an evidentiary hearing “in which [the defendant] hopes to learn how [he] was prejudiced.” See, e.g., Commonwealth v. George, supra (loss of evidence alone does not constitute actual prejudice).
Review pursuant to G. L. c. 278, § 33E. The defendant argues that we should reverse his convictions in light of the “cumulative effect” of the errors he has alleged, particularly his allegations of prosecutorial misconduct. In the alternative he asks us either to grant him a new trial or to order an evidentiary hearing on his motion for a new trial. We have reviewed the entire record pursuant to our statutory obligation and discern no reason to grant the defendant’s requested relief.
Conclusion. For the reasons set forth above, we affirm the defendant’s convictions and the denial of his postconviction motions.
So ordered.
The defendant’s first trial ended in a mistrial when the Commonwealth disclosed that it had a box of relevant materials the police had failed to disclose to the defense.
Two other individuals were charged with murder in the first degree based on their involvement. James Rakes was tried separately and was convicted on two indictments charging murder in the first degree. His appeal is pending. Patricia Rakes pleaded guilty to so much of the indictments as charged manslaughter and received a sentence of from seven to ten years committed followed by ten years’ probation.
Sweeney was an investor in the business, sold its stock, and worked on a boat in the Bahamas, where he came to realize the enterprise was a scam.
Because he was fearful of the defendant, Trundley, at that time, led police to believe that he did not know anything. The jury were not told why it took *312until 2002 for the defendant to be indicted. In an affidavit submitted with the Commonwealth’s opposition to the defendant’s motion for a new trial, the prosecutor stated that Trundley would not cooperate with police before then.
Although Trundley testified that he saw plastic masks in the defendant’s gym bag, whether (or what) the defendant and his accomplices did to prevent the victims from recognizing them was not brought out at trial.
The medical examiner’s testimony corroborated this account. Buchanan died as a result of two gunshot wounds to the head. Schlosser had a “clean-through” gunshot wound to the right wrist consistent with his having raised his arm defensively as he was shot in the right temple.
The proffer was as follows: (1) an individual from Florida, Mark Alvord, was connected through the drug trade to Schlosser; (2) Alvord was “doing business” with a “big Miami drug dealer” named Jose Loriedo; (3) Schlosser’s telephone records indicated he had telephoned Stuart, Florida, as well as Jose Loriedo, in Miami, in 1986 and 1987; (4) Schlosser traveled to Florida in 1986 and 1987 to buy drugs; (5) sometime in the spring of 1987, a drug deal between Schlosser, together with an individual named Andrew DeCaro, and dealers in New York fell through because of DeCaro, and Schlosser allegedly told DeCaro that their relationship was over and that the people Schlosser dealt with would kill DeCaro; and (5) Schlosser was expecting friends from Miami to see the Fourth of July parade in Norwood.
On appeal, the defendant does not challenge this particular ruling. He challenges the judge’s decision concerning the use of third-party culprit information only as it pertains to the defense of an inadequate police investigation.
Sweeney and Trundley were asked specifically about Alvord and Loriedo, and whether a drug deal “went bad” in Florida for Sweeney. Sweeney also was asked about a Stephen Kidman, as well as whether he was involved with anyone from Colombia, and whether he recalled telling anyone that people were taking “pot shots” at him. Sweeney’s and Trundley’s responses to these inquiries were denials or statements indicating that they did not know or did not recall the person or event.
This case was tried before we decided Commonwealth v. Silva-Santiago, 453 Mass. 782 (2009).
The judge appears to have applied the analysis for hearsay bolstering a third-party culprit defense when she concluded that there was no substantial basis for the defendant’s assertion that the murders resembled those committed by Colombian drug dealers in Florida. However, a “substantial connecting links” standard of admissibility only applies to situations where third-party culprit hearsay information is being introduced to support a third-party culprit defense. When the same third-party culprit information is used to bolster an inadequate police investigation defense, “[bjecause it is not hearsay, it need not meet the standard we set to admit hearsay evidence regarding a third-party culprit, most formidably, the substantial connecting links.” Commonwealth v. Silva-Santiago, supra at 802-803.
See, e.g., Commonwealth v. Williams, 450 Mass. 645, 647 (2008) (victim wrapped in duct tape; shot five times, including head). See also Commonwealth v. Almeida, 452 Mass. 601, 603 (2008) (victim shot in head); Commonwealth v. Jones, 439 Mass. 249, 251 (2003) (victim bound in duct tape and strangled).
The testimony, over defense objection and subsequent motion to strike, was as follows:
The prosecutor: “Did you ask him whether or not he killed [the victims]?”
The witness: “Yes, I did.”
The prosecutor: “And, sir, after you asked that question, did you make observations of [the defendant]?”
The witness: “I noticed that he got nervous. I noticed that his chin was twitching and his legs were moving back and forth.”
The defendant also objected during testimony concerning firearms and bullets. In its brief, the Commonwealth argues that the defendant did not properly preserve his objections to all of the firearms evidence. We need not consider this issue because, in any event, there was no error.
The judge did not err in denying the defendant’s request for an evidentiary hearing and discovery concerning Sullivan, where “defense counsel was provided the evidence that was available concerning Sullivan prior to trial. . . . [And ejven if Sullivan were required to testify on this issue, her memory is not likely to have improved in the passage of time.”
We also conclude that the judge did not err in denying the defendant’s cursory request for documents concerning the grand jury, where the judge concluded that the Commonwealth timely provided all relevant materials, and where the defendant “fails to state with [specificity] what he hopes to uncover in this request that could raise a ‘substantial issue.’ ” See Commonwealth v. Morgan, 453 Mass. 54, 62 (2009), quoting Commonwealth v. Daniels, 445 Mass. 392, 407 (2005) (in requesting postconviction discovery, defendant must show that “discovery is reasonably likely to uncover evidence that might warrant granting a new trial”).
The transcripts from the defendant’s trial show that counsel cross-examined a now-retired police detective about the box of evidence and used details in the materials during cross-examination. See generally Commonwealth v. Molina, 454 Mass. 232, 237 (2009), citing Commonwealth v. Marrero, 436 Mass. 488, 497 (2002) (failure to ask for continuance on late disclosure of evidence undermines assertion that counsel had no time properly to prepare for cross-examination).