Cordy, J.
In the early evening hours of February 21, 1994, Joseph Dozier was shot and killed on the steps in front of Boston Latin Academy in the Roxbury section of Boston. His body was riddled with bullets fired from two handguns. More than three years later, Kenyatti Jordan was indicted for the killing, and, after a jury trial, was convicted of murder in the first degree and possession of a firearm. On appeal, Jordan claims that incriminating statements he made to Boston police detectives were either made under the protection of a letter of immunity or were the involuntary product of police deception and should have been suppressed. He also claims that the trial judge unfairly restricted his cross-examination of one of the detectives involved in the deception, and inadequately instructed the jury on the issue of the voluntariness of his statements. Finally, Jordan contends that the judge erred when he rejected three of Jordan’s peremptory challenges of white male jurors, after finding a pattern of excluding such jurors without adequate explanations based on race-neutral and gender-neutral grounds. We affirm the convictions.
1. Motion to suppress. Before trial, Jordan moved to suppress [49]*49statements he made to Boston detectives during their investigation on January 9, 1997, at the office of the United States Attorney; on April 16, 1997, at the Bristol County house of correction; and on May 7, 1997, at the same location, immediately after his indictment for Dozier’s murder. The gravamen of Jordan’s complaint is that the statement he made on January 9 was induced by a promise made by Federal law enforcement agents (in the presence of the detectives) that it would not be used against him in the murder investigation. If that promise was not effective, he contends that the inducement was the product of police deception and his resulting statement was involuntary. He further claims that his subsequent statements to the detectives on April 16 and May 7 were either covered by the initial promise of immunity or irremediably tainted by the deception that prompted his statement on January 9.
In the three statements at issue, Jordan denied being involved in the shooting but admitted being present at the shooting, being armed, and being in the company of the person who he claims actually shot Dozier. These statements were pivotal in the homicide investigation and prosecution because, although there had been an eyewitness who had observed two men confront and shoot Dozier, she could not identify the individuals. Consequently, Jordan’s admissions, combined with the testimony of the eyewitness that both individuals shot the victim, and ballistic evidence that guns of two different calibers were used, formed the core of the Commonwealth’s case against him.1
The motion prompted a pretrial suppression hearing, at which a number of detectives and Federal law enforcement officers testified. The motion judge made extensive findings of fact regarding the circumstances in which Jordan’s statements were made, ultimately concluding that the Commonwealth had sustained its burden of proving beyond a reasonable doubt that they were voluntary and admissible. In reviewing the judge’s ruling on voluntariness, we “accept[] the judge’s subsidiary [50]*50findings of fact absent clear error, [and] give[] substantial deference to the judge’s ultimate findings and conclusions of law.” Commonwealth v. Vao Sok, 435 Mass. 743, 751 (2002), quoting Commonwealth v. Mello, 420 Mass. 375, 381 n.8 (1995).
As backdrop to the statements challenged by Jordan, the judge found that Jordan began working as an informant for various Federal and State law enforcement agencies in 1996, making undercover drug purchases in a major drug distribution investigation. When the State police learned that Jordan was a suspect in the 1994 Dozier homicide, they informed the Federal agents involved in the drug investigation, and ultimately accompanied Jordan to a meeting with Detective Herbert Spell-man of the Boston police department on December 10, 1996. Spellman noted that Jordan had been interviewed about the murder in 1994, and had told police that he had had no involvement in it and had been in the company of a friend, Antonio Jones, and a couple of girls the evening it occurred. Jones had been a prime suspect in 1994 after police found ammunition in his apartment matching the spent ammunition found at the scene of Dozier’s murder.2 Spellman asked Jordan whether he was going to continue to provide Jones an “alibi” in the case. Jordan responded that he was. The interview concluded.
Jordan was also on probation in December, 1996, as the result of other unrelated crimes, and his probation officer was pressing to have his probation revoked because of new arrests. Federal agents had been rebuffed in their efforts to persuade the probation officer to postpone Jordan’s revocation proceeding, scheduled for January 3, 1997, so that Jordan could continue working in their drug investigation. As a consequence, sometime after the December 10 meeting between Detective Spellman and Jordan, one of the Federal agents contacted Boston detectives offering Jordan’s further help in the Dozier murder investigation in exchange for their intervention on Jordan’s behalf in the probation proceedings. This offer led to the fateful meeting in the United States Attorney’s office in Boston on January 9, 1997, attended by Federal agents, an assistant United States at[51]*51torney, the detectives (including Detective Spellman), and Jordan.
The motion judge found that the participants in the meeting approached it from significantly different perspectives. The detectives thought Jordan was involved in the murder and were under the impression that he was prepared to implicate himself. The Federal agents viewed the meeting as an opportunity for Jordan to provide helpful information about the murder so that the detectives would intercede with Jordan’s probation officer. The assistant United States attorney began the meeting by typing up a Federal “proffer immunity” letter and explaining that if Jordan told the truth nothing he said could be used against him directly but that the police could follow up on the information. The detectives said nothing in response to the statements of the assistant United States attorney, knew that they had no authority to enter such an agreement, did not sign the letter, and believed that the proffer letter had no application to proceedings in State court.3 The meeting ended and the detectives proceeded to enter a separate room to interview Jordan. The Federal agents were told that, as a matter of police policy, they could not participate in the interview but that Jordan could come out to speak to them whenever he wished.
The interview began by Detective Spellman’s explaining that he wanted to speak to Jordan about the killing of Dozier. Spell-man informed Jordan that he was a suspect and that he could not offer him any inducements or make any promises, but that he would take anything that Jordan told them to the Suffolk County district attorney. Spellman then took out a card containing the Miranda warnings and went through them one at a time. Jordan stated that he understood each of the rights explained to him. Spellman then asked Jordan if he wanted to talk, and Jordan responded that he wanted to leave the room and talk to one of the Federal agents first, which he did. Jordan told the agent that Spellman said he had “no” immunity. The agent entered the room to talk to Spellman, who told him that only the district attorney could grant immunity. The agent left, conferred with Jordan, and told him to “tell the truth.” Jordan [52]*52returned to the room and agreed to be interviewed. He did not, however, tell the truth. Instead, the judge found that Jordan told a story that he thought would not be self-incriminating. In essence, he told the detectives that he had been with Jones on the night of the murder; that Jones received a telephone call to meet someone and asked Jordan to come along; that he did not know what the meeting was to be about; and that he remained far away when Jones met Dozier in front of Boston Latin Academy. Jordan did admit, however, that he saw Jones shoot Dozier and that he and Jones had then fled the scene together. Jordan further told the detectives that Jones went to the meeting armed with two handguns, and that although he, Jordan, also was armed, he did not fire his gun. The interview then ended.
With regard to this critical meeting between Jordan and the detectives, the judge concluded that whatever impression Jordan may have had about the effect of the “proffer immunity” letter when he initially entered the interview room with the detectives, before he agreed to be interviewed he knew that “it did not provide protection from the use of anything he might say against him in state court.” The judge also found that the interview was noncustodial, that Jordan was informed of and fully understood his Miranda rights, that the interrogation was not coercive, that Jordan was alert and lucid and had had extensive experience in the criminal justice system, and that he acted in a calculated way, hoping to provide enough information to avoid a probation revocation (and incarceration) without incriminating himself in the crime. The judge ultimately concluded that Jordan’s statement to the detectives on January 9 was a “product of his free will and rational intellect and was voluntary.”
The judge’s findings of fact regarding the circumstances in which Jordan’s statement was taken are supported by the evidence adduced at the hearing on the motion to suppress. His conclusion, based on an examination of the totality of the circumstances, that Jordan’s statement was voluntary and properly obtained, is, in turn, fully supported by the judge’s findings of fact. It is also consistent with our holdings in cases involving statements made during police interrogations in which discussions regarding cooperation or leniency may have [53]*53occurred. Compare Commonwealth v. Mandile, 397 Mass. 410, 414-415 (1986) (police statements that cooperation would be brought to attention of district attorney did not render confession involuntary), and Commonwealth v. Williams, 388 Mass. 846, 855 (1983) (same), with Commonwealth v. Meehan, 377 Mass. 552, 564-565 (1979), cert, dismissed, 445 U.S. 39 (1980) (confession involuntary where induced by police statements that confession would “help” defense, and that “truth” was going to be “good defense”). The touchstone is whether the police “assured” the defendant that his confession would aid his defense or result in a lesser sentence. Id. at 564. The judge’s findings of fact make clear that such was not the case here.
Contrary to Jordan’s argument on appeal, the Federal “proffer immunity” letter and its terms were not binding on the Commonwealth. Neither the Commonwealth, the Suffolk County district attorney’s office, nor the Boston police department was a party or signatory to the letter. Moreover, Jordan was not deceived or misled regarding its effect in the State criminal proceedings. See Commonwealth v. Groome, 435 Mass. 201, 216-217 n.21 (2001) (police deception can eviscerate voluntariness of defendant’s statement). The judge found that Jordan knew the letter had no legal or practical effect in State proceedings at the time he made his statement. These findings are supported by the testimony regarding the January 9 meeting and further borne out by Jordan’s statements made to other detectives in an interview occurring on April 16. In that interview, arranged without Federal assistance, and tape recorded in part, Jordan confirmed that he had been aware on January 9 that what he was then telling the detectives was not protected from use in State court proceedings, and that he had spoken to them because he was tired of being suspected of something he did not do. Although some of the circumstances of the January 9 meeting may have been unusual, the judge’s findings make clear that the detectives accurately advised Jordan of the unrestricted basis on which his statement was being sought before the interview began, and Jordan was fully cognizant of that fact when he agreed to proceed. While Jordan may have miscalculated his ability to manipulate the situation to his advantage, his statement was voluntary and not the product of deception on the part of the Commonwealth.
[54]*54Because Jordan’s challenge to his January 9 statement fails, his allegations of either immunity or taint regarding the statements he subsequently made to Boston detectives on April 16 and May 7 also fail.4 Each of those statements was preceded by Miranda warnings, properly given, fully understood, and waived. Each statement was progressively more inculpatory. In his final statement, while still denying that he shot Dozier, Jordan admitted to being right next to Jones when the shooting occurred; knowing that Jones intended to shoot Dozier at the meeting; and understanding that Jones expected Jordan to shoot Dozier as well. The judge properly denied Jordan’s motion to suppress both of these statements as well.
2. Cross-examination. At trial, Detective Spellman was cross-examined extensively regarding his conduct at the January 9 meeting in the United States Attorney’s office and in the interview of Jordan that took place immediately thereafter. This cross-examination included a line of inquiry directed at exposing Spellman’s attitude toward the Federal agents and his reasons for keeping them out of the interview room during his interview of Jordan. Spellman testified that he kept his opinion about the ineffectiveness of the “proffer letter” with respect to State court proceedings to himself at the meeting; that he made no comments to the assistant United States attorney about it; that, although he had neglected to bring a Miranda waiver form to the meeting, he chose not to ask the Federal agents to supply him one5; and that the “policy” that he cited in asking the Federal agents not to be present during the interview was not an official, written policy of the Boston police department. Spell-man also testified that he was not concerned that Jordan would “clam up” if the Federal agents were present during the interview, but did not want Jordan to feel like he was being “gang[ed] up” by the presence of more than two investigators.
[55]*55Defense counsel then asked Spellman, “Was it your concern that in the privacy of this meeting when you started to discuss Miranda issues that [the Federal agents] might object to Jordan’s testimony?” The prosecutor objected and the judge sustained the objection. Jordan claims that the judge’s action in sustaining the objection violated his constitutional right to confront and cross-examine witnesses against him.
While the Sixth Amendment to the United States Constitution may restrict the discretion of a trial judge to reject relevant evidence offered by a defendant, Pettijohn v. Hall, 599 F.2d 476, 480 (1st Cir.), cert, denied, 444 U.S. 946 (1979), it has long been recognized that a defendant’s right to cross-examine a witness is not absolute. Commonwealth v. Doherty, 394 Mass. 341, 349-350 (1985). As long as the judge does not completely bar inquiry into a relevant subject he has broad discretion to limit the scope and extent of the inquiry. Commonwealth v. Jackson, 419 Mass. 716, 727 (1995). The judge did not abuse his discretion here. To the extent that the question was relevant to bias or credibility, it was only marginally so and was cumulative. To the extent that it sought to elicit Spellman’s speculation on what might have happened if he had allowed the Federal agents to be present, it was immaterial to the voluntariness of Jordan’s statements. There was no error.
Jordan also complains that he was unfairly restricted in his direct examination of one of the Federal agents who was present outside of the interview room on January 9. That agent testified as to what occurred at the meeting in the United States Attorney’s office and to a conversation he had with Jordan when Jordan left the interview room and told him that the detectives were saying that he had no immunity. The agent testified that he went into the room, without Jordan, and was told by the detectives that only the district attorney could agree to immunity. He then testified that one of the detectives (not Spellman) said, “You know, you can trust us on this.” The prosecutor objected and the judge struck the answer. Defense counsel voiced no objection to the judge’s mling. It is unclear from the record and the briefs whether the judge struck the entire conversation between the detectives and the agent or just that portion quoted above. In any event, the judge did not abuse his discretion. The [56]*56detective’s statements were not made in Jordan’s presence nor were they conveyed to him. Even if we were to conclude that the judge should have permitted this testimony to stand, his ruling striking it did not create a substantial likelihood of a miscarriage of justice. The jury had before them the testimony of numerous witnesses called by both parties from which they could fairly judge the voluntariness of the statement Jordan gave to the detectives on January 9.
3. Voluntariness instruction to the jury. Jordan next contends that the judge’s instruction to the jury on the issue of voluntariness was inadequate because it did not specifically direct them to consider the impact of the Federal “proffer immunity” letter on the voluntariness of his statements.
Where the voluntariness of a statement by a defendant is at issue, the judge is required to instruct the jurors on two points: first, that they may not consider the statement unless the Commonwealth proves beyond a reasonable doubt that the defendant made it freely, rationally, and voluntarily; and second, that they should consider all the evidence, or alternatively the totality of the circumstances, in determining whether the statement was voluntary. Commonwealth v. Cryer, 426 Mass. 562, 571-572 (1998). Here, the judge satisfied both of these requirements by instructing the jury in the following terms:
“[I]n this case, you, the jury, heard testimony about statements that were made by the defendant concerning the offense for which he is charged. You may not consider any such statement in your deliberations unless from all of the evidence in the case, the Commonwealth has proved beyond a reasonable doubt that the defendant made the statement that he is alleged to have made and that he made it voluntarily, freely, and rationally. . . .
“In determining whether or not any statement made by the defendant was made voluntarily, you may consider all of the surrounding circumstances. . . . Your decision does not turn on any one factor. You must consider the totality of the surrounding circumstances.”
We have also noted that in giving a voluntariness instruction it is advisable for the judge to recite some of the factors for the [57]*57jury to consider as they weigh the totality of the circumstances. See Commonwealth v. Cryer, supra at 572. The judge in this case did just that. He informed the jury that they could take into account “the nature of any conversations that the police officers have with the defendant and the duration of any questioning,” “where the statement was made and when,” and “the defendant’s physical and mental condition, his intelligence, training, education, and experience and personality.” He also specifically instructed that any statement had to be voluntary “in the sense that it was not forced or tricked out of the defendant.” Given the nature of the cross-examination of the Commonwealth’s witnesses, the witnesses offered by the defense, and defense counsel’s closing that sharply focused the jurors on the issue of the representations made on January 9, the instructions given by the judge were adequate to inform the jury that they could legitimately take evidence regarding the immunity letter and any other representations made to Jordan by the detectives or Federal agents into account in assessing the voluntariness of Jordan’s statements to the police. Jordan may have wished for a more generous instruction, but he was not entitled to one. There was no error.
4. Disallowance of Jordan’s peremptory challenges. Jordan’s final argument alleges an error of law by the trial judge during jury selection. After the initial jury panel had been seated and the Commonwealth had exercised three peremptory challenges, the defendant challenged nine jurors. The Commonwealth objected to the challenges, claiming that their effect was to exclude all five of the white men from the panel. Defense counsel argued that he had not challenged jurors on the basis of their race, pointing to three white women who remained on the panel, or on the basis of their gender, pointing to noncaucasian males who also remained on the panel. The judge found, however, that there was “a pattern where white males were being excluded from the jury.” The judge then gave counsel an opportunity to explain his reasons for each challenge. The judge credited some of the explanations,6 but ultimately disallowed [58]*58three of the challenges to white men, finding counsel’s reasons for them not to be satisfactory.* *7
Jordan argues on appeal that the judge erred in rejecting these three peremptory challenges. He claims that the challenges violated neither the rule against race-based strikes nor the rule against gender-based strikes, because the category of “white males” is neither a race-based nor a gender-based category. In response, the Commonwealth argues that combined race-gender groups should be recognized as impermissible targets of peremptory challenges. This is the first occasion we have had to address this issue.
Long before the United States Supreme Court concluded that peremptory challenges based on race8 or on gender9 violated the equal protection clause of the United States Constitution, this court held such challenges to be violative of art. 12 of the Massachusetts Declaration of Rights.10 In Commonwealth v. Soares, 377 Mass. 461, cert, denied, 444 U.S. 881 (1979), the court held that the exercise of peremptory challenges to exclude members of discrete groups delineated by sex, race, color, creed, [59]*59or national origin solely on the basis of bias presumed to derive from their membership in those groups contravened the inherent requirement of art. 12 that a jury of one’s peers be drawn from a representative cross section of the community.11 In criminal cases, both the defendant and the Commonwealth are equally entitled to have their case tried before a representative jury, and have the right to be protected from the improper use of peremptory challenges to exclude discrete groups from the jury panel. Commonwealth v. Soares, supra at 489-490 n.35.
The question before us is whether the protections against the improper use of peremptory challenges extend to groups delineated not just by one of the affiliations protected in Commonwealth v. Soares, supra, but by the intersection of two of them: race and gender. In other words, is the use of a peremptory challenge to exclude a juror solely on the basis of bias presumed to derive from that juror being, for example, a white male or a black female forbidden by the principles enunciated in Commonwealth v. Soares, supra. We conclude that it is.
The United States Supreme Court has not yet confronted the question whether the Federal constitutional protections afforded race-based groups in Batson v. Kentucky, 476 U.S. 79 (1986), and gender-based groups in J.E.B. v. Alabama ex rel. T.B., 511 U.S. 127 (1994), extend to combined race-gender groups. In the absence of guidance from the Supreme Court, lower Federal courts addressing the issue have generally declined to recognize such groups as being protected from discrimination in the jury selection process by the United States Constitution. See, e.g., United States v. Nichols, 937 F.2d 1257, 1262 (7th Cir. 1991), cert, denied, 502 U.S. 1080 (1992) (declining to recognize black females as cognizable group); United States v. Dennis, 804 F.2d [60]*601208, 1210 (11th Cir. 1986), cert, denied, 481 U.S. 1037 (1987) (declining to recognize black males as discrete group).12
In contrast, those State courts that have wrestled with the issue under their own Constitutions and precedent have generally recognized the existence of combined race-gender groups as discrete groups deserving of protections similar to those extended to discrete groups defined exclusively by race or gender. See, e.g., People v. Motton, 39 Cal. 3d 596, 605-606 (1985) (holding black women to be “cognizable group”); People v. Garcia, 217 A.D.2d 119, 120 (N.Y. 1995), opinion after remand, 238 A.D.2d 605 (N.Y.), and appeal denied, 90 N.Y.2d 905 (1997) (holding that “black females are protected from being peremptorily challenged on a discriminatory basis”); State v. Shepherd, 989 P.2d 503, 511 n.4 (Utah Ct. App. 1999) (calling trial judge’s assumption that white males could not be protected group “erroneous”)13; State v. Gonzales, 111 N.M. 590 (Ct. App. 1991) (remanding case to trial court to determine [61]*61whether prosecution’s use of peremptory challenges to eliminate all Hispanic men was improperly based on race, gender, or both). But see People v. Washington, 257 Ill. App. 3d 26, 33-34 (1993), cert, denied, 516 U.S. 875 (1995) (refusing to recognize black males as cognizable group).14,15
The right to peremptory challenges in the Commonwealth has deep roots in both the common law and statute16; it remains, however, merely a tool and not an end in itself. As Justice Blackmun, writing for the majority, so aptly noted in Georgia v. McCollum, 505 U.S. 42, 57 (1992): “[Peremptory challenges are not constitutionally protected fundamental rights; rather they are but one state-created means to the constitutional end of an impartial jury and a fair trial.” Our decision in Commonwealth v. Soares, supra, was founded on a well of jurisprudence firmly establishing that the essence of the right to an impartial jury and a fair trial is the right to “a petit jury that is as near an approximation of the ideal cross-section of the community as the [62]*62process of random draw permits.” Id. at 488, quoting People v. Wheeler, 22 Cal. 3d 258, 277 (1978). See Commonwealth v. Arriaga, 438 Mass. 556, 571 (2003) (fair jury represent cross section of community selected free from discrimination against groups therein); Commonwealth v. Martin, 357 Mass. 190, 191 (1970), quoting Smith v. Texas, 311 U.S. 128, 130 (1940) (“It is part of the established tradition in the use of juries as instruments of public justice that the jury be a body truly representative of the community”); Commonwealth v. Ricard, 355 Mass. 509, 512 (1969) (“A fair jury is one that represents a cross section of community concepts”). Such a cross section assures a “diffused impartiality” and a “sharing in the administration of justice [as] a phase of civic responsibility.” Taylor v. Louisiana, 419 U.S. 522, 530-531 (1975), quoting Thiel v. Southern Pac. Co., 328 U.S. 217, 227 (1946) (Frankfurter, J., dissenting).
In this context, it would seem anomalous and inconsistent with the primary end of ensuring an impartial jury and a fair trial to conclude that the protection we afford to groups defined by race or gender against impermissible exclusion from jury panels ought not extend to groups defined by race and gender. We decline to do so, and conclude that art. 12 proscribes the use of peremptory challenges to exclude prospective jurors solely by virtue of their membership in a group delineated by race and gender.
Turning to the jury selection in the present case, the trial judge proceeded in accord with the mechanism first outlined in Commonwealth v. Soares, 377 Mass. 461, 489-492 (1977). See Commonwealth v. Burnett, 418 Mass. 769, 771-772 (1994). He initially made a finding that there had been a “pattern” on Jordan’s part of excluding white males from the jury, and that there was a likelihood that they were being excluded solely by reason of their group affiliation. That finding is fully supported in the record of the case. He next offered defense counsel an opportunity to provide race-neutral and gender-neutral explanations for his challenges to white males. After considering the explanations offered, he accepted some as bona fide while finding others to be insufficient or “specious.” These findings are also supported by the record. We find neither abuse of discretion nor other error of law in the judge’s disallowance of the three peremptory challenges in question.
[63]*635. General Laws c. 278, § 33E, review. We have reviewed the entire record of the proceedings pursuant to G. L. c. 278, § 33E, and find no independent reason to reverse or reduce Jordan’s murder conviction.
Judgments affirmed.