J. The defendant, Alberto Torres, was convicted of murder in the first degree, on a theory of extreme atrocity or cruelty, in connection with the beating death of fourteen month old Clyde Harper, Jr., and was convicted on two indictments charging assault and battery by means of a dangerous weapon, two indictments charging assault and battery, and four indictments charging permitting bodily injury to a child (G. L. c. 265, § 13J), stemming from the abuse of Clyde and his two older siblings. Before us is the defendant’s direct appeal from those *556convictions, and his appeal from the order denying his motion for a new trial. The defendant contends that (1) the evidence against him was insufficient to support a guilty verdict on any of the indictments; (2) certain statements should have been excluded because they were obtained in violation of his right to counsel as guaranteed by the Sixth Amendment to the United States Constitution; (3) hearsay evidence of an accusation against him by the children’s mother was improperly admitted; (4) improper evidence of his refusal to speak to the police was introduced; (5) he was erroneously precluded from introducing evidence of an injury to one of the children that had occurred prior to his arrival in the household; (6) the prosecutor made an improper closing argument; and (7) the multiple indictments were improperly joined for trial.1 He also asks that we exercise our power under G. L. c. 278, § 33E, to grant him a new trial or reduce his degree of guilt. For the following reasons, we affirm the conviction of murder in the first degree, and decline to grant relief under G. L. c. 278, § 33E; we reverse the conviction of one of the indictments charging assault and battery by means of a dangerous weapon, and remand for a new trial on that indictment; and, in all other respects, we affirm the remaining convictions and the order denying the defendant’s motion for a new trial.
1. Facts. Viewed in the light most favorable to the Commonwealth, the evidence at trial was as follows. In August, 1996, Torres began living in a small apartment in Holyoke with his girl friend, Susan Fappiano, and her three children. The oldest child, Jeffrey Columbus, was five years old; his sister, Shy-la Harper, was three years old; Clyde was one year old. Prior to the defendant’s moving in, and continuing thereafter, several friends and neighbors observed Fappiano beating Jeffrey and Shy-la with various objects (a belt, a wooden spoon, a sandal, a cable wire), striking them with her hand, or kicking them. However, despite frequent observations of Fappiano’s striking *557the older two children, no one ever saw her hit Clyde, the baby, who was described as Fappiano’s “favorite.”
Neighbors also observed the defendant strike Jeffrey “hard” in the face. On one occasion, after he struck Jeffrey, the defendant and Jeffrey went back into the apartment, whereupon Fappiano began hitting Jeffrey with a wire. Although no one saw the defendant strike Shy-la, a neighbor once came upon Shy-la, crying with red marks and a “handprint” on her face. Shy-la told the neighbor that “Daddy” had hit her, and, later that day when the neighbor returned out of concern, the defendant grabbed Shy-la “real hard,” took her into another room, and slammed the door.
That same neighbor was also concerned about Clyde. She had come to the apartment sometime in September, the month following the defendant’s arrival, to find Clyde lying on the couch crying. When she picked him up and tried to stand him up, he continued to cry. He was unable to walk.2 The defendant told the neighbor that Clyde had fallen off the sofa, and she saw the defendant roughly apply a bandage to the child’s leg. The neighbor attempted to massage the leg. As the child’s loud crying continued unabated, the neighbor expressed the view that the leg was broken and that the child should be taken to a hospital. The defendant insisted that the leg was not broken.
The following month, the same neighbor was in the apartment again. The defendant became angered for some reason, picked Clyde up, and threw him “real hard” onto the couch, handling him “very rough.” The baby bounced off the surface of the couch, lost his breath and, when he regained his breath, began screaming. Fappiano came into the room and picked the baby up, whereupon the defendant began arguing with her as she held the screaming child. The neighbor left them arguing.
During the mid-afternoon of October 20, 1996, the day that Clyde died, another neighbor was at the apartment. Clyde was lying in a car seat and crying. The defendant picked him up and put him down again, yelling at him to “shut up.” When the child continued to cry, the defendant picked him up and shook him, again yelling at him to “shut up.” The child screamed *558even louder, and the defendant’s yelling at him continued. The neighbor left the apartment, with the defendant still yelling and the baby screaming ever louder.
At 7:50 p.m., emergency personnel were dispatched to the apartment in response to a “911” call from Fappiano. They found the defendant holding Clyde, who was by then “lifeless,” with evident bruises “over his entire body.” Attempts to revive the child at the scene were unsuccessful, and he was pronounced dead within minutes of his arrival at the hospital. Radiologic examination of his body confirmed that his left femur had been fractured two to eight weeks before his death (a time period consistent with the neighbor’s lay diagnosis of a broken leg), and experts opined that a fall from a couch (the event that the defendant had identified as the cause of the injury to Clyde’s leg at the time) would not have caused such an injury. That type of fracture would be consistent with a fall from a considerable height, or an automobile accident. It could also be inflicted by twisting a child’s leg, or swinging him by the leg. Clyde also had bruises — “too many of them to even count” — over most of his body. Many of them were “pattern” bruises, consistent with being hit with various objects that would leave those patterns. Some of the bruises were “fresh,” while others were “days” old. Clyde had also suffered lacerations to his anus and rectum; those injuries were thought to be one to two days old.
An autopsy revealed significant internal injuries, in particular, a tear of the small intestine, caused by a single blow of “massive force.” That blow, inflicted from “front to back,” had pushed the small intestine up against the spine and tom it in two. The force required to inflict such an injury was described as “[ejxtreme,” “very significant,” “extremely directed and forceful,” a “blow of very, very extensive force.”3 From the focused nature of the resulting damage, the pathologist opined that the injury was most likely inflicted by a single blow with a fist, not by multiple blows and not with something as large as a foot or a knee (which would have caused more widespread damage to other parts of the abdomen).
*559The pathologist estimated that the blow to the abdomen had been inflicted at approximately 8 a.m. on October 20, some twelve hours prior to the child’s death. Such an injury would inflict severe pain, followed by the onset of peritonitis when the tom intestine released fecal material into the abdominal cavity. Medical experts described the course that that infection would take.4 Initially, the child would be crying in pain. He would be unable to walk; a child suffering peritonitis would be in pain even if still, and would suffer “extraordinary pain” if moved. Severe abdominal pain would also render the child unable to eat. His complexion would become “pale and ashen and gray.” His abdomen would become extremely swollen and rigid, and he would likely vomit.5 The rapid progression of the infection would cause him to become increasingly lethargic and unable to breathe, with a drop in heart rate and blood pressure, ultimately leading to unconsciousness, shock, and death. These stages would have occurred over a matter of many hours, and an adult observer would recognize such a child’s condition as “very abnormal.” By 6 p.m., approximately two hours prior to death, the child would have been in an “extreme” state, lapsing in and out of consciousness, and suffering severe pain if he were still conscious. At no time would he have gone into convulsions or seizures.
While at the scene, the officers also observed obvious bruising on Shy-la, and both Shy-la and Jeffrey were treated at a hospital. Shy-la had many braises and abrasions on her arms, back, buttocks, legs and genital area. The injuries had been inflicted at various times, ranging from a day to four or five days old. Jeffrey also had multiple bruises, and a bone scan *560revealed that he had several fractured ribs. Expert witnesses opined that many of the injuries to Shy-la and Jeffrey had been inflicted with objects and with considerable force.
Officers spoke with the defendant and Fappiano together at the apartment that night, asking them for an explanation of the bruises on Clyde. Fappiano told them that Clyde had fallen out of his stroller during a walk in the woods. The defendant nodded in agreement with Fappiano’s answer. When one of the officers asked the defendant what happened to the baby, the defendant “threw his arms up,” saying that he had “done nothing wrong,” and tried to walk away.
The defendant gave two statements at the police station later that night. He said that, at approximately 6 p.m. that day, Clyde fell while in the living room, and the defendant took him to his crib and fed him a bottle of milk. He left Clyde with the bottle, returning a while later to find that he had finished about one-half of it. A while later, he heard the child vomiting. He went to retrieve him, and brought him into the master bedroom. The child looked pale, and appeared as if he were about to vomit again. He then stopped breathing, and Fappiano dialed 911 to summon help.
In his further statement later that night, the defendant denied that he ever struck any of the children, and denied that Fappiano abused her children. He claimed that he had only seen her “slap their hands.” The defendant said that he and Fappiano had been home at the apartment with the children all day. He again repeated the scenario of Clyde’s falling in the living room at about 6 p.m., drinking a bottle thereafter, vomiting, and suddenly being unable to breathe.
Speaking to a neighbor that same night, the defendant told her that Jeffrey had “stepped on” Clyde’s stomach. Two days later, speaking with another neighbor, he stated that Jeffrey had “jumped on” Clyde’s stomach. At the time he gave these explanations of the child’s death, he did not yet know the results of the autopsy.
The defendant next spoke with two State troopers on October 28, one week after Clyde’s death. One of them advised the defendant that Fappiano was “blaming [him] for what happened,” whereupon the defendant stated that he “didn’t do *561anything” and that it was Fappiano who had “abused the kids.” He also stated that it was Fappiano who told him that Clyde’s earlier leg injury had occurred as a result of his falling off the couch. The defendant said that he did not want to say anything more about Fappiano’s abuse of the children at that time, but he agreed to meet with them again in future and made an appointment to do so.
In his next statement, given on October 30, the defendant reiterated his earlier version of the events on the day of Clyde’s death. However, he said that he had seen Fappiano strike all three of the children “quite a few times,” and acknowledged that he had lied on that subject in his earlier statements. He gave specifics of one incident where Fappiano had struck Jeffrey with a sandal, three incidents where she had struck Shy-la with her hand, and one incident where she had told a crying Clyde to “[sjhut up” and struck him on the leg. The defendant claimed that he told Fappiano not to hit Clyde, threatening that he (the defendant) would hit Fappiano if he ever saw her do that again. He claimed that Fappiano promised not to hit the baby again, but stated that the baby “aggravate^]” her. The defendant again claimed that he never struck any of the children himself, but that, if they misbehaved, he would “give them to [Fappiano].” With regard to Clyde’s broken leg, the defendant claimed that he had come home from work and picked up Clyde, and that the baby had cried when the defendant touched his leg. Fappiano told him that Clyde had fallen off the couch, and he asked her whether she was going to take the baby to the hospital. She said she would do so the next day if the baby were not better. The next day, Fappiano told the defendant that she had taken Clyde to the hospital, and that the doctor had advised her that the leg was not broken. The defendant told Fappiano that he did not believe her.
On May 31, 1997, the defendant spoke with two State troopers at a house of correction.6 The defendant again denied any involvement in the abuse of the children, telling the troopers that Jeffrey would tell lies about being hit. The officers told him *562they knew the baby had been “screaming” that day. The defendant replied that Clyde had been “fussy.” They expressed the view that the defendant’s statements had been inconsistent; that his statements were inconsistent with Fappiano’s; and that both their statements were inconsistent with what the doctors were saying.7 The defendant then said that Fappiano “must have caused it,” and called her a “fucking bitch.” The troopers told him that they knew that he knew what had happened to Clyde. The defendant dropped his head, shook his head from side to side, and appeared on the verge of tears.
The interview ended, and the troopers left the room. Moments later, as the defendant was being prepared to be returned to his cell, he gestured to one of the troopers and asked him to come over. The defendant said that he wanted to tell the troopers what happened to Clyde, and that he knew what Fappiano had done that killed the child because he had “seen this shit happen.” The trooper asked him what Fappiano had done, to which the defendant replied that he could not tell him then but that he would get in touch with them later and tell them what happened.
Later that afternoon, the defendant asked to speak to one of the correction officers.8 The defendant told the officer that the State police had been talking to him because he was a witness to his former girl friend’s killing her child, and that she “fucking killed him.” He stated that the girl friend “kicked him repeatedly, and grabbed him by the hair and just kept kneeing and kicking him.” He said that the baby began having convulsions and then went unconscious.
2. Discussion, a. Sufficiency of the evidence. The defendant contends that the evidence was insufficient to convict him on any of the indictments, and that his motions for a required finding of not guilty should have been allowed. We apply the familiar standard “whether, after viewing the evidence in the *563light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt” (emphasis in original). Commonwealth v. Latimore, 378 Mass. 671, 677 (1979), quoting Jackson v. Virginia, 443 U.S. 307, 318-319 (1979). At trial, the Commonwealth proceeded on theories of both principal and joint venture liability, and all indictments were submitted to the jury on both theories. The evidence, although entirely circumstantial, was sufficient to support both theories with respect to all but one of the indictments.
i. Murder in the first degree. The evidence concerning Clyde’s injuries and the manner of his death readily support the conclusion that the perpetrator acted with malice and that one or more of the factors identified in Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983), was present. The fatal blow to the child’s abdomen was delivered with tremendous force, warranting the inference that the perpetrator had an actual intent to inflict grievous bodily injury, or that a reasonable person would have known that such a blow would create a plain and strong likelihood of death. Either second or third prong malice was readily inferable on this evidence. As to extreme atrocity or cruelty, there was ample evidence of the child’s extreme suffering over a period of many hours, and evidence of indifference to his suffering during that slow and painful death. Indeed, the evidence was that the defendant had shaken Clyde, and yelled at him to “[sjhut up,” hours after the fatal blow had been inflicted and at a time when the child was obviously in great pain.
The defendant’s argument focuses on alleged gaps in the evidence identifying him as the person who had inflicted the fatal blow to the child. He contends that this case is the equivalent of Berry v. Commonwealth, 393 Mass. 793 (1985), where a small child died while in the care of two adults, either one of whom could have inflicted the blows that killed the child. There, where the evidence was insufficient to distinguish which of the two was responsible, the defendant was entitled to a required finding of not guilty as to his culpability as a principal. Id. at 796. “When the evidence tends equally to sustain either of two inconsistent propositions, neither of them *564can be said to have been established by legitimate proof.” Id., citing Commonwealth v. Carter, 306 Mass. 141, 147 (1940). There, where both of the child’s caretakers had equal opportunity to kill the victim, both were fully capable of striking her with the force necessary to produce her injuries, and both were equally disposed to do so, a determination that one as opposed to the other was the actual perpetrator could not be made without resorting to speculation. Berry v. Commonwealth, supra.
The issue, then, is whether the evidence pointing to this defendant as the actual perpetrator was in equipoise with the evidence pointing to Fappiano, or whether there was instead evidence pointing more strongly in the direction of the defendant such that the jury could rationally infer that he was the principal. Various aspects of the evidence tilted toward the defendant as the perpetrator. To begin with, the defendant had, on various occasions, exhibited hostility toward Clyde, treating him roughly at a time when his leg was broken some weeks prior to his death, giving a false account of how the leg had been injured, and rejecting a neighbor’s suggestion that he seek medical attention for that broken leg; on another occasion, throwing him on the couch so hard that the baby lost his breath, and screaming at him when the baby regained his breath and resumed crying; and, on the day of his death, while the child was in obvious distress from his life-threatening injuries, shaking him and yelling at him for crying. In comparison, while there was considerable evidence of Fappiano’s abuse of the two older children, the neighbors and friends who had witnessed that abuse had never seen her mistreat Clyde. To the contrary, Clyde was her “favorite” child. The only person to accuse Fappiano of abusing Clyde was the defendant himself, and that occurred only after he was informed that Fappiano was blaming him for the baby’s death. The jury could rationally decide that the numerous witnesses, who had no compunction about accusing Fappiano of abuse that they had seen, but who uniformly stated that they had never seen her inflict any abuse on Clyde, were more credible than the defendant’s self-serving accusation of Fappiano.
Of great importance in distinguishing between the evidence pointing to Fappiano and the evidence pointing to the defendant *565is the fact that, when the defendant ultimately gave his account of how Fappiano had ostensibly kneed and kicked Clyde repeatedly until he went into convulsions and died, that account itself was completely at odds with the forensic evidence concerning the nature of the child’s injuries and the progression of symptoms that would have ensued. The forensic evidence indicated that the child had suffered a single blow, not multiple blows; that the blow had not been delivered with something as large as a foot or a knee, but had instead been inflicted by a fist; that many hours would have elapsed between the infliction of that blow and the child’s death, with a gradual progression of worsening symptoms, not the rapid death that the defendant described; and that at no point would the infection and shock have triggered convulsions or seizures. In other words, the jury had ample grounds to conclude that the defendant’s final accusation of Fappiano was false, as that accusation included many details that had been shown to be medically impossible. If he had in fact witnessed Fappiano striking Clyde, and had decided to stop covering for her (as he had ostensibly done in his earlier statements), there would be no reason for him to give so wildly inaccurate and impossible an account. Where, however, his accusation of Fappiano was demonstrably false in so many respects, the jury could logically conclude that that accusation had been invented to cover up his own culpability for the child’s death.9 If Fappiano were the perpetrator, the defendant, once he decided to stop protecting her, would not *566have conjured up such a wholly implausible account of Clyde’s injury and death. Thus, a rational jury could conclude that, although Fappiano had an equal opportunity to inflict the fatal injury, it was the defendant, and not Fappiano, who had displayed hostility to the child, and it was the defendant who was concocting false accusations of Fappiano. The evidence, rationally analyzed, pointed to the defendant as the actual perpetrator.
The alternative joint venture theory was equally supportable on this evidence. From the demonstrated pattern of abuse inflicted on the two older children by both Fappiano and the defendant, evidence of repeated injury to Clyde over a period of weeks prior to his death, and evidence of the defendant’s hostility to Clyde, the jury could rationally infer that both Fappiano and the defendant were similarly engaged in a pattern of abuse inflicted on Clyde.10 Their mutual involvement in that abuse would have the effect of encouraging and aiding the other in each ongoing act of abuse, whichever of them inflicted any particular blow on the child. In the immediate aftermath of Clyde’s death, both Fappiano and the defendant were concurring in the same false statements with respect to the circumstances surrounding that death, suggesting consciousness of guilt on both their parts and cooperation between them in an attempt to cover up their culpability. It is not necessary for the Commonwealth to present precise evidence of what acts each member of a joint venture committed with respect to such ongoing abuse, or to identify which of them inflicted the final act of abuse that proved fatal. See, e.g., Commonwealth v. Maynard, 436 Mass. 558, 565 (2002).
Here, there was evidence that the defendant had been present at the time of that fatal act of abuse — his own statements indicated that he had witnessed Fappiano’s final assault on *567Clyde (although his description of the assault itself was wholly incredible). Beyond those statements, his evident awareness of the fact that that fatal injury had been to the child’s stomach (as demonstrated by his initial false explanation that Jeffrey had “stepped on” or “jumped on” Clyde’s stomach) suggested that he had either landed that blow himself or seen it land.
The defendant and Fappiano shared an intent to inflict grievous bodily injury on Clyde, as evidenced by the significant injuries that had already been inflicted on him (e.g., his broken leg). The defendant argues that, at the precise moment of the final blow, his own intent could not have been proved, as he might not have foreseen that Fappiano would inflict a blow of such force. That argument parses the concept of a joint venturer’s shared intent too finely. From a pattern of intentional abuse being committed by two or more persons, the jury may infer that that intent remains operative as the abuse continues, without requiring specific evidence of a venturer’s state of mind at the precise moment of each separate abusive act by other members of the joint venture. Here, in addition to that pattern, the jury had evidence of the defendant’s intent that the child suffer bodily harm from the injuries being inflicted on him, as evidenced by the defendant’s treatment of Clyde at times when he knew that the child was already injured — rough handling in the aftermath of his broken leg, and shaking him in anger while the child was in obvious and severe distress a few hours prior to his death. If, as the defendant contends, he did not share any intent with Fappiano that the child suffer injury from this ongoing abuse, one would expect at least more sympathetic handling of the child in the aftermath of that abuse, not treatment that would only aggravate his already severe injuries. Assuming that Fappiano was the principal perpetrator of this abuse, the jury could readily infer that the defendant shared her malicious intent.
ii. G. L. c. 265, § 13J. The indictments under G. L. c. 265, § 13J, specified that the defendant was being charged under the third paragraph of subsection (b), which provides that “[wjhoever, having care and custody of a child, wantonly or recklessly permits bodily injury to such child or wantonly or recklessly permits another to commit an assault and battery upon such *568child, which assault and battery causes bodily injury, shall be punished . . . .” The defendant contends that there was no evidence that he had “care and custody” of the children, as he was not their legal parent or custodian. The term “[pjerson having care and custody” is defined as “a parent, guardian, employee of a home or institution or any other person with equivalent supervision or care of a child, whether the supervision is temporary or permanent” (emphasis added). G. L. c. 265, § 13J (a). The statute is not limited to persons with the formal role of parent or legal guardian. Here, the defendant lived in the home with the children, and assisted Fappiano with their daily care. The children called him “Daddy,” and he referred to Fappiano and the children as his “family,” signifying their mutual understanding that the defendant had a parental role in the household. Whether their role as caregiver has been imposed by law or by their own less formal arrangements, § 13J imposes obligations on caregivers to whom children look for care and protection, including an obligation to avoid reckless conduct that would “permit” those children to be assaulted and battered.
The defendant had such a role with respect to these children, and, despite abundant evidence that Fappiano was inflicting serious and repeated injury on them, he effectively encouraged her to continue doing so. In the circumstances known to him, a reasonable person would have recognized a high likelihood of substantial harm to the children (thus satisfying the standard of recklessness). Whatever forms of conduct might come within the term “permitting]” another to commit assault and battery, encouraging such batteries by hitting the children himself, and then turning them over to Fappiano for further abuse, would surely come within the concept of “permitting]” such a battery. There was sufficient evidence that the defendant violated § 13 J (b) with respect to all three children.11
iii. Other charges. As to the charge of assault and battery by *569means of a dangerous weapon on Clyde, the evidence was sufficient to convict the defendant as either a principal or a joint venturer. Again, where no one had seen Fappiano abuse or demonstrate hostility toward Clyde, the jury could rationally conclude that the defendant was the perpetrator with respect to all of the multiple injuries inflicted on him, including the many that had been inflicted with physical objects on various parts of his body. In the alternative, for the reasons discussed above with respect to the murder of Clyde, the jury could conclude that the defendant acted in conjunction with Fappiano in the ongoing abuse of Clyde, making the defendant a joint venturer with her with respect to the various batteries by means of dangerous weapons.
With respect to the charges of assault and battery on Jeffrey and Shy-la, there was evidence that the defendant had struck both of the children himself, as well as evidence that he participated as a joint venturer in Fappiano’s abuse of them. See note 10, supra.
Concerning the indictment charging assault and battery of Shy-la by means of a dangerous weapon, the evidence was sufficient to support a theory of joint venture with Fappiano, as the defendant’s conduct effectively encouraged her repeated beating of Shy-la with various objects. However, there was no evidence that the defendant himself had ever hit Shy-la with any object. Given the abundant evidence that Fappiano regularly beat Shy-la with a variety of objects, the various injuries to Shy-la were readily explainable by those beatings. Absent speculation, there was no basis to conclude that the defendant himself had ever used a dangerous weapon during any battery of Shy-la, and thus insufficient evidence of his liability as a principal. Where this indictment charging assault and battery by means of a dangerous weapon was submitted to the jury on theories of both principal and joint venture liability, the evidence was sufficient only as to one theory, and the jury returned a general verdict, a *570new trial must be ordered on that indictment. See Commonwealth v. Flynn, 420 Mass. 810, 818-819 (1995).
b. Violation of the defendant’s Sixth Amendment right to counsel. In a pretrial motion to suppress the various statements the defendant made, the defendant raised only the claim that he had not been properly advised of and did not understand his rights at the time he made those statements, and that his statements were not voluntary. After an evidentiary hearing, the motion judge found that the defendant had made a knowing and voluntary waiver of his rights, and that the defendant’s statements were voluntary. On appeal, the defendant does not challenge the motion judge’s resolution of those issues.
However, in his motion for a new trial, the defendant contended that his counsel had been ineffective for failing to raise violation of the defendant’s right to counsel under the Sixth Amendment to the United States Constitution as a basis for suppressing his May 31, 1997, statement to the troopers, with his ensuing statements to the correction officer being the fruit of that Sixth Amendment violation.12 The judge denied the motion, reasoning that the defendant’s right to counsel had not yet attached at the time he made his May 31, 1997, statements, because he had not yet been arraigned, and that trial counsel therefore had not committed any error in failing to pursue a suppression motion on Sixth Amendment grounds.
Contrary to the judge’s analysis,- the defendant’s Sixth Amendment right to counsel had attached as a result of his being indicted for these crimes on May 30, 1997. “The Sixth Amendment right to counsel is triggered ‘at or after the time that judicial proceedings have been initiated . . . “whether by way of formal charge, preliminary hearing, indictment, information, or arraignment” ’ ” (emphasis added). Fellers v. United States, 540 U.S. 519, 523 (2004), quoting Brewer v. Williams, 430 U.S. 387, 398 (1977). See Patterson v. Illinois, 487 U.S. 285, 290-291 (1988). Thus, while arraignment is one procedural *571step in criminal proceedings that will trigger the Sixth Amendment right to counsel, other steps occurring prior to arraignment may operate to initiate criminal proceedings and trigger those rights at an earlier stage. “[A] person is entitled to counsel once the government has ‘committed itself to prosecute, and . . . the adverse positions of government and defendant have solidified. It is then that a defendant finds himself faced with the prosecutorial forces of organized society, and immersed in the intricacies of substantive and procedural criminal law.’ ” Commonwealth v. Smallwood, 379 Mass. 878, 884 (1980), quoting Kirby v. Illinois, 406 U.S. 682, 689 (1972). In ascertaining when a particular defendant’s Sixth Amendment right to counsel attached, we must identify, based on the particular procedural devices employed in that defendant’s case, the earliest event that initiated formal criminal proceedings against him.
Here, the Commonwealth proceeded by way of direct indictment. The formality of an indictment, with the prosecutor’s presentation of the case to the grand jury and the grand jury’s return of a true bill, represents the commencement of proceedings against the defendant for purposes of the Sixth Amendment. See Fellers v. United States, supra, Patterson v. Illinois, supra.13 That the defendant had not yet been arraigned on the indictment did not preclude his Sixth Amendment rights from attaching.
However, an accused may waive his Sixth Amendment right to counsel. “[Njothing in the Sixth Amendment prevents a suspect charged with a crime and represented by counsel from voluntarily choosing, on his own, to speak with police in the absence of an attorney.” Michigan v. Harvey, 494 U.S. 344, 352 (1990). We “indulge in every reasonable presumption against waiver.” Brewer v. Williams, 430 U.S. 387, 404 (1977). To be *572valid, the waiver must be voluntary, and there must be an informed and intentional relinquishment of a known right. Id. For these purposes, Miranda warnings, although devised to inform suspects of their Fifth Amendment rights, are also sufficient to convey the substance of Sixth Amendment rights. Patterson v. Illinois, supra at 296. An accused who has received Miranda warnings “has been sufficiently apprised of the nature of his Sixth Amendment rights, and of the consequences of abandoning those rights, so that his waiver on this basis will be considered a knowing and intelligent one.” Id.
Here, although the motion judge’s legal analysis of the defendant’s motion to suppress focused on the Fifth Amendment theory that had been raised, her findings of fact effectively address the knowing and voluntary waiver of the defendant’s Sixth Amendment rights as well. Specifically, the motion judge found that the day after the indictments were issued, the troopers went to the house of correction formally to serve the defendant with the indictments and arrest warrant.14 They had been advised by the assistant district attorney not to question the defendant, but merely to serve the indictments and warrant on him. When they arrived, they met with the defendant, and told him that he had been indicted and that they had a warrant for his arrest on those indictments. From prior dealings with the defendant, they knew that the defendant could understand spoken English, but that he could not read English. Thus, as part of the service of the indictments, one of the troopers began to read the indictments to him out loud. After hearing just the first indictment, the defendant interrupted, saying that he had not hit any of the children. The trooper told him to stop, and the trooper resumed the reading of the remaining indictments. The defendant interrupted again. At that point, “in an excess of caution,” the trooper read the defendant his Miranda warnings. *573Beyond the standard warnings, the trooper also told the defendant that he knew the defendant had a lawyer15 and that he (the defendant) should not say anything about the new charges.16 The defendant replied that his lawyer had told him there was nothing to worry about, and that he wanted to speak to the officers. The trooper asked him whether he really wanted to do so, reminding him of the rights that had been read to him and that he already had a lawyer. The defendant insisted that he wanted to talk. The trooper then read the defendant his Miranda rights a second time, and the defendant acknowledged that he understood each of those rights. The defendant then gave a statement, the contents of which were introduced at trial.
The troopers asked the defendant if he would be willing to reduce his statement to writing. The defendant declined to do so, telling them that his attorney had advised him not to sign anything. However, the defendant continued to speak with the officers, and thereafter stated that Fappiano “must have” killed the baby. That interview ended when the defendant became teary-eyed, hung his head, and said that he wanted to talk to his lawyer.17 The defendant, “upset because he had just been served *574with the murder indictment,” and, in an agitated state, made spontaneous statements to the correction officer on the way back to his cell, and initiated a further conversation with another officer later that day.
According to the motion judge’s findings, the defendant received Miranda warnings twice, along with express reminders that he had counsel. The defendant’s repeated insistence that he nevertheless wanted to talk to the officers thus constituted a voluntary, informed, and intentional relinquishment of his Sixth Amendment rights. In analyzing the motion for a new trial, the trial judge correctly noted that the motion judge’s findings were dispositive of the issues of an informed and intentional waiver.
However, the defendant contends that the troopers’ visit to serve him with the indictments and warrant was itself contrived in an effort to get him to make a statement, and that they “deliberately elicited [the statement] from him after he had been indicted and in the absence of his counsel.” Fellers v. United States, 540 U.S. 519, 523 (2004), quoting Massiah v. United States, 377 U.S. 201, 206 (1964). Where government agents “deliberately and designedly set out to elicit information” from a defendant after Sixth Amendment rights have attached, such conduct violates those rights. Brewer v. Williams, 430 U.S. 387, 399 (1977). See Fellers v. United States, supra at 524, and cases cited. For example, in Fellers, officers went to arrest the defendant at his home after he had been indicted on drug distribution charges. When they arrived, they told the defendant that “they had come to discuss his involvement in” that drug distribution, and simultaneously told him that he had been indicted and that they were there to arrest him. They told the defendant that the indictment referred to other persons involved in his drug distribution, and named four of them. The defendant then made a statement concerning his acquaintance with those four people and his use of drugs with them. Id. at 521. Where the officers had identified to the defendant that their purpose “was to discuss [the defendant’s] involvement in the distribution of methamphetamine and his association with certain charged co-conspirators,” and they obtained no informed “waiver of [his] Sixth Amendment rights,” there was “no ques*575tian” that the officers had “deliberately elicited” information from the defendant. Id. at 524.
Here, however, the motion judge’s findings preclude any claim of such “deliberate elicitation.” Unlike the Fellers case, the troopers did not tell the defendant that they were there to “discuss” anything with him. To the contrary, they told him they were there to serve him with the indictments and to arrest him on the warrant, and, when he started to speak, they told him not to interrupt. They advised him (more than once) not to speak to them, and did so in conjunction with a reminder that he had a lawyer. And, again unlike the Fellers case, they gave him Miranda warnings (two separate times) and obtained his express waiver. In claiming “deliberate elicitation,” the defendant is essentially asking us to substitute our assessment of the troopers’ testimony on these points for that of the motion judge, suggesting that the troopers in fact went to serve the indictments and read them aloud to the defendant in the hope that he would be tricked into making some statement. Whatever suspicions the defendant might have on that subject, the motion judge’s findings with respect to what the troopers actually said to the defendant once they got to the jail would belie the defendant’s theory — if their intention and hope had been that reading the indictments out loud would prompt the defendant to start making a statement, they would not have cut off his attempt to do so during the reading of the indictments, nor would they have advised him against speaking to them when he did so a second time, nor would they have suggested that he speak instead with his lawyer. We thus see no need for a further evidentiary hearing on the issues of deliberate elicitation and waiver, as the findings already made conclusively establish that there was no violation of the defendant’s Sixth Amendment rights.
c. Admission of hearsay evidence. The defendant contends that, over objection, the prosecutor was allowed to introduce hearsay evidence that Fappiano had blamed him for Clyde’s death. The evidence was not admitted substantively, but only for a limited purpose, and with a forceful limiting instruction (delivered twice). Specifically, after the defendant had denied any knowledge of Fappiano’s abuse of the children in his initial *576statements to police, his October 28 statement (a week after the child’s death) was the first statement in which he accused Fappiano of abusing the children, and he gave the officers a more detailed account of that abuse two days later.
The issue of concern to the prosecutor was how the jury might interpret what motivated the defendant to retract his earlier statement exculpating Fappiano and instead give a new statement accusing her of abusing the children. At the start of the interview on October 28, the trooper had told the defendant that Fappiano was “blaming you” for Clyde’s death, and the prosecutor suggested that that was the trigger for the defendant’s about-face. Absent any awareness of the fact that the interview had begun with that confrontation about Fappiano, it could be made to appear that the defendant’s change in his version was the product of a spontaneous desire to help the police and a genuine change of heart about whether covering up for Fappiano was the right thing to do. Instead, with the information about what the defendant was told at the start of the October 28 interview, the progression from the defendant and Fappiano jointly covering up their involvement in the events of October 20 to the defendant’s increasingly specific accusations of Fappiano could be viewed in a very different light. Given the significance of the precise sequence and evolution of the defendant’s ever-changing false statements, an inaccurate or misleading impression about the motivations for those changes was of legitimate concern to the prosecutor. Recognizing the potentially problematic issues that would be raised by any reference to what Fappiano had said, the judge heard the parties at length on this issue before ultimately allowing the prosecutor to introduce evidence of what the trooper had told the defendant about Fappiano’s statement.
We are satisfied that, on these facts, there was a legitimate nonhearsay purpose for the introduction of this evidence. See Commonwealth v. Brum, 438 Mass. 103, 116-117 (2002); Commonwealth v. Furr, 58 Mass. App. Ct. 155, 161 (2003). The Commonwealth did not offer evidence of Fappiano’s statement for the truth of that statement, but to provide the context for the *577defendant’s own decision to accuse Fappiano.18 Moreover, what was introduced in evidence was a single phrase, the phrase that had been used to convey this information to the defendant (that Fappiano was “blaming [the defendant] for what happened”), not a statement containing any factual detail provided by Fappiano. When this evidence was introduced, the judge gave an immediate limiting instruction, informing the jury that this alleged statement by Fappiano was not being admitted for its truth, but solely to put the defendant’s response “in some form of perspective,” to give the jury “a context” for what the defendant himself said. The judge told the jury, repeatedly, that they were not to consider that evidence “for the truth of the statement in any way, shape or form.” When the second State trooper who had been present at the October 28 interview also testified to this single phrase, the judge again gave an immediate limiting instruction. There was no further reference to this phrase during either trooper’s testimony. The prosecutor made a single brief reference to it in her closing argument, but that reference was focused on the limited purpose for which the Commonwealth had introduced the evidence in the first place, namely, to show what might explain the difference between the defendant’s initial statements implicating Jeffrey stomping on the baby’s stomach and his statements accusing Fappiano one week later.19 We are satisfied that there was no error in the introduction of this evidence, that the prosecutor did not misuse the evidence for any purpose beyond its limited permissible purpose, and that the judge’s instructions adequately addressed the potential that the jury might misuse the evidence that Fappiano was “blaming [the defendant] for what happened.”
d. Evidence of refusal to speak to troopers. The defendant *578contends that the evidence concerning the end of his encounter with the troopers on May 31, 1997, was improperly introduced. There was no objection at trial. The jury heard evidence that, after one of the troopers advised him that they knew that he knew how Clyde had died, the defendant became tearful, hung his head, and shook his head from side to side. The jury heard that the interview ended at that point, but did not hear that the defendant had told the troopers that he wanted to speak to his lawyer. The defendant now complains that the Commonwealth used this evidence as an admission by silence, when it was in fact part of his invocation of his right to counsel. Whatever it was, the defendant’s behavior in response to the trooper’s statement was not the equivalent of “silence,” nor was it so portrayed. Shaking his head back and forth, a gesture that is commonly understood to mean “no,” would presumably be interpreted as a denial of the accusation just made by the trooper. Nor, in light of his subsequent statement to one of the troopers and to the correction officer, would the jury interpret it as a refusal to speak with law enforcement.
Moreover, even if so interpreted, we have recognized that, in some rare circumstances, a defendant’s invocation of his right to remain silent may be presented to the jury in order to avoid juror confusion about why an interview ended abruptly. See Commonwealth v. DePace, 433 Mass. 379, 384 (2001); Commonwealth v. Habarek, 402 Mass. 105, 110 (1988), S.C., 421 Mass. 1005 (1995). Here, where the defendant had been speaking with the troopers, some explanation for the termination of the interview would have been appropriate, and the evidence introduced, if interpreted as an invocation of the right to remain silent as opposed to a substantive denial of the trooper’s accusation, would not give rise to any substantial likelihood of a miscarriage of justice.
e. Exclusion of evidence concerning prior injury to Jeffrey. The defendant sought to introduce evidence that Jeffrey had sustained a broken arm when he was two years old, some three years prior to the defendant’s arrival. However, the medical records pertaining to that incident revealed that a former boy friend of Fappiano had acknowledged responsibility for that injury to the child, and that the evidence concerning that incident *579therefore shed no light on Fappiano’s own abuse of Jeffrey or on the likelihood that Fappiano had inflicted the later injuries to Clyde. The judge recognized that, if the defendant had any evidence to suggest that Fappiano was the culprit in that earlier incident, that incident would be relevant and he would allow evidence of it to be introduced. The defendant acknowledged that he had no such evidence, and the boy friend’s admission, reflected in the medical records, would affirmatively indicate that Fappiano was not responsible. We see no error in the judge’s determination that the proffered evidence was irrelevant.20
f. Prosecutor’s closing argument. The defendant alleges various errors in the prosecutor’s closing argument, none of which was objected to at the time. The claimed errors are either taken out of the context in which the argument points were made, or in some cases constitute inaccurate characterizations of the transcript. The prosecutor did not say that none of the children had any bones fractured prior to the defendant’s arrival (thereby taking advantage of the exclusion of evidence concerning Jeffrey’s broken arm); she stated only that Clyde had no history of broken bones and that Jeffrey had no broken ribs until the defendant’s arrival, both of those statements being accurate with or without the excluded evidence. The defendant now protests the prosecutor’s use of the term “discipline” or “disciplining” the children (e.g., arguing to the jury that the defendant assisted Fappiano “in disciplining this child to his death”), contending that there was no evidence that Fappiano’s conduct would qualify as “discipline” of her children. During her closing argument, the prosecutor made clear that Fappiano’s behavior was not legitimate “discipline,” and her use of the term would not have been misunderstood by the jury.
The defendant contends that the prosecutor made an improper comment on the defendant’s not testifying at trial when she *580pointed out to the jury that no “witness that testified” gave any evidence of Fappiano hitting Clyde and that the only such evidence came from the defendant’s “statements.” Pointing out the discrepancy between a defendant’s statements to the police and the testimony of other witnesses is not an improper comment on a defendant’s silence at trial. Moreover, the judge instructed the jury that the defendant had a right not to testify, and that they should not infer anything from the fact that he did not testify.
Finally, the defendant argues that the prosecutor misstated the evidence with respect to Clyde having asthma. The point being made in her argument, supported by the evidence but minor in consequence, was that the defendant and Fappiano did not give an accurate or complete medical history for Clyde at the time that medical personnel were trying to revive him.
g. Joinder. The defendant claims error in the joinder of the indictments for trial, complaining that the evidence of the various batteries on the other children had an improper “spillover effect” on the jury’s assessment of the murder indictment. We see no error in joinder of all the indictments. The pattern of abuse inflicted on the other two children was relevant to prove the defendant’s culpability for similar abuse that was simultaneously being perpetrated on Clyde. See Commonwealth v. Gallison, 383 Mass. 659, 672-673 (1981) (evidence of abuse of one child in household relevant to prosecution of homicide of second child in same household, as it was relevant to defendant’s state of mind and demonstrated “common course of conduct regarding the two children”).
h. G. L. c. 278, § 33E. The defendant suggests that relief under G. L. c. 278, § 33E, is warranted because, in a separate trial, Fappiano was convicted only of murder in the second degree. That fact, standing alone, does not warrant relief. See Commonwealth v. Rolon, 438 Mass. 808, 825-826 & n.20 (2003), and cases cited; Commonwealth v. Valentin, 420 Mass. 263, 275 (1995).
He also contends that he should be accorded a new trial in order to have a “ ‘gatekeeper’ assessment of the reliability” of the medical evidence presented, in particular the expert opinion concerning whether the fatal blow to Clyde was inflicted by a *581fist. See Canavan’s Case, 432 Mass. 304, 310-315 (2000); Commonwealth v. Lanigan, 419 Mass. 15, 25-26 (1994). The defendant proffers no reason to question the reliability of this expert testimony, other than to point out that the experts themselves expressed their opinions with slight variations and with differing levels of confidence. These differences do not suggest that any of the opinions were unreliable or based on an unsound methodology, but instead indicate that the jury heard a detailed and balanced range of opinion from different experts.
We have reviewed the record in its entirety, and we see no reason to reduce the murder verdict to a lesser degree of guilt or to order a new trial.
3. Conclusion. For the foregoing reasons, the defendant’s conviction of assault and battery by means of a dangerous weapon on Shy-la Harper (indictment no. 97-1072) is set aside and that indictment is remanded for a new trial; the remaining convictions are affirmed; the order denying the defendant’s motion for a new trial is affirmed; and the defendant’s request for relief pursuant to G. L. c. 278, § 33E, is denied.
So ordered.
Some of these claimed errors were preserved by timely objection. With respect to those that were not preserved, the defendant contends that those failures to object were due to the ineffective assistance of counsel. Because we find no error, we need not separately address the claims of ineffective assistance.
By that time in his development, Clyde had been walking for about one month.
Indeed, the medical experts testified that, while they had seen cases of partial tearing of the intestine as a result of trauma, the complete tearing of Clyde’s small intestine was more severe than anything they had ever seen before.
This forensic evidence with respect to the course of the baby’s decline over that day was lengthy and graphic. It was, however, highly relevant to both the issue of extreme atrocity and cruelty and to the defendant’s consciousness of guilt and knowledge of how the baby’s injuries were inflicted. As discussed below, each of the defendant’s varying accounts of Clyde’s final day of life included details of the baby’s alleged behavior and activities. The forensic evidence demonstrated that, in numerous different respects, the defendant’s accounts were medically impossible. While the defendant now suggests that this forensic evidence of the baby’s extreme suffering was overly long, excruciatingly detailed, and needlessly repetitive, it was critical to the Commonwealth’s case and properly admitted.
The officers responding to the scene had found vomit in the child’s crib.
The defendant sought to suppress that statement pursuant to the Fifth Amendment to the United States Constitution and, in his motion for a new trial, claimed that it should have been suppressed under the Sixth Amendment *562to the United States Constitution. Those suppression issues, and the further facts concerning the defendant’s theories of suppression, are addressed below.
The judge gave a limiting instruction to the jury with respect to the troopers’ statements to the defendant.
That correction officer had no knowledge of the charges against the defendant, and no information whatsoever about the underlying case.
For these purposes, we place less weight on the defendant’s earlier false and inconsistent versions of how Clyde was injured. Although they could rationally be viewed as compelling evidence of consciousness of guilt, they would arguably be explainable by a desire to cover up for Fappiano. Fappiano, after all, was telling equally false versions, indicative of either her own consciousness of guilt or a desire to cover up for the defendant. Fappiano was the source for the initial false claim that Clyde had been injured when he fell out of his stroller, with the defendant indicating his agreement with that false version. A later version from the defendant, to the effect that Jeffrey had “stepped on” or “jumped on” Clyde’s stomach, could have been invented to cover up for either himself or Fappiano. Yet another version from the defendant was that Clyde had fallen at 6 p.m., had consumed a bottle of milk in his crib, and then vomited and stopped breathing. That version was also impossible, given that the child would have been in obvious distress long before that time, unable to walk, and unable to eat or drink, but that false version could still be the product of a desire to cover up for Fappiano. However, *566once the defendant decided to implicate Fappiano, the incredible aspects of his version of events take on new significance, as they can no longer be explained by reference to a desire to protect Fappiano. From that point on, the falsity of the defendant’s version of events points directly to the defendant as the actual perpetrator.
That the defendant’s abuse of the children was undertaken in tandem with Fappiano was illustrated by the incident during which the defendant first struck Jeffrey and went into the apartment with him, whereupon Fappiano immediately took over beating the child with cable wire.
The defendant’s argument that the statute is unconstitutionally vague as applied to him essentially restates his argument with respect to the sufficiency of the evidence. For the same reasons, we reject the claim of vagueness.
He also complains that the jury were not instructed with regard to Fappiano’s privilege to use reasonable force when disciplining her children, and that the existence of that privilege must temper his own obligation under § 13J. See Commonwealth v. O’Connor, 407 Mass. 663, 667-668 (1990). He *569did not request any such instruction, and none was warranted. On any view of the evidence, Fappiano’s frequent beating of these very young children — striking them with different objects, inflicting blows to many parts of their bodies, causing broken bones and plainly visible bruises — would not come within that privilege. Compare Cobble v. Commissioner of the Dep’t of Social Servs., 430 Mass. 385 (1999).
In the motion, the defendant also claimed a violation of his right to counsel under art. 12 of the Massachusetts Declaration of Rights, but did not differentiate between his rights under art. 12 and his rights under the Sixth Amendment. On appeal, the defendant articulates his argument solely in terms of the Sixth Amendment.
Because of the nature of complaint and arrest warrant procedure in Massachusetts, a procedure that is “often done in informal fashion” and entirely ex parte, Commonwealth v. Smallwood, 379 Mass. 878, 885 (1980), and that does not necessarily result in a prosecution of the charge, we have held that that procedure does not trigger the Sixth Amendment right to counsel. See Commonwealth v. Beland, 436 Mass. 273, 285 (2002), and cases cited; Commonwealth v. Smallwood, supra. In his motion for a new trial, the defendant suggested that this line of precedent is contrary to the Supreme Court’s articulation of what steps suffice to trigger Sixth Amendment rights. Where this defendant’s Sixth Amendment rights attached on his being indicted, we need not consider the argument.
The defendant was being held on an unrelated matter. The defendant now protests that service should have been made by the sheriff, not by the State police. See G. L. c. 277, § 65 (if defendant is in custody at time of indictment for murder, indictment “shall forthwith be served by the sheriff or his deputy”). Having failed to object to any technical defect in service, the defendant cannot raise such a defect as a basis for setting aside the verdict. See Commonwealth v. Pike, 324 Mass. 335, 337-338 (1949) (provisions of G. L. c. 277, § 65, are “directory and not jurisdictional”).
Counsel had been assigned to the defendant in connection with the grand jury proceedings, see G. L. c. 277, § 14A, and had advised the defendant with respect to the assertion of his Fifth Amendment right to refuse to testify before the grand jury. With the conclusion of grand jury proceedings, that representation was technically at an end. While it was apparently anticipated that the same lawyer would be assigned to represent the defendant on the charges themselves (and the same lawyer was later assigned to represent him), the defendant was not actually represented by counsel on May 31, 1997.
When the troopers testified at trial, the various references to the defendant’s lawyer were deliberately omitted.
The motion judge’s findings did not address the additional brief conversation that the defendant had with one of the troopers a few minutes after he had invoked his right to consult with counsel. On appeal, the defendant raises no issue with respect to that conversation. Considering it as part of our review under G. L. c. 278, § 33E, we see no substantial likelihood of any miscarriage of justice. As described at both the evidentiary hearing and at trial, it was the defendant who called the trooper over, told the trooper that he ostensibly knew about Fappiano’s killing Clyde, and then chose not to discuss it further at that time, saying he would do so later. We see no violation of either the Fifth Amendment or art. 12 in this exchange initiated by the defendant. See Edwards v. Arizona, 451 U.S. 477, 486 n.9 (1981); Commonwealth v. Sarourt Nom, 426 Mass. 152, 157-158 (1997); Commonwealth v. Phinney, 416 Mass. 364, 371 (1993).
Nor did the Commonwealth suggest that Fappiano herself was a reliable or credible source. To the contrary, the Commonwealth had demonstrated that Fappiano’s initial statements to the police (made in the defendant’s presence with the defendant nodding his concurrence) were false, and the prosecutor unambiguously argued to the jury that Fappiano was guilty of these crimes. At no time did the Commonwealth suggest that any statement by Fappiano should be believed.
“What changed? What changed for the defendant on October 30th of ’96? He’s told by Sergeant O’Brien that Susan Fappiano is pointing the finger at him and blaming him for what happened. What’s his October 30th response? No longer Jeffrey. It was her.”
We also note that the jury heard abundant evidence of Fappiano’s abuse of Jeffrey and Shy-la during the time period leading up to Clyde’s death, and the Commonwealth affirmatively argued to the jury that Fappiano chronically abused her children. Evidence with respect to child abuse in that household three years earlier would not have impacted the jury’s assessment whether the defendant joined with Fappiano in that abuse when he became part of that household in August, 1996.