MASSING, J.

The defendant, James S. Winquist, appeals from two convictions of second-degree murder. He claims that two statements of Eric Snow, his joint venturer in the murders, were erroneously admitted against him as coconspirator statements; that the trial judge erred by denying his midtrial request for a hearing under Franks v. Delaware, 438 U.S. 154 (1978); that the prosecutor's closing argument was improper; and that a key witness, Kelly Burgess, was incompetent to testify. We affirm.

Facts.1 One morning in May, 2005, the badly decomposed bodies of two homeless men, William Chrapan and David Lyon, were discovered inside an abandoned cement bunker at Bare Cove Park in Hingham. The victims each had suffered complex skull fractures, the result of blunt force and "semi-sharp" injuries. Chrapan's body was missing its right hand. The victims had been dead for approximately three weeks. Two months later, two men walking their dogs near the power lines on Elm Street in Bridgewater discovered the hand that had been severed from Chrapan's body when one of their dogs ran off and returned carrying a plastic bag containing the hand.

In September, 2007, more than two years after the discovery of the bodies, a grand jury indicted the defendant for the murders of Chrapan and Lyon. The defendant's friend Eric Snow also was charged with the murders, but he committed suicide in jail in March, 2012, about six months before the trial commenced. The jurors did not hear any evidence about the charges against Snow or the reasons for his absence from the trial.2

The defendant, Snow, and Michael Alfano were the core members of a group called the "Brotherhood of Blood" (Brotherhood), which Alfano had formed in prison so that fellow inmates who shared "white pride" or "neo-Nazi" beliefs could "look out" for one another. The defendant joined Alfano's group in 2004, when they were both serving sentences at the correctional facility in Plymouth. Snow and Alfano had known each other since they were in corrective school together as youths. Among the Brotherhood, Snow went by the nickname "Killer," Alfano was called "Mental," and the defendant was known as "Twisted."

In April, 2005, the defendant was living in Hingham, down the street from Bare Cove Park. One day the defendant, his girlfriend, Snow, and Kelly Burgess, a woman who had recently befriended Snow and the defendant,3 went for a walk to Bare Cove Park, where they encountered two homeless men washing up by the water. When Burgess offered them money to buy coffee, Snow slapped the money from her hand and made disparaging comments about them.

A day or two later, Burgess was hanging out at the defendant's house with the defendant and Snow. Around 11:00 P.M., Snow asked Burgess to drive him and the defendant down the street. She gave them a ride to the Stop and Shop parking lot, across the street from Bare Cove Park, and Snow asked her to return thirty minutes later to pick them up. After watching an episode of "The Honeymooners" at the defendant's house, Burgess drove back to the Stop and Shop and waited. Within a few minutes the defendant and Snow emerged from the woods across the street and got into Burgess's car. She drove them back to the defendant's house, where they all went downstairs to the basement. Burgess saw that Snow was covered with blood, and the defendant had blood on the bottom of his pants and boots. Each was carrying a baseball bat; bloody spikes protruded from the bat in Snow's hands.

The defendant and Snow changed clothes, putting the blood-soiled clothes and the bats in a bag on the floor. Snow told the defendant to "get rid of them," and the defendant said that he would. Burgess asked Snow what he was talking about, and he replied it was none of her business. Burgess and Snow then left together, but before they left, Snow told the defendant that "he made his bones." Among members of the Brotherhood, this expression meant "killing somebody, putting in work that would prove you worthy" of membership in the group.

Burgess drove Snow to his mother's home in Bridgewater. Snow directed her to drive to the dirt road behind the house, near the power lines. Snow took a black bag from the back seat and left it in the car while he walked over to a telephone pole and started digging a hole with his bare hands. Burgess peeked into the bag and saw that it contained a human hand. Snow buried the bag containing the hand in the hole he had dug.

David Courage, who lived across the street from the defendant in Hingham, was at the defendant's house the day that news broke of the discovery of the victims' bodies in Bare Cove Park. In the basement, the defendant pointed out to Courage that the handsaw and the spiked baseball bat that he kept there were missing. The defendant told Courage that he and Snow had rousted the victims from their tent at the park, "started whacking them" with the spiked bat, and "cut the hand off as a souvenir."

Katelyn Glynn, a friend of the defendant's girlfriend, visited the defendant's house almost every day that summer. There she met the defendant, Snow, Alfano, and Courage. Toward the end of the summer, she heard the defendant and Snow talking about the Bare Cove Park murders. The defendant told Snow "that he had a present for Michael [Alfano] when he got out of jail and it was a hand." A few months later, when Glynn learned that Snow had been arrested, she asked the defendant if Snow's arrest was related to the murders. The defendant said, "No, because if that was the case, I'd be fucked, too."

In July, 2005, at a party at the defendant's house, Courage showed Alfano a bag containing a human hand and told Alfano that he had "made his bones." In February, 2006, Alfano returned to jail. He was released after testifying before a grand jury that Courage had told him that Courage had killed the two men at Bare Cove Park and had showed him the hand to prove it. In May, 2006, Alfano asked the defendant about the murders and whether Courage or the Brotherhood had really been involved. The defendant told Alfano that "he and Eric [Snow] had, in fact, gone down there, Eric brought him down there, and that, in fact, it was not Courage." The defendant told Alfano that Burgess had driven them to the park and that "they walked up to the campsite, found the guys sleeping. Eric hit one guy with a bat. And hit him again. Apparently the other guy come [sic] to and was asking what was going on. And they hit him, too, with the bat."

On April 26, 2007, Snow, who was then in prison serving an unrelated sentence, wrote a letter to the defendant on the occasion of the second anniversary of the murders.4 In the letter, Snow wrote, "You made your bones while the rest smoked them." Suspecting that certain of their friends were planning to tell the police about the murders, Snow said, "[W]e know who the real threats are and what needs to become of them." He provided the defendant with the address of Kelly Burgess and another individual, Jack Amaral, on East Main Street in Brockton, and instructed him to "make sure you take out Beast5 as well."

In June, 2007, the defendant drove to East Main Street in Brockton, where Burgess lived with Amaral. Amaral saw the defendant park his car and open the trunk, revealing a white, five-gallon bucket. As the defendant was climbing the stairs to Burgess and Amaral's apartment without the bucket, Amaral confronted him. The defendant told Amaral that Snow had sent him there to set their house on fire.

Instructed on first-degree murder on theories of extreme atrocity and cruelty and deliberate premeditation, second-degree murder, and joint venture liability, the jury convicted the defendant of two counts of second-degree murder.

Admission of coconspirator statements. The defendant contends that the trial judge wrongly admitted two statements attributed to Eric Snow against him under the coconspirator or joint venture exception to the hearsay rule: Burgess's testimony that as the defendant and Snow were disposing of their bloody clothes and weapons immediately after the crime, Snow told the defendant that "he made his bones," and the letter that Snow wrote to the defendant from prison on the second anniversary of the murders, also saying, "You made your bones."

"Out-of-court statements by joint venturers are admissible against the others if the statements are made during the pendency of the criminal enterprise and in furtherance of it." Commonwealth v. Carriere, 470 Mass. 1, 8 (2014), quoting from Commonwealth v. Burton, 450 Mass. 55, 63 (2007). See Mass. G. Evid. § 801(d)(2)(E) (2014) ("A statement of a coconspirator or joint venturer made during the pendency of the cooperative effort and in furtherance of its goal when the existence of the conspiracy or joint venture is shown by evidence independent of the statement" is not excluded by the hearsay rule). This rule is rooted in "a belief that `[t]he community of activities and interests which exists among the coventurers during the enterprise tends in some degree to assure that their statements about one another will be minimally reliable.'" Commonwealth v. Bongarzone, 390 Mass. 326, 340 (1983), quoting from Commonwealth v. White, 370 Mass. 703, 712 (1976).

To dispel the first of the defendant's contentions on appeal, we observe that the admission of the coconspirator statements does not present any issue under the confrontation clause of the Sixth Amendment to the United States Constitution or under Bruton v. United States, 391 U.S. 123, 135-136 (1968) (Bruton). The defendant's right to confrontation is not implicated because statements made by coconspirators during their joint venture are not created for use at trial and are therefore not "testimonial" within the meaning of Crawford v. Washington, 541 U.S. 36 (2004). See Commonwealth v. Carriere, supra at 8-9. Bruton has no application because if Snow's out-of-court declarations qualify as coconspirator statements, they are admissible against the defendant personally. See Commonwealth v. Clarke, 418 Mass. 207, 218 (1994).

Nonetheless, the statements must qualify for the joint venture exception to be admissible. The defendant argues that Burgess's testimony concerning Snow's first statement to the defendant was not admissible as a coconspirator statement because Burgess was not a member of the conspiracy. The defendant did not make this argument at trial.6

Although Burgess was not a joint venturer with Snow and the defendant, the fact that she overheard the conversation between them does not disqualify it from the coconspirator exception. Burgess was not a "stranger[] or third part[y] unsympathetic to the goals of the venture." Commonwealth v. Bright, 463 Mass. 421, 433 n.16 (2012). To the contrary, she was a friend of the two men and assisted, perhaps unwittingly, in the concealment of highly incriminating evidence. Unlike the attorney-client privilege, see Commissioner of Rev. v. Comcast Corp., 453 Mass. 293, 306 (2009), the mere presence of third parties does not make the coconspirator exception inapplicable. See, e.g., Commonwealth v. Clarke, supra at 210 (statement of defendant's joint venturer to victim's cousin in an effort to prevent him from reporting crime admissible against defendant as coconspirator statement); Commonwealth v. Braley, 449 Mass. 316, 319-320 (2007) (testimony of joint venturer's girlfriend concerning coconspirator statements joint venturer made during conversation with defendant, defendant's wife, and witness-girlfriend admissible); Commonwealth v. Wood, 469 Mass. 266, 278-281 (2014) (joint venturer's statements to his girlfriend both a few hours and a few days after crime admissible under coconspirator statements exception). Accordingly, Burgess's testimony qualified for the joint venture exception to the hearsay rule, and its admission did not create any risk of a miscarriage of justice.

With respect to the statement in Snow's letter, the defendant argues that it was inadmissible because it was written two years after the crime and long after the object of the conspiracy had been achieved.7 In general, statements made by coconspirators "shown to have taken place after the conspiracy came to an end ... are not admissible against the other defendants." Commonwealth v. Shea, 323 Mass. 406, 414 (1948). Commonwealth v. Bongarzone, supra at 340 n.11. However, our cases have recognized that acts of concealment performed in the aftermath of a joint venture may extend the duration of the conspiracy "so that declarations of one coventurer furthering the concealment [can] be put in evidence against another." Commonwealth v. White, 370 Mass. at 709-710 & n.8. We "regard both the commission of the crime and the attempt to evade arrest for the crime as part of a single, continuous joint venture." Commonwealth v. Bright, supra at 436. See Commonwealth v. Stuart, 207 Mass. 563, 567 (1911) (recognizing the viability of the coconspirator exception for statements regarding the concealment of evidence or fruits of the crime "after the paramount object of the conspiracy [has] been attained").8

The defendant correctly points out, however, that no Massachusetts case has permitted the admission of coconspirator statements for the purpose of concealment more than a few weeks after the conclusion of the conspiracy, let alone two years later. See, e.g., Commonwealth v. Clarke, supra at 218-219 (coconspirator statements made one day after crime for purpose of avoiding detection properly admitted); Commonwealth v. Bright, supra at 425, 436-437 (statements made "in the days following the shooting"); Commonwealth v. Ali, 43 Mass.App.Ct. 549, 562 (1997) (statements made during concealment phase "during the four days following the crime").

At the outside limit of this line of cases is Commonwealth v. Angiulo, 415 Mass. 502, 519-520 (1993), where the challenged statements were made approximately three weeks after the object of the conspiracy was attained, but still marked "a desire to conceal the fact of the killing and the identity of the killers." Because the statements were "in furtherance" of the initial criminal conspiracy, they were still "minimally reliable" and thus properly admitted. Id. at 518, 520.

The defendant argues that the admission of Snow's letter strains to the breaking point the rule and rationale for admitting coconspirator statements, which requires not only that the statements be "in furtherance of" the conspiracy, but also "during the pendency" thereof. Commonwealth v. Carriere, 470 Mass. at 8. After all, "every conspiracy will inevitably be followed by actions taken to cover the conspirators' traces." Grunewald v. United States, 353 U.S. 391, 402 (1957). Taken to its extreme, the Massachusetts rule would "extend indefinitely the time within which hearsay declarations will bind co-conspirators." Ibid.

We do not address the defendant's argument that Snow's letter, written two years after the murders9 with a purpose to prevent witnesses from coming forward to reveal the crime, was not admissible as part of "a single, continuous joint venture" with the defendant, Commonwealth v. Bright, supra at 436, because the record presents an adequate, alternative ground for admitting the letter. See Commonwealth v. Va Meng Joe, 425 Mass. 99, 102 (1997) (appellate court may affirm ruling on grounds or legal theory different from that relied on by trial court judge if basis for affirmance is supported by record).

Even in jurisdictions that do not recognize efforts towards concealment as a "continuing subsidiary phase of the conspiracy," Krulewitch v. United States, 336 U.S. 440, 443 (1949), such statements may nonetheless be admitted if there is "an express original agreement among the conspirators to continue to act in concert in order to cover up, for their own self-protection, traces of the crime after its commission," Grunewald v. United States, supra at 404, or if concealment is the objective of a separate agreement formed after completion of the original conspiracy. See United States v. Upton, 559 F.3d 3, 14 (1st Cir.), cert. denied, 558 U.S. 949 (2009) ("[A]cts of concealment done after these central objectives have been attained for the purposes of covering up after the crime" admissible if government presents "some proof of an express original agreement to engage in the acts of concealment"); Blecha v. People, 962 P.2d 931, 938 (Colo. 1998) (coconspirator statements made after conspirators attain objective of conspiracy not admissible unless proponent shows "the objectives of the original conspiracy include such an agreement or that there exists a separate conspiracy to conceal"); State v. Harris, 141 Idaho 721, 725 (2005) (same).

We are satisfied that the evidence presented at trial, independent of Snow's letter, showed an "adequate probability of the existence of a common venture," Commonwealth v. Bright, 463 Mass. at 435 (citations omitted), between the defendant and Snow to silence witnesses, so that the statements in Snow's letter were admissible as part of "a new and distinct joint venture," Commonwealth v. Bongarzone, 390 Mass. at 343, with the defendant. After receiving a letter from Snow, the defendant went to the apartment where Burgess and Amaral lived, with the intent to burn it down. Amaral saw the defendant open the trunk of his car, which contained a white, five-gallon bucket. When Amaral intercepted the defendant (who was empty handed) on the stairs, the defendant admitted he had come, at Snow's request, to burn the house down. Accordingly, the contents of the letter were admissible under the joint venture exception.

Finally, the defendant argues that Snow's statement was inadmissible because he wrote the letter while he was incarcerated. The coconspirator exception generally does not apply after "a joint venturer has been apprehended and imprisoned." Commonwealth v. Colon-Cruz, 408 Mass. 533, 543 (1990). Once the participants in the joint venture have been arrested, their commonality of interest gives way to individual concerns about criminal liability and punishment — the paradigmatic "prisoner's dilemma."10 See Commonwealth v. Santos, 463 Mass. 273, 293 & n.20 (2012). See also Commonwealth v. Drew, 397 Mass. 65, 71 (1986) ("Because [joint venturer's] statement was made long after the crime while he and the defendant were imprisoned, the statement was not admissible").

Here, however, Snow's imprisonment was not inconsistent with the joint venture exception. Unlike the joint venturers in Commonwealth v. Santos, supra at 293, who "had been arrested for their involvement in the killing," Snow was in custody on an unrelated matter and before anyone was charged with the Bare Cove Park murders. See Commonwealth v. Leach, 73 Mass.App.Ct. 758, 766 (2009) (although the joint venturers were imprisoned, statements were admissible because they were made shortly after the crime and for the purpose of concealment).

Renewed motion for a Franks hearing. The defendant also argues that Snow's letter, which the police found in a box in the defendant's bedroom during the execution of a warrant to search his Weymouth home, should have been suppressed. He claims that the application for the search warrant contained statements11 that were either intentionally false or made with reckless disregard for the truth in violation of Franks v. Delaware, 438 U.S. 154, 155-156 (1978) (Franks), and that the trial judge erred by denying his midtrial motion for a Franks hearing.

On the seventh day of trial, the defendant filed a renewed motion for a Franks hearing12 after Courage testified, in apparent contradiction of the affidavit in support of the search warrant application, see note 11, supra, that he had never been to the defendant's home in Weymouth and that he never told anyone that he had. The defendant appeals from the trial judge's denial of the renewed request.

A hearing on a Franks motion is required upon "a substantial preliminary showing" that the affiant made a material, false statement either intentionally or with reckless disregard for the truth. Commonwealth v. Ramos, 402 Mass. 209, 215 (1988). Commonwealth v. Douzanis, 384 Mass. 434, 437-441 (1981). The defendant did not make a substantial showing. Courage was an extremely unreliable witness. He claimed to have a head injury, and the judge found it necessary to suspend his testimony, have him examined by a court clinician, and recall him the next day. The affiant, Sergeant Leonard Coppenrath, testified at trial that he "believed" Courage had told him that the defendant kept letters and other artifacts both at his house in Hingham and in Weymouth. Coppenrath's affidavit further stated that Courage was not the only witness who provided this information. "There was no showing that the affiant had any reason to doubt the truth of the statements given to him." Commonwealth v. Nine Hundred & Ninety-Two Dollars, 383 Mass. 764, 775 (1981).

Prosecutor's closing argument. The defense at trial was that Eric Snow committed the murders — possibly with the assistance of David Courage — and that the defendant was "nothing more than a pathetic pawn." With respect to the views that Snow expressed in telephone conversations with the defendant, recorded while Snow was in prison, defense counsel argued that the defendant "was not capable of having that type of viewpoint."

During the prosecutor's summation, he replayed portions of a telephone conversation between the defendant and Snow. In this conversation, referring to photographs of Burgess's children that Snow had received, the defendant said, "Hey, you should cut the pictures up, and you should mail [her] the pieces of them.... Like, mail her a hand." The prosecutor then commented:

The defendant claims that these comments require reversal of his convictions because the prosecutor improperly urged the jurors to consider the defendant's conduct long after the crime had been committed on the issue of the defendant's intent. The defendant timely objected at trial. Noting that consciousness of guilt evidence is not normally relevant to the issues of deliberate premeditation or malice aforethought, see Commonwealth v. Blaikie, 375 Mass. 601, 605-606 (1978); Commonwealth v. Cohen, 412 Mass. 375, 392 (1992); Commonwealth v. Niland, 45 Mass.App.Ct. 526, 529 (1998),13 the defendant argues that the same principle should apply to any evidence of the defendant's behavior or statements after the crime.

We disagree. If the jurors viewed Snow as the leader of the venture to murder the victims, an important issue at trial was whether the defendant shared Snow's intent. See Commonwealth v. Jones, 6 Mass.App.Ct. 750, 758-759 (1978) ("It is well settled that to hold a person criminally responsible for the acts of another it must be shown that the passive party shared the mental state required to convict the active party of the crime charged and that the passive party intentionally assisted the active party in that crime"). In this regard, the defendant's boasts about his involvement in the murders are probative of his active participation and relevant to his culpability. See Commonwealth v. Chaleumphong, 434 Mass. 70, 80 (2001); Commonwealth v. DiRenzo, 44 Mass.App.Ct. 95, 102 (1997) (Kass, J., concurring in part and dissenting in part). Even in the context of consciousness of guilt evidence, "indications of a defendant's state of mind, coupled with other evidence, can be sufficient to establish guilt." Commonwealth v. Vick, 454 Mass. 418, 424 (2009).

"Prosecutors are entitled to argue theories supported by the evidence and to suggest fair inferences from the evidence (which inferences need only be reasonable and possible, not necessary or inescapable)." Commonwealth v. Correia, 65 Mass.App.Ct. 27, 31 (2005). The prosecutor's remark did "not exceed the bounds of fair inference." Ibid.

Competency of Burgess to testify. The defendant argues that Kelly Burgess's answers to questioning on cross-examination cast doubt as to her competency as a witness and that the judge should have held a competency hearing sua sponte. See Commonwealth v. Hill, 375 Mass. 50, 54 (1978); Commonwealth v. Robbins, 431 Mass. 442, 447-448 (2000), quoting from Pate v. Robinson, 383 U.S. 375, 385 (1966) ("The judge ... must raise the question sua sponte if sufficient reason exists to doubt the [witness's] competency").

Defense counsel cross-examined Burgess with several prior inconsistent statements in, and omissions from, her grand jury testimony. After pressing her with her prior testimony, defense counsel repeatedly asked Burgess, "Did you lie at the grand jury in a first degree murder case?" She repeatedly responded, "I didn't lie," and further defended herself with explanations such as, "I bury things," "I can't handle it," "I was scared to be involved in something like that," and "I didn't tell them everything at first."

Burgess's responses to defense counsel's vigorous cross-examination did not demonstrate an insufficient understanding of the difference between truth and falsehood. See Commonwealth v. Brusgulis, 398 Mass. 325, 329 (1986). Indeed, she acknowledged that she had omitted facts from her grand jury testimony. The judge's action in ordering an evaluation of David Courage showed that he was keenly aware of the issue of witness competency. He did not abuse his wide discretion by failing to raise the issue of Burgess's competency sua sponte.

Judgments affirmed.