In 1995, the defendant was convicted by a Superior Court jury of murder in the first degree. In his direct appeal to this court, we affirmed the conviction, denied relief under G. L. c. 278, § 33E, and affirmed the denial of the defendant’s motion for a new trial. See Commonwealth v. Hardy, 431 Mass. 387 (2000) (Hardy). In 2008, the defendant filed a second motion for a new trial, alleging his counsel was ineffective for failing to raise certain alleged errors at trial and on direct appeal.1 A judge of the Superior Court (who was not the trial judge) denied the motion without an evidentiary hearing. The defendant sought leave to appeal from the denial of his motion by a petition to a single justice of this court pursuant to the “gatekeeper” provision of G. L. c. 278, § 33E, and the single justice allowed the petition. We affirm the denial of the defendant’s second motion for a new trial.
Background. The body of Thomas Moran was discovered in a Medford park at approximately 5:30 a.m. on April 28, 1994. Moran had suffered seventy-nine stab wounds and a gunshot wound to the face. A grand jury returned an indictment charging the defendant with Moran’s murder, and after a trial lasting over three weeks, the defendant was convicted of murder in the first degree by reason of deliberate premeditation and extreme atrocity or cruelty. As stated, we affirmed the defendant’s conviction, affirmed the denial of the defendant’s motion for a new trial, and denied relief under G. L. c. 278, § 33E.2 See Hardy, supra at 400.
In this appeal from the denial of his second motion for a new *662trial, the defendant now claims that his counsel was deficient at trial and on direct appeal by failing to raise the following alleged constitutional errors of the trial judge: (1) twice closing the court room during trial; (2) precluding the defendant from cross-examining a witness about any inducement the Commonwealth had provided to the witness in order to obtain his testimony; (3) denying the defendant’s request to give a Bowden instruction, see Commonwealth v. Bowden, 379 Mass. 472, 485-486 (1980); and (4) permitting the jury to infer the defendant’s consciousness of guilt from false statements he had made to police concerning his whereabouts on the night of the killing. Additionally, the defendant asserts that his counsel failed to raise a claim at trial and on direct appeal that the prosecutor had improperly vouched for the credibility of a witness.
Discussion. 1. Standard of review. The defendant comes before us on the denial of his second motion for a new trial, after plenary review of his conviction and of the denial of his first motion for a new trial by this court, pursuant to G. L. c. 278, § 33E. In such circumstances, we review an unpreserved claim of error by considering whether the alleged error created a substantial risk of a miscarriage of justice. See Commonwealth v. Smith, 460 Mass. 318, 320-321 (2011).3
When a defendant attributes the failure to preserve a claim to the ineffective assistance of counsel, however, “we use the ineffectiveness of counsel standard set forth in Commonwealth v. Saferian, 366 Mass. 89, 96 (1974), because, ‘whether we view the unpreserved claim of error. . . [by] utilizing the substantial risk of a miscarriage of justice standard, or. . .by focusing on counsel’s ineffectiveness in failing to object to the error, our approach is essentially the same, and ... the result would be the same.’ ” Commonwealth v. Lavoie, ante 83, 89 (2013), quoting Commonwealth v. Azar, 435 Mass. 675, 686-687 (2002).4 “Counsel is ineffective where his conduct falls ‘below that *663which might be expected from an ordinary fallible lawyer’ and prejudices the defendant by depriving him ‘of an otherwise available, substantial ground of defence.’ ” Commonwealth v. Lavoie, supra at 89-90, quoting Commonwealth v. Saferian, supra,
2. Public trial. We address first the defendant’s claim that his trial counsel was ineffective for failing to object to two court room closures — a complete closure of the court room during jury selection and a partial closure of the court room during the reading of the verdict — that he asserts violated his constitutional right to a public trial under the Sixth Amendment to the United States Constitution.* **5 See, e.g., Commonwealth v. Cohen (No. 1), 456 Mass. 94, 106 (2010).
We conclude that, on the particular facts of this case, counsel’s failures to object to the closures were objectively reasonable decisions that did not fall “below that which might be expected from an ordinary fallible lawyer.” See Commonwealth v. Safer-ian, supra. We have recognized that defense counsel may have good reason to refrain from objecting to the exclusion of the public from a defendant’s trial. See, e.g., Commonwealth v. Cohen (No. 1), supra at 118 n.35. Here, undisputed facts drawn from the trial judge’s 1998 decision denying the defendant’s first motion for a new trial (1998 decision) and the trial transcript disclose that, throughout the trial proceedings, the judge and the parties were aware of tensions between those who supported the defendant and those who supported the victim.
As stated in the judge’s 1998 decision, “this case was fraught with events and circumstances many of which were extraneous to the trial itself but impacted upon same in the form of control and tension that evolved from the conduct of others.” According to the judge, the “family and friends of the defendant and the victim divided into actively antagonistic factions; a situation that continued up to and throughout the trial[,] requiring court action on more than one occasion” to maintain control of the *664court room. Indeed, just before trial began, defense counsel informed the judge that she had received death threats.
Based on these circumstances, the judge conducted a bench conference before jury selection began during which the judge informed the parties that the court room would be cleared of all spectators, both supporters of the defendant and of the victim, during jury selection. In response, defense counsel repeated several times, “I understand, Your Honor.” Counsel also informed the judge that she had told the defendant’s supporters to go home until the jury had been selected.
The specter of potential violence continued to loom over the trial. In the 1998 decision, the judge noted that a defense witness had been shot at near the court house after having testified. On a view of the park where the victim’s body was found, spectators shouted at the jury, “[The defendant] is a murderer.” Hardy, supra at 391. And, during a recess in the proceedings toward the end of trial, the defendant’s father was arrested after attacking the victim’s mother in the corridor just outside the court room. These events prompted the judge to order that the entire floor of the court house on which the court room was located be closed, and that only eight spectators supporting the victim, and eight spectators supporting the defendant, would be allowed in the court room during the reading of the verdict.6 Neither defense counsel nor the prosecutor objected.7
Defense counsel now avers that she did not appreciate the full scope of the public trial right at the times the court room was closed. That assertion distinguishes this case from Commonwealth v. Lavoie, supra at 88-89, in which we held that an *665attorney may make a substantive waiver of a defendant’s right to a public trial by failing to object to a court room closure, but only where the failure to object “is a tactical decision as part of counsel’s trial strategy.” In that case, the defendant’s attorney knowingly refrained from objecting to a court room closure in order to benefit his client. See id. at 85. By contrast, trial counsel in this case asserts that she “was not fully aware of” the public trial right, and therefore we cannot interpret her silence as constituting a knowing waiver of the defendant’s constitutional right to a public trial.8
Nonetheless, on a claim of ineffective assistance of counsel, our review of counsel’s performance is objective. See Commonwealth v. Saferian, 366 Mass. 89, 96 (1974) (counsel’s performance is compared to “that which might be expected from an ordinary fallible lawyer”). See also Ouber v. Guarino, 293 F.3d 19, 27-28 (1st Cir. 2002) (on ineffective assistance of counsel claim, court considers “potential justifications for the attorney’s actions, given what he knew or should have known at each relevant moment in time”). In light of the circumstances *666surrounding the trial, which were known to defense counsel, it was not objectively unreasonable for her to refrain from objecting to the closures in order to protect her client’s interest in a fair trial, one in which the jury were not exposed to distracting events. See Commonwealth v. Horton, 434 Mass. 823, 833 (2001) (no ineffective assistance of counsel where “the less public setting for the voir dire in all likelihood helped rather than harmed the defendant”). Compare Owens v. United States, 517 F. Supp. 2d 570, 576 (D. Mass. 2007) (ineffective assistance where “[rjeasonable counsel with the requisite knowledge of the law would have objected — not just on learning that a particular person had been barred from the court room, but at the trial court’s statement that the court room would be cleared”). We therefore conclude that defense counsel was not constitutionally ineffective in failing to object to the court room closure.9,10
3. Cross-examination. The defendant argues that the trial judge erred by limiting the defendant’s ability to cross-examine Steven Murphy, a witness for the prosecution, about an agreement Murphy may have made with the Commonwealth in exchange for his testimony, and that his counsel was ineffective for failing to object to the error. The defendant bases his assertion that there was such an agreement on a notice of discovery the Commonwealth provided to the defendant before trial, which stated that the prosecutor had told Murphy’s attorney “that the Commonwealth was interested in [Murphy] as a witness. Without any request from the witness, the Commonwealth agreed to *667recommend [two] years in a House of Correction with one year to serve” as a sentence on his then-pending, unrelated charge of larceny.
At trial, Murphy testified that the Commonwealth had made no promises to him in exchange for his testimony, and that he had received no immunity for his own involvement in the victim’s murder. On cross-examination, defense counsel elicited that Murphy received a sentence of two and one-half years, with one year to serve, for the unrelated larceny charge. Murphy testified that he received the sentence after making a statement to police and testifying before the grand jury in connection with the defendant’s case, but denied that he had spoken with the prosecutor about receiving assistance with his larceny charge.
After Murphy denied the existence of such an agreement, defense counsel requested to be heard at sidebar, where she argued that such an agreement existed, and that she should be permitted to question Murphy about whether the prosecutor communicated an agreement to Murphy through Murphy’s attorney. According to defense counsel, an attorney with whom she shared an office had been told by Murphy’s attorney that there was such an agreement; the prosecutor denied its existence. The judge ruled that Murphy could not testify about anything the prosecutor communicated to him through his attorney, because of the attorney-client privilege, but that Murphy could testify about any conversations he himself had had with the prosecutor. Defense counsel did not pursue this line of inquiry.
It is well established that a defendant is entitled to reasonable cross-examination of a witness for the purpose of showing bias. See Commonwealth v. Michel, 367 Mass. 454, 459 (1975), S.C., 381 Mass. 447 (1980). “This right of cross-examination may assume constitutional dimensions under the confrontation clause of the Sixth Amendment to the Constitution of the United States, and art. 12 of the Declaration of Rights of the Constitution of the Commonwealth.” Id. The right of cross-examination includes the right to inquire “into whether a witness expects favorable treatment in return for his testimony.” Commonwealth v. Birks, 435 Mass. 782, 787 (2002), S.C., 462 Mass. 1013 (2012). “If the witness’s credibility is a critical issue in the case, the requirements of due process may also mandate that the jury be aware *668of ‘evidence of any understanding or agreement as to a future prosecution.’ ” Id.., quoting Giglio v. United States, 405 U.S. 150, 155 (1972).
When properly applied, the attorney-client privilege “should present no obstacle to inquiry into promises made to the Commonwealth’s witnesses.” Commonwealth v. Michel, supra at 460. A prosecutor’s communication of any promises to a witness in exchange for his testimony, whether or not made through the witness’s attorney, is not privileged. Id. See Commonwealth v. Birks, supra at 788.
In light of these principles, the Commonwealth properly concedes that defense counsel should have been able to cross-examine Murphy about whether the prosecutor made any promise to Murphy, either to Murphy directly or through Murphy’s attorney, as an inducement to testify. The trial judge’s ruling provided too generous a cloak over attorney-client communications based on privilege, and improperly limited the scope of the defendant’s cross-examination. See Commonwealth v. Michel, supra.
The defendant has, however, failed to show that he was prejudiced by his counsel’s failure to object to the error. Defense counsel was able to elicit on cross-examination that, after making a statement to police and testifying before the grand jury in connection with the defendant’s case, Murphy had received a sentence of two and one-half years’ incarceration, with one year to serve, on an unrelated charge. Whether cross-examination about conversations between his attorney and the prosecutor would have revealed that Murphy received this sentence in exchange for his trial testimony depends on the existence of any such agreement.
In support of his claim that further examination would have revealed the existence of such an agreement, the defendant offers only the uncorroborated affidavit of his trial counsel containing hearsay statements made by an unnamed attorney with whom defense counsel had shared an office. This does not establish the existence of an agreement between Murphy and the Commonwealth. According to the affidavit, Murphy’s attorney made “admissions of a deal” to the unnamed attorney. As the judge observed, the defendant did not submit affidavits from *669either Murphy’s attorney or the attorney with whom trial counsel had shared an office. The judge correctly concluded that the defendant’s submissions were insufficient to establish that the error prejudiced him, entitling him to a new trial, because the defendant could not have impeached Murphy if such an agreement did not exist. See Commonwealth v. Hudson, 446 Mass. 709, 714-715 (2006) (“burden of establishing the grounds for a new trial rests on the defendant. . . even if memories have faded and rendered his task more difficult”). We thus conclude that counsel’s failure to object to this error did not deprive the defendant of an “otherwise available, substantial ground of defence” and was not ineffective assistance of counsel. See Commonwealth v. Saferian, 366 Mass. 89, 96 (1974).11
4. Claims raised on direct appeal. On direct appeal, we resolved several claims of alleged error, discussed below, on the basis of Massachusetts law. See Hardy, supra at 388. The defendant now argues that his first appellate counsel was ineffective for failing to cite Federal law to support these claims, reasoning that we would have reversed his conviction on direct appeal had we considered Federal law. Because a better result would not have been obtained had the claims been made under the United States Constitution, we reject the defendant’s argument. See, e.g., Commonwealth v. Richard, 398 Mass. 392, 393, cert, denied, 479 U.S. 1010 (1986) (to establish ineffective assistance of appellate counsel, defendant must show that better work might have accomplished something material for defense).
a. Prosecutor’s closing argument. In Hardy, supra at 396-397, we concluded that the prosecutor had made improper argu*670ments when he “attempted to use the authority of this court to vouch for [a witness’s] credibility” and implied that the defendant had killed before. We considered the prosecutor’s comments “in the context of the argument and the case as a whole” and concluded that reversal of the defendant’s conviction was not warranted. Id. at 397-398.
This standard is reflected in decisions considering similar issues under the United States Constitution. As stated in Donnelly v. DeChristoforo, 416 U.S. 637, 643 (1974), a defendant’s conviction must be reversed if, upon “examination of the entire proceedings in [the] case,” a court determines that the prosecutor made a statement that “so infected the trial with unfairness as to make the resulting conviction a denial of due process.” See Darden v. Wainwright, 477 U.S. 168, 179-183 (1986) (prosecutor’s improper comments, considered in context of case as a whole, did not render trial fundamentally unfair so as to warrant reversal under due process clause). Because resolution of the defendant’s claim under Massachusetts law was consistent with this standard, our consideration of Federal law would not have changed the outcome.
b. Failure to give a Bowden instruction. We also held in Hardy, supra at 395, that the trial judge did not err by declining to give a Bowden instruction. See Commonwealth v. Bowden, 379 Mass. 472, 485-486 (1980). The defendant points to Matthews v. United States, 485 U.S. 58, 63 (1988), for the proposition that “a defendant is entitled to an instruction as to any recognized defense for which there exists evidence sufficient for a reasonable jury to find in his favor,” but that principle has no application here. “The defendant’s reliance on Federal cases is misplaced. . . . Bowden does not create a ‘defense’ in the sense that it creates an element of proof that the Commonwealth must prove or disprove beyond a reasonable doubt, such that a particular instruction is required. Bowden merely recognizes that a defendant is entitled to present evidence that ‘certain tests were not conducted or certain police procedures not followed [that] could raise a reasonable doubt as to the defendant’s guilt in the minds of the jurors.’ ” Commonwealth v. Lao, 460 Mass. 12, 23 (2011), quoting Commonwealth v. Bowden, supra at 486.
*671c. Instruction on consciousness of guilt. We concluded in Hardy, supra at 394-395, that the trial judge properly instructed the jury that they could infer consciousness of guilt from evidence showing that the defendant had lied to police about his whereabouts on the night of the killing. We determined that the evidence could “show that the defendant’s false statements were motivated by the murder,” although other explanations for the falsehood were possible. Id. at 395.
The judge’s instruction did not violate any of the defendant’s Federal constitutional rights. The instruction allowed, but did not require, the jury to infer the defendant’s consciousness of guilt from evidence proving that he had given a false statement. This form of jury instruction creates what the United States Supreme Court has called a “permissive inference” because the instruction “suggests to the jury a possible conclusion to be drawn if the State proves predicate facts, but does not require the jury to draw that conclusion.” Francis v. Franklin, 471 U.S. 307, 314 (1985). A jury instruction creating a permissive presumption violates the due process clause of the United States Constitution “only if the suggested conclusion is not one that reason and common sense justify in light of the proven facts before the jury.” Id. at 314-315. See, e.g., Hill v. Maloney, 927 F.2d 646, 649 (1st Cir. 1990). As stated, the evidence in this case could reasonably support an inference that the defendant’s false statement reflected his consciousness of guilt. See Hardy, supra. This satisfies the standard under the United States Constitution for jury instructions creating permissive inferences.
Order denying motion for a new trial affirmed.
The defendant’s trial counsel also represented the defendant on his direct appeal. See Commonwealth v. Hardy, 431 Mass. 387, 388 (2000).
The defendant asserts in his brief that, prior to filing his second motion for a new trial in the Superior Court, he filed a petition for habeas corpus in the United States District Court for the District of Massachusetts, and that that court stayed the proceeding pending resolution of the defendant’s State claims in a Massachusetts court. The record on appeal does not include a copy of this petition or any order of the United States District Court, nor does it appear that the defendant provided these documents to the Superior Court in connection with his second motion for a new trial.
“The substantial likelihood of a miscarriage of justice standard that is associated with plenary review under G. L. c. 278, § 33E, and which we have said is more forgiving to a defendant than the substantial risk standard applicable in other criminal cases ... is limited to the direct appeal.” Commonwealth v. Smith, 460 Mass. 318, 321 n.2 (2011).
“Any claim of ineffectiveness of counsel presented in a subsequent appeal from the denial of a motion for a new trial, authorized by a single justice of *663this court, [is] not. . . tested under the [G. L. c. 278,] § 33E[,] standard but on the applicable constitutional standards, State and Federal.” Commonwealth v. Wright, 411 Mass. 678, 682 n.l (1992).
The Sixth Amendment to the United States Constitution provides that “[i]n all criminal prosecutions, the accused shall enjoy the right to a. . . public trial. . . .”
On March 30, 1995, the judge, with the approval of the Chief Justice of the Superior Court, issued an order limiting the “family members and friends” of the victim and the defendant to eight persons each, “[i]n light of the problems that have been attendant upon the actions and emotions of persons as spectators at [the] trial, together with the need for enhanced security and control measures.” The order did not apply to members of the press or to law enforcement.
In an affidavit submitted in support of the defendant’s second motion for a new trial, defense counsel asserts that she objected to this partial court room closure. Her assertion, which is not supported by the record, contradicts the judge’s 1998 decision, which states that neither side objected to the closure. The defendant concedes in his brief that “there was no objection to the closures and partial closures at trial in this case.”
We are confident that, in these unusual circumstances, had counsel been aware of the defendant’s public trial right and objected to the court room closures, thereby providing the trial judge with the opportunity to make case-specific findings, those findings would have met the four requirements set out in Waller v. Georgia, 467 U.S. 39, 48 (1984) (Waller): “[1] the party seeking to close the hearing must advance an overriding interest that is likely to be prejudiced, [2] the closure must be no broader than necessary to protect that interest, [3] the trial court must consider reasonable alternatives to closing the proceeding, and [4] it must make findings adequate to support the closure.” The judge’s thoughtful findings, set forth in her 1998 decision denying the defendant’s first motion for a new trial, indicate that she closed the court room to ensure that the defendant would have the benefit of an impartial jury and none of the participants or spectators would be harmed, and that she carefully tailored the closures to protect those interests. See Owens v. United States, 483 F.3d 48, 62 (1st Cir. 2007), citing United States v. Sherlock, 962 F.2d 1349, 1356 (9th Cir.), cert, denied sub nom. Charley v. United States, 506 U.S. 958 (1992), and cases cited (“Most justifications for trial closure have involved the need to protect witnesses or maintain courtroom order”). The judge’s findings, and the manner in which she narrowly limited the closures, reflect her implicit consideration of reasonable alternatives to closure. Had there been a timely objection, the judge could have articulated her consideration of such alternatives in her written findings. As it was, in the circumstances of this case, where one of the attorneys was threatened, a witness was shot at, and the specter of potential violence loomed over the trial, we are satisfied that the spirit of Waller was met.
Because we decide that counsel was not ineffective, we do not reach the question whether the defendant was prejudiced. See Commonwealth v. Lavoie, ante 83, 91 n.13 (2013), citing Commonwealth v. Saferian, 366 Mass. 89, 96 (1974). We therefore need not address the defendant’s argument that, under Owens v. United States, supra at 64-65, prejudice must be presumed because the public trial right is structural.
Bucci v. United States, 662 F.3d 18, 30-31 (1st Cir. 2011), cert, denied, 133 S. Ct. 277 (2012), is not to the contrary. There, the United States Court of Appeals for the First Circuit determined that the failure to object to a complete closure of the court room “may in general be an unsound trial strategy. . . Id. at 31. We agree with the premise, implicit in that statement, that a complete closure generally will harm the defendant. But, where the circumstances are such that a complete closure will contribute to an orderly trial process that assures the defendant will receive a fair trial, we do not presume that defense counsel’s failure to object was due to incompetence.
Nor does the defendant’s submission raise a substantial issue warranting an evidentiary hearing. See Commonwealth v. Jewett, 442 Mass. 356, 357, 365-366 (2004). In Commonwealth v. Jewett, supra at 365, the defendant argued that the prosecution had failed to disclose certain inducements made to a witness in exchange for the witness’s testimony. The defendant premised this claim on the existence of a “covert deal” between the witness and the prosecutor. Id. at 365. In support of this assertion, the defendant submitted an affidavit from his appellate counsel and an excerpt from the transcript of an unrelated hearing involving the witness, but failed to submit affidavits from the witness or the witness’s attorney. See id. at 365-366. “Given the tenuousness of the evidence filed in support of the defendant’s motion,” we held that the motion judge did not err by denying the defendant’s motion for a new trial without holding an evidentiary hearing. Id. at 366.