The defendant appeals from the denial of his amended motion for new trial. Mass. R. Crim. P. 30, 378 Mass. 900 (1979). Following a jury trial with a codefendant, Robert Stewart, in November, 1974, the defendant was convicted of murder in the second degree (the Sherter murder), and of armed assault in a dwelling house with intent to rob. He appealed the convictions under G. L. c. 278, §§ 33A-33G, and we affirmed.1 Commonwealth v. Doherty, 371 Mass. 413 (1976). The defendant filed an amended motion for new trial in May, 1982. Following discovery, a judge of the Superior Court2 conducted an evidentiary hearing in November and December, 1982, on the motion and denied the motion in July, 1983. The defendant appealed the denial in August, 1983. We granted the defendant’s application for direct appellate review.

At issue is whether the motion judge erred in denying the defendant’s amended motion for new trial by: (1) refusing to grant immunity at the evidentiary hearing on the amended motion for new trial to a witness (Goldman) who had testified for the Commonwealth at the initial trial; (2) finding no substantial newly discovered evidence; (3) finding no merit in the defendant’s claim of an improper limitation of cross-examinatian by the trial judge; and (4) finding no merit in the defendant’s claim of an improper charge to the jury by the trial judge. We affirm the judge’s denial of the defendant’s amended motion and his refusal to grant immunity to the witness. The evidence at trial and the facts relating to the underlying crime are detailed in our first review of these convictions, Commonwealth v. Doherty, supra, and in the companion case, Commonwealth v. Stewart, 375 Mass. 380 (1978) (Stewart I).

*3431. Defense witness immunity. At the 1982 evidentiary hearing on the defendant’s amended motion for a new trial, the defendant called as a witness Lawrence Goldman, an unindicted participant in the Shelter murder and assault who had testified against the defendant without immunity at the 1974 trial. At the hearing, Goldman, represented by counsel, repeatedly asserted his privilege under the Fifth Amendment to the United States Constitution not to incriminate himself, and refused to answer questions relating to whether there had been an undisclosed arrangement between him and the Commonwealth in exchange for his testimony against the defendant at the trial. At the hearing, Goldman’s attorney defended Goldman’s refusal to testify by suggesting that because Goldman had testified at the 1974 trial that no deal existed, if his answers now revealed that a deal did exist, he might incriminate himself and be subject to a perjury charge. The motion judge denied the defendant’s request for a grant of immunity to Goldman.

The defendant contends that the motion judge’s refusal to grant immunity to Goldman violates the defendant’s right to present evidence and confront and cross-examine witnesses as guaranteed by the Fifth and Sixth Amendments to the United States Constitution, see Davis v. Alaska, 415 U.S. 308, 315-317 (1974); Washington v. Texas, 388 U.S. 14, 19 (1967); Commonwealth v. Turner, 393 Mass. 685 (1985), and his “right to produce all proofs, that may be favorable to him [and] to meet the witnesses against him face to face ...” under art. 12 of the Massachusetts Declaration of Rights. The defendant argues that this court should grant the witness “judicial immunity” under its broad supervisory powers, G. L. c. 211, § 3, or remand the case to the trial court for the same remedy in order to vindicate his constitutional rights.3

*344We have recently declined to recognize a defendant’s constitutional right to a judicial grant of immunity to defense witnesses. Commonwealth v. Upton, 390 Mass. 562, 576-577 (1983), reversed and remanded on other grounds sub nom. Massachusetts v. Upton, 466 U.S. 727 (1984). Commonwealth v. Curtis, 388 Mass. 637, 643-645 (1983). Although “[w]e recognize that the assertion by a witness of his Fifth Amendment right may in some cases hinder a defendant’s ability to present his most effective defense ... we do not believe that this potential problem justifies creation of a general doctrine of judicial immunity for defense witnesses. . . . ‘ [T]he constitutional right of the accused to call witnesses is not without limit. ’ Commonwealth v. Blaikie, 375 Mass. 601, 608-610 (1978). Nor is the defendant’s right to present witness testimony in his own behalf absolute.” Commonwealth v. Curtis, supra at 646. The decision whether to grant immunity generally lies in the hands of the prosecutor. Id. at 645.4

The defendant’s reliance on Government of the V.I. v. Smith, 615 F.2d 964 (3d Cir. 1980), is misplaced. As we noted in Curtis, supra at 644-645, “‘Smith involved a totally bizarre *345situation. ’ . . . The office of the Attorney General of the Virgin Islands, which had exclusive jurisidiction to prosecute the witness, agreed to grant use immunity for the witness, but, as a matter of ‘prosecutorial courtesy,’ conditioned its approval upon the consent of the United States Attorney, who inexplicably refused to consent. ... To the extent that the court’s decision was based on broader constitutional grounds we find its reasoning unpersuasive and generally agree with the reasoning put forth by the other Federal circuits in rejecting such claims for defense witness immunity” (citations omitted). See n.4.

Barring, “some unique circumstances,” Commonwealth v. Curtis, supra at 646, any inquiry into the question of immunity is foreclosed if the prospective witness is an actual or potential target of prosecution. Commonwealth v. Upton, supra at 577. In applying the Curtis standard to the case at hand, we find that there were no “unique circumstances” requiring a grant of judicial immunity to Goldman. See Commonwealth v. Stewart, 383 Mass. 253, 258-259 (1981) (Stewart II);5 Commonwealth v. Toney, 385 Mass. 575 (1982). The judge found that there was no evidence to support the existence of an undisclosed “deal” between Goldman and the Commonwealth. It was within his discretion to exclude affidavits which alleged there was a deal, see infra at 346-347, and to conclude from testimony offered at the evidentiary hearing that no deal existed, and that at most there was an expectation on Goldman’s part, later fulfilled, of favorable treatment from the Commonwealth if he testified against the defendant. Even if there were evidence of a secret deal, however, “ [ijmmunity will be denied if the proffered testimony is found to be ambiguous, not clearly exculpatory, cumulative or . . . relate[s] only to the credibility of the government’s witnesses.” Government of the V.I. v. Smith, supra at 972-973. Here, the evidence of a deal, if it existed, would merely raise again the question of Goldman’s motives for testifying against the defendant. Defense counsel *346adequately explored this issue at the trial through cross-examination. The trial judge fully instructed the jury on motive and bias. Stewart II, supra at 258.

Because the motion judge’s factual findings do not support the defendant’s claim of “unique circumstances” which would warrant Goldman’s immunization, the judge properly declined to order immunity outside the prescribed statutory scheme. Commonwealth v. Upton, supra at 577; Commonwealth v. Curtis, supra at 646.

2. Newly discovered evidence. A new trial may be granted under Mass. R. Crim. P. 30 (b), 378 Mass. 900 (1979), “if it appears that justice may not have been done.’’ The defendant’s motion for a new trial is directed to the sound discretion of the judge. Stewart II, supra at 257. Commonwealth v. Cook, 380 Mass. 314, 320 (1980). Commonwealth v. Heffernan, 350 Mass. 48, 53-54, cert. denied, 384 U.S. 960 (1966). “If however the original trial was infected with prejudicial constitutional error the judge has no discretion to deny a new trial.” Earl v. Commonwealth, 356 Mass. 181, 184 (1969).

(a) Evidence regarding a “deal”. The motion judge found that there was no substantial newly discovered evidence regarding promises, rewards or inducements made to Lawrence Goldman warranting a new trial. See Stewart II, supra at 259. It was within the judge’s discretion to find that the evidence of favorable treatment provided to Goldman after the trial did not merit the conclusion that a pretrial deal was made between the Commonwealth and Goldman. Commonwealth v. Cassesso, 360 Mass. 570, 575 (1971), vacated on other grounds sub nom. Limone v. Massachusetts, 408 U.S. 936 (1972).6

(b) Extrajudicial statements. The defendant argues that the motion judge should have admitted in evidence at the hearing a number of affidavits which he contends establish the existence *347of a deal.7 The judge correctly ruled that all of the affidavits and the testimony of a lawyer who spoke to Goldman were hearsay and inadmissible. In Stewart II, supra at 258, we said of one of the very same affidavits that the defendant presents us with here: “The Hurley affidavit is hearsay, and, at its best, therefore is admissible solely for its impeachment value. It is ‘one step removed from an affidavit of recantation’ . . . and bears no indicia of reliability sufficient to bring it within any exception to the hearsay rule” (citation omitted).8

The defendant’s argument that the extrajudicial statements are admissible in evidence as admissions is without merit because the declarant, Goldman, is not a party. P.J. Liacos, Massachusetts Evidence 275-277 (5th ed. 1981). The defendant also claims that Goldman had made remarks which could be viewed as against Goldman’s penal interest because the statements might subject him to a charge of perjury. Even assuming the affidavits, some of which contain multi-level hearsay, were to be viewed as statements against Goldman’s penal interest, the judge, before he admitted them, also could have considered “the degree of disinterestedness of the witnesses ... as well as the plausibility of [the proffered evidence] in the light of the rest of the proof.” Commonwealth v. Carr, 373 Mass. 617, 624 (1977). Viewing the affidavits with these factors in mind, we conclude that the motion judge did not err in his determination that the affidavits should be excluded.

(c) Evidence of perjury. The defendant argues that a new trial was also warranted because newly discovered evidence established that Goldman committed perjury at trial by denying the existence of inducements or rewards and that the Commonwealth improperly permitted Goldman’s testimony to go uncorrected and did not disclose the inducements to the defendant. *348As we said above, the judge found there was no deal.9 Because the judge found that there was no deal, there if therefore no evidence of Goldman’s having committed perjury, or of the Commonwealth’s having improperly allowed a false statement at trial to go uncorrected or improperly failing to disclose information about any deals.

(d) Exculpatory evidence. The defendant also contends that a new trial is warranted because the Commonwealth suppressed two statements made by Goldman in 1973 which contain exculpatory evidence and indicate that the Commonwealth knowingly used peijured testimony. Through discovery motions on the defendant’s amended motion for a new trial, the judge, in October, 1982, granted the defendant discovery of two statements made by Goldman in November and December, 1973, to investigating officers. There are statements concerning the Sherter murder which, the defendant contends, vary from Goldman’s testimony at trial and therefore could have been used to impeach his credibility.

However, a discrepancy between Goldman’s statements and his trial testimony would not merit a new trial, because the material disclosed was not exculpatory.10 The defendant argues that access to the statements at the trial would have been helpful in impeaching Goldman’s credibility. However, for us to conclude that there was a constitutional violation, the defendant must show that the statements clearly are exculpatory. United States v. Turner, 490 F. Supp. 583, 609 (E.D. Mich. 1979), *349aff’d, 633 F.2d 219 (6th Cir.), cert. denied, 450 U.S. 912 (1981); United States v. Agurs, All U.S. 97 (1976), and material to a finding of guilt. Brady v. Maryland, 373 U.S. 83, 87 (1963). “Material evidence is that evidence which ‘on a consideration of the entire record . . . “creates a reasonable doubt that did not otherwise exist.’”” Commonwealth v. Wilson, 381 Mass. 90,107 (1980), quoting United States v. Oliver, 510 F.2d 397, 402 (1st Cir. 1978). The statements were not in themselves exculpatory and any discrepancy with Goldman’s trial testimony merely would further impeach Goldman. Neither statement related to a material issue on the homicide or the elements of armed assault in a dwelling house with intent to rob nor established evidence of perjury which the Commonwealth had a duty to correct.

3. Adequacy of cross-examination at trial. The defendant argues that he was not given an adequate opportunity to cross-examine Goldman at the trial. During cross-examination, the defendant attempted to introduce evidence of pending indictments against Goldman to establish his bias or motive for testifying against the defendant. When he tried to detail the nature of the offenses and the bail arrangements, the judge limited him by stating that he could only set forth that there were pending indictments and ask whether there had been any promises, inducements or hopes of reward. Although the defendant now alleges that this limitation improperly prevented him from impeaching Goldman’s credibility by suggesting to the jury that he had received or expected to receive favorable treatment from the Commonwealth, the motion judge properly found that it was the defense counsel’s misunderstanding of the limitation that caused him not to go forward with questioning about inducements and rewards.

The trial judge did not preclude all inquiry into the indictments. Contrast Commonwealth v. Martinez, 384 Mass. 377, 379-381 (1981), and Commonwealth v. Lewis, 12 Mass. App. Ct. 562, 571-573 & n.20 (1981). It was within the judge’s discretion to limit the questioning to promises, inducements or hopes of reward and to exclude questions concerning the facts of the pending charges. See Commonwealth v. Jackson, *350388 Mass. 98, 112-113 (1983). The defendant was accorded “reasonable cross-examination for the purpose of showing bias.” Commonwealth v. Martinez, supra at 380.

4. Jury charge. The defendant challenges the judge ’ s charge to the jury. We review the claims based on newly developed constitutional issues. See Commonwealth v. Rembiszewski, 391 Mass. 123, 126 (1984). We find the new cases inapplicable. See id. at 130; Commonwealth v. Watson, 388 Mass. 536, 544 (1983); Commonwealth v. Moran, 387 Mass. 644, 651 (1982); Commonwealth v. Matchett, 386 Mass. 492, 506-507 (1982); Commonwealth v. Watson, 377 Mass. 814 (1979); Commonwealth v. Rodriguez, 370 Mass. 684, 691 (1976).

(a) Reasonable doubt instruction. The defendant asserts that the judge’s instruction on “reasonable doubt” trivialized the Commonwealth’s burden of proof and analogized it to decisions about events in the lives of the jurors. As we analyze the paragraph of this instruction as reproduced in the margin,11 *351addressing “reasonable doubt” as a whole, we noted that the judge unambiguously defined a reasonable doubt as “one which prevents a juror from reaching a degree of certainty that satisfies the judgment and the conscience of the jurors, as reasonable men and women . . . [and] which prevents the jury from having that degree of certainity which leaves in the minds of the jurors, as reasonable men and women, a clear and settled conviction of guilt.” The instruction was consistent with the concept of reasonable doubt as explained in Commonwealth v. Webster, 5 Cush. 295, 320-321 (1850). Although the defendant argues that several cases decided since the trial have further developed the constitutional theory, the cases cited do not support his argument. In Commonwealth v. Rodriguez, 370 Mass. 684, 691 (1976), unlike in the present case, the judge’s charge as to reasonable doubt was ambiguous and was found violative of due process principles specifically on the issue of proving beyond a reasonable doubt the absence of self-defense.12 Similarly, the defendant’s contention that Commonwealth v. Rembiszewski, supra, supports his argument is inapposite because our disapproval of the charge in that case was based on the judge’s reference to important decisions in the jurors’ lives when he explained reasonable doubt, id. at 128 n.1, 130-135; whereas here the judge alluded to ordinary incidents when charging the jury on reasonable inference. See Commonwealth v. Pomerleau, 10 Mass. App. Ct. 208, 213 (1980). The instruction on reasonable doubt was adequate.

(b) Instruction on alibi evidence. The defendant’s assertion that the judge’s instruction on alibi evidence shifted the burden of proof to the defendant is also without merit. The defendant criticizes (1) the judge’s instruction to consider the testimony of “so-called” alibi witnesses and (2) the judge’s question, “Do they have any interest in this case which would impel them to tell an untruth in order to bail out a relative or friend? ” In Commonwealth v. Berth, 385 Mass. 784, 787 (1982), we criticized the following sentence in the alibi instruction: “You *352either believe one side or you believe the other side as to what took place.” No such language or any other words impermissibly shifting the burden of proof were used here. See Commonwealth v. McLeod, 367 Mass. 500, 502 (1975). The wording in the instruction in this case is also dissimilar to that criticised in Commonwealth v. Bowden, 379 Mass. 472, 480 (1980).

(c) “Tuey-Rodriquez” charge. The defendant argues that the judge’s premature delivery of a “Tuey-Rodriquez” charge and omission of the proper standard of reasonable doubt coerced the jury and impermissibly shifted the burden of proof to the defendant. See Commonwealth v. Rodriquez, 364 Mass. 87, 98, & app. (1973). All but one of these cases the defendant cites to support his argument were decided before his conviction. Because the defendant did not object to the charge at trial or raise the issue in his first appeal, we will only review the claim insofar as new constitutional law has developed since his conviction. Commonwealth v. Pisa, 384 Mass. 362, 366 (1981).

Unlike the instant case, the supplemental “Tuey-Rodriquez” instruction in Potter v. United States, 691 F.2d 1275, 1278 (8th Cir. 1982), the only case cited by the defendant and decided after his first appeal, omitted any reference to the burden of proof, failed to state that the defendant was to be acquitted if there was reasonable doubt as to guilt, omitted a clear statement that the majority, as well as minority, should reexamine their position, and omitted any caution as to the effect of the charge. The judge here clearly referred to the burden of proof and the need to acquit the defendant if there was reasonable doubt as to his guilt, and these instructions did not have to be repeated during the supplemental “Tuey-Rodriquez” charge. See Commonwealth v. Peters, 372 Mass. 319, 324 (1977); Commonwealth v. Redmond, 357 Mass. 333, 342-343 (1970). Nor did the judge use the majority and minority language criticised in Potter. Moreover, the judge followed the suggestion in Potter that the “Tuey-Rodriquez” charge be given as part of the regular jury charge so as to avoid undue coercion of the minority at the time of the deadlock. Id. at 1278. There is no error.

*353(d) Felony-murder instruction. The defendant further contends that the judge’s felony-murder instruction impermissibly shifted the burden of proof to the defendant and violated the defendant’s constitutional rights. The charge is similar to the charge in Commonwealth v. Dickerson, 372 Mass. 783, 795-797 (1977), and suffers from the same flaws concerning the various factors which may be considered by the jurors in deciding between murder in the first degree and murder in the second degree. In this case, as in Dickerson, “the error [rendered the instruction] more favorable to the defendant than that to which he was entitled.” Id. at 797. See Commonwealth v. Puleio, ante 101 (1985).

The defendant also suggests that the judge, in effect, stated to the jury that if they find that the defendant was committing a felony, and the victim died in the course of that felony, then the jury must find the defendant guilty of either first or second degree murder. This result and the felony-murder rule itself, the defendant argues, unconstitutionally relieve the Commonwealth of its burden of proving malice in a murder case, and thus violate due process requirements as set forth in In re Winship, 397 U.S. 358, 364 (1970). We do not agree.

We have said that the felony-murder rule may be applied “only if the jury find from the circumstances of the felony that the defendant consciously disregarded risk to human life.” Commonwealth v. Moran, 387 Mass. 644, 651 (1982). The only underlying felony presented for the jury’s consideration was armed assault in a dwelling house with intent to rob. Commonwealth v. Doherty, at 414. An armed assault (by means of a gun) in a dwelling house “inherently involved a conscious disregard of risk to human life so as to justify [Doherty’s] conviction of murder in the first degree on the theory of [felony-murder].” Commonwealth v. Watson, 388 Mass. 536, 543-544 (1983).

In sum, the judge’s charge as a whole provides no basis for the granting of a new trial. We conclude that there was no error in the judge’s refusal to grant immunity to Goldman, or in the denial of the defendant’s amended motion for a new trial. The order denying the motion for a new trial is affirmed.

So ordered.

(concurring). I agree with the result reached by the majority but concur to express my dissatisfaction with the rule requiring corroboration of declarations against penal interest offered to exculpate the accused. See Commonwealth v. Carr, 373 Mass. 617, 623 (1977). I did not participate in the Carr decision, but welcomed it as a step toward rationality in contrast to the previous common law doctrine followed by this court; that doctrine totally barred the admission of declarations against penal interest.

It is unnecessary for me to set forth the history of our prior opinions, since Justice Kaplan’s excellent and thoughtful opinion sets it out in adequate detail. See Commonwealth v. Carr, supra at 620-623. The exception to the hearsay rule in the case of declarations against interest was at one time limited to statements against the declarant’s own pecuniary or proprietary interests. 5 J. Wigmore, Evidence § 1476 (Chadbourn rev. 1974). Wigmore described the refusal of the courts to allow declarations against penal interest to qualify as an exception to the hearsay rule as a “barbarous doctrine.” Id. § 1477, at 360.

In recent years, this and other courts have modified the rule to allow admission of declarations against penal interest, with the limitation that when offered to exculpate the accused, the statement must be accompanied by corroborating circumstances which clearly indicate its trustworthiness. Carr, supra at 621-622. Cf. Fed. R. Evid. 804(b)(3); Proposed Mass. R. Evid. 804 (b) (3).

Such a limitation cannot be justified on grounds of policy. “The only plausible reason of policy that has ever been advanced for [the old rule of exclusion of statements against penal interest] is the possibility of procuring fabricated testimony . . . .” Wigmore, supra § 1477, at 358. This policy cannot justify the corroboration requirement, for fear of fabrication “would be a good argument against admitting any witnesses at all.” Id. at 359. I believe that the corroboration requirement is particularly unnecessary in the hearing on a motion for a new trial where, as here, a judge, presumably astute at discerning perjury, hears the evidence rather than a jury.