The defendant, Armand R. Therrien, appeals from a denial of his fifth motion for a new trial, which raises the issue of the judge’s instructions in light of Cage v. Louisiana, 498 U.S. 39 (1990). A single justice allowed the defendant’s application for leave to appeal from the order denying his motion for a new trial. See Commonwealth v. Ambers, 397 Mass. 705, 706 (1986). We affirm the order denying the motion for a new trial.
On September 17, 1975, the defendant was convicted of murder in the first degree (two indictments), of assault with intent to murder, of assault and battery by means of a dangerous weapon, and of unlawful possession of a weapon. A description of the facts surrounding these convictions is reported at Commonwealth v. Therrien, 371 Mass. 203 (1976).
*608In 1996, the defendant filed his fifth motion for a new trial, arguing that the jury instruction using “moral certainty” as the standard for defining reasonable doubt violated his constitutional right to a fair trial.1 The motion was denied. The defendant filed a motion for reconsideration asserting that recent developments in the law concerning the use of “moral certainty” in defining reasonable doubt entitled him to a new trial. After hearing, the defendant’s motion was denied by a Superior Court judge.2 The defendant then petitioned a single justice of this court, pursuant to the “gatekeeper” provision, see G. L. c. 278, § 33E, for leave to appeal the denial of his postconviction motion. See Commonwealth v. Smith, 427 Mass. 245, 247 (1998); Ambers, supra at 706. The single justice allowed the defendant’s appeal on the jury instructions in light of recent cases criticizing the use of “moral certainty” language.3 We turn now to the defendant’s appeal.
Moral certainty. The defendant contends that the judge erred *609in explaining reasonable doubt to the jury by employing the term “moral certainty” without adequately explaining or giving content to that phrase. The defendant asserts that the judge’s use of the term “moral certainty” alone “failed to impress upon the jury the ‘high degree of certainty’ required to convict the defendant . . . beyond a reasonable doubt.” In reviewing the defendant’s claim, we review the instructions on “moral certainty” to determine whether “a reasonable juror could have used the instruction incorrectly.” Commonwealth v. Rosa, 422 Mass. 18, 27 (1996). See Commonwealth v. Smith, supra at 249 n.6. The only issue now before us is whether the term “moral certainty” was explained adequately.4
Relying in part on Cage v. Louisiana, 498 U.S. 39 (1990), the defendant contends that the judge’s instructions “failed to impress upon the jury the high degree of certainty required to find the defendant guilty beyond a reasonable doubt.” In Cage, *610the trial judge defined reasonable doubt as “such doubt as would give rise to a grave uncertainty . . . . It is an actual substantial doubt. . . . What is required is ... a moral certainty.” Cage, supra at 40. The United States Supreme Court held that the use of these statements could have suggested a “higher degree of doubt than is required for acquittal under the reasonable doubt standard.” Id. at 41.
In Victor v. Nebraska, 511 U.S. 1 (1994), the United States Supreme Court criticized the use of “moral certainty” language in the abstract. Id. at 13-16. However, the Supreme Court said that “moral certainty” language, if used with language which lends content and meaning to the phrase, is not reversible error. Id. at 14, 16. In Victor, the jurors were told they needed “an abiding conviction, to a moral certainty, of the truth of the charge.” Id. at 14. The jurors were instructed that their conclusions had to be based “on the evidence in the case . . . [and that they] must not be swayed by mere sentiment, conjecture, sympathy, passion, prejudice, public opinion or public feeling.” Id. at 16. Because the jurors were so instructed in Victor, the Supreme Court held that “there [was] no reasonable likelihood that the jury would have understood moral certainty to be disassociated from the evidence. [The Court did] not think it reasonably likely that the jury understood the words ‘moral certainty’ ... as suggesting a standard of proof lower than due process requires.” Id. at 16.
We also have reversed a conviction for murder in the first degree based on a faulty “moral certainty” instruction. See Commonwealth v. Pinckney, 419 Mass. 341 (1995). In Pinck-ney, we said that the combination of moral certainty language, conflicting and incorrect definitions of reasonable doubt, and a misstatement of a disfavored charge from Commonwealth v. Madeiros, 255 Mass. 304 (1926), “lead us to the conclusion that the instruction failed to convey accurately to the jury the meaning of reasonable doubt.” Pinckney, supra at 349. We noted, however, that use of “moral certainty” language “was not reversible error where it was used with an additional instruction which impressed upon the fact finder the need to reach a subjective state of near certitude of the guilt of the accused.” Id. at 344.
Similarly, in Commonwealth v. Bonds, 424 Mass. 698, 703 (1997), we reversed a conviction because the judge equated proof beyond a reasonable doubt with moral certainty, “and *611then [gave] no content to the phrase ‘moral certainty’ except to compare it with the certainty required to make important personal decisions.” Again, we stressed that “moral certainty” language must be explained adequately.5
The defendant contends that the instructions in his case were analogous to the unconstitutional instructions in Cage, Pinck-ney, and Bonds. He argues that the judge used moral certainty language without adding content or meaning to the phrase.6 We disagree.
Contrary to the defendant’s contention, the instructions at his trial were closer to those upheld in Victor than to those in Cage or Pinckney. The judge instructed the jurors that they “should evaluate the testimony and the exhibits, place them against each other, use [their] common sense and try to come to a determination of whether or not the Commonwealth has proven . . . that the defendant is guilty of the crimes beyond a reasonable doubt.” The judge stated that the defendant need not “prove that there is some other explanation of the evidence.” The judge *612stated, “[I]f there is any other reasonable explanation of the evidence of what [the jurors] find happened, if that has caused [the jurors] to have serious unanswered questions about the guilt of the defendant, then he must be given the benefit of the doubt and acquitted.” The judge added reasonable doubt “means in simple language that before [the jurors could] convict a person of a crime, [they] must be sure, sure to a moral certainty.” The judge stated that the standard of proof required “that, when the case [was] all over, no matter which way it goes, that the twelve [jurors should] be able to five with each other and [them]selves.” The judge then restated that the reasonable doubt standard required “evidence which would enable . . . jurors to live with [them]selves and with one another.” Finally, the judge warned the jurors that the reasonable doubt instruction did not mean “anything based on emotion or sympathy.”
Taken as a whole, these instructions adequately conveyed the meaning and content of the phrase “moral certainty.” Indeed, the judge’s emphasis of the need for the jurors to be “sure” accords with our requirement that jurors reach a subjective state of near certitude of the guilt of the accused. See Pinckney, supra at 344. Unlike the erroneous instructions in Cage, nothing the judge said suggested a “higher degree of doubt than is required for acquittal under the reasonable-doubt standard.” Cage, supra at 41. Therefore, we conclude that a reasonable juror could not have used the instruction incorrectly. See Rosa, supra at 27.7
Order denying motion for a new trial affirmed.
The defendant first unsuccessfully moved for a new trial in September, 1975, arguing that the trial judge erred in charging the jury by citing to the Commonwealth’s evidence when distinguishing between murder in the first degree and murder in the second degree. The defendant then challenged his ponvictions before this court, arguing that the judge erred by: (1) citing to the Commonwealth’s evidence in the jury instructions; (2) giving instructions which invited an emotional verdict; and (3) explaining to the jurors that the defendant must be acquitted if the jurors had “serious unanswered questions” about the defendant’s guilt. We affirmed the defendant’s conviction. See Commonwealth v. Therrien, 371 Mass. 203, 209 (1976). In December, 1976, the defendant unsuccessfully moved for a new trial, based on alleged ineffective assistance of counsel. In November, 1980, the defendant filed a third motion for a new trial, arguing that the jury instructions regarding malice were erroneous. The motion was denied in September, 1981, and a single justice of this court denied leave to appeal to the full court in 1983. In March, 1985, the defendant was denied habeas corpus relief by a Federal District Court.- The First Circuit affirmed, concluding that there was no error in the jury instruction’s explanation of malice and that the instructions did not establish wrongly a presumption in favor of the Commonwealth. See Therrien v. Vose, 782 F.2d 1 (1st Cir.), cert. denied, 476 U.S. 1162 (1986). In January, 1987, the defendant filed a fourth motion for a new trial, this time challenging the felony-murder instructions. The motion was denied and a single justice of this court denied leave to appeal to the full court.
The trial judge had retired by the time of the fourth motion for a new trial.
The order of the single justice allowed the Commonwealth to assert that the cases relied on by the defendant clearly were foreshadowed and therefore the new trial motion did not present anything “new and substantial.” Commonwealth v. Smith, 427 Mass. 245, 248 (1998); Commonwealth v. Ambers, 397 Mass. 705, 707 (1986).
The Commonwealth argues that the defendant’s claim should be deemed waived because problems associated with moral certainty language were foreshadowed well before the defendant’s prior postconviction motions. There is merit to the Commonwealth’s argument. See, e.g., Hopt v. Utah, 120 U.S. 430, 440 (1887) (“the words ‘to a reasonable and moral certainty’ add nothing to the words ‘beyond a reasonable doubt;’ one may require explanation as much as the other”); United States v. Drake, 673 F.2d 15, 21 (1st Cir. 1982) (“As for ‘moral certainty’ language our disapproval of it as a definition of proof beyond a reasonable doubt is by now well-settled”); United States v. Indorato, 628 F.2d 711, 720-721 (1st Cir.), cert. denied, 449 U.S. 1016 (1980) (“The interchangeable use of the phrases ‘morally certain’ and ‘reasonably certain’ is ... of dubious value”); United States v. Ariza-Ibarra, 605 F.2d 1216, 1228 (1st Cir. 1979) (“[W]e have cautioned previously against use of language suggesting that [reasonable doubt] means proof to a moral certainty”); Dunn v. Perrin, 570 F.2d 21, 24 (1st Cir.), cert. denied, 437 U.S. 910 (1978) (“Authorities differ on the advisability of equating proof beyond a reasonable doubt with establishment of guilt to a moral certainty”); United States v. Byrd, 352 F.2d 570, 575 (2d Cir. 1965) (“ ‘Doubt’ and ‘certainty’ are antithetical and . . . the use of them in this manner and for this purpose would tend to create more confusion than light in the minds of the jury”); People v. Brigham, 25 Cal. 3d 283, 300 (1979) (Mosk, J., concurring) (“Moral certainty” has “drawn . . . scholarly and judicial criticism over the years”); Commonwealth v. Kloiber, 378 Pa. 412, 427, cert. denied, 348 U.S. 875 (1954) (“the use of the words ‘moral certainty’ serves to confuse and befog the jury”). On the view we take of the defendant’s appeal, we need not address this argument.
We disagree with the implication inherent in Simpson v. Matesanz, 29 F. Supp. 2d 11 (D. Mass. 1998), that the problems associated with “moral certainty” language were not foreshadowed prior to the decision in Cage v. Louisiana, 498 U.S. 39 (1990).
The Federal Judicial Center has recommended the following definition of reasonable doubt: “Proof beyond a reasonable doubt is proof that leaves you firmly convinced of the defendant’s guilt. There are very few things in this world that we know with absolute certainty, and in criminal cases the law does not require proof that overcomes every possible doubt. If, based on your consideration of the evidence, you are firmly convinced that the defendant is guilty of the crime charged, you must find him guilty. If on the other hand, you think there is a real possibility that he is not guilty, you must give him the benefit of the doubt and find him not guilty.” Pattern Criminal Jury Instructions, Instruction 21 (1988).
The defendant also asserts that the instruction that the jury must acquit if the jurors had “serious unanswered questions” was equivalent to the “grave uncertainty” language criticized in Cage v. Louisiana, 498 U.S. 39 (1990). This argument lacks merit. First, the use of the term “serious unanswered questions” was unsuccessfully challenged on direct appeal. Commonwealth v. Therrien, supra at 208. Second, the motion judge found, reading the instruction as a whole, the word “serious,” as employed, did not mean “grave.” Rather, a reasonable juror would have understood the term to mean “being in earnest.” The term was used to distinguish reasonable and unreasonable unanswered questions. We note that trial counsel, who heard the language in context, did not object to the term.
The defendant also argues matters not before the single justice and not addressed below. We do not discuss these issues as they are not properly before us. However, we note that the issues about which the defendant complains were well developed during the course of the defendant’s repeated posttrial proceedings. See, e.g., Commonwealth v. Bumpus, 362 Mass. 672 (1972), vacated and remanded on other grounds, 411 U.S. 945 (1973), aff'd on rehearing, 365 Mass. 66 (1974).
We disagree with the defendant’s contention that the recent decision in Simpson v. Matesanz, 29 F. Supp. 2d 11, 13 (D. Mass. 1998), should alter our conclusions. In Simpson, the judge (1) instructed that the jurors had to be “sure to a moral certainty,” (2) equated the degree of certainty required for conviction with that required for “decisions of importance” in the lives of the jurors, and (3) instructed that if the jurors had serious unanswered questions about the defendant’s guilt, the defendant must be acquitted. Citing the compounding effect of these three problematic instructions and the lack of redeeming language, a Federal District Court granted the defendant’s habeas corpus petition.
The instructions here are distinguishable. First, unlike in Simpson, the judge did not introduce the concept of important life decisions. Rather the defense *613attorney compared reasonable doubt to important life decisions in closing argument. The judge then reacted to this comparison by stating that the examples given by the defense attorney “were close, but” that he believed that reasonable doubt should be described differently. After stating that the jurors “must be sure” in order to convict a defendant, the judge defined the certainty required as that which, “when the case [was] all over, no matter which way it [was decided], that the twelve [jurors would] be able to live with each other and [them]selves.” The judge’s brief reference to the defense attorney’s examples by itself or in conjunction with the term “moral certainty” does not amount to reversible error.
Second, unlike the instructions in Simpson, here there was sufficient “redeeming language” to lend content and meaning to the other problematic instructions. The judge stated that the jurors “must be sure” and twice repeated that the certainty required for conviction was such that jurors be able to live with themselves and each other after the trial. This instruction, absent in Simpson, informed the jurors of the level of certitude required for conviction. Cf. Cage v. Louisiana, 498 U.S. 39, 41 (1990) (erroneous instructions suggested a “higher degree of doubt than is required for acquittal under the reasonable doubt standard,” a problem not found in these instructions).