Early in the morning of October 14, 1995, the defendant entered a house on Prescott Road in Lynn, climbed the stairs to the second-floor bedroom of the sleeping victim, Michael Barg, and, motivated by jealousy, hacked Barg to death with a sword. A jury found the defendant guilty of murder in the first degree on the theories of deliberate premeditation, felony-murder, and extreme atrocity or cruelty.1
The defendant accepted that he had killed the victim in the way shown by the evidence. He asserted that his consumption *868of alcohol and drugs prevented him from having the mental capacity to commit murder.2 The defendant also argued that he lacked criminal responsibility for his conduct. There was abundant evidence that the defendant became considerably upset because his former girl friend became romantically involved with the victim.
1. The defendant argues that he was denied due process of law and fundamental fairness because the judge submitted to the jury the theories of deliberate premeditation and extreme atrocity or cruelty as bases for his conviction of murder in the first degree. This novel argument lacks both precedential support and persuasive force. The law of the Commonwealth has long recognized three theories of murder in the first degree. G. L. c. 265, § 1. A defendant may be convicted on one, two, or all of these theories without running afoul of any constitutional prohibition. See Schad v. Arizona, 501 U.S. 624, 644-645 (1991); Commonwealth v. Berry, 420 Mass. 95, 111 & n.15 (1995) . Each theory is independent of the other; none is a lesser offense within another. See Commonwealth v. Diaz, 426 Mass. 548, 553 (1998); Commonwealth v. Cunneen, 389 Mass. 216, 227 (1983); Commonwealth v. Tucker, 189 Mass. 457, 494-495 (1905); Commonwealth v. Gilbert, 165 Mass. 45, 58-59 (1895). The defendant does not claim that the evidence did not warrant submission to the jury of all three theories of murder in the first degree.
2. The defendant argues that the judge’s instructions on criminal responsibility were erroneous. He asserts that the judge erred in failing, in response to a question from the jury, to define mental disease or defect, words that appeared in her instruction on criminal responsibility based on Commonwealth v. McHoul, 352 Mass. 544, 546-547 (1967). The defendant did not raise this issue at trial, either by a requested instruction or by an objection to the omission of such an instruction. The issue here, therefore, concerns only the question of the existence of the substantial likelihood of a miscarriage of justice. There was no error. We have not required the giving of such an instruction. See Commonwealth v. Goudreau, 422 Mass. 731, 737 (1996) . The matter lies in the judge’s discretion. See Commonwealth v. Torres, 420 Mass. 479, 484 (1995).
*869The defendant objected to the judge’s instruction that “you may consider the fact that a great majority of the people are sane and that [szc] the resulting probability that any particular person, including the defendant, is sane.”3 Before us in one sentence, without citation of authority, the defendant argues that such an instruction on the presumption of sanity improperly shifted the burden of proof to him and stated a conclusion that was based on statistical data not in evidence.
We approved an instruction in Commonwealth v. Kappler, 416 Mass. 574, 585-587 (1993), that had language substantially identical to that challenged here. See Commonwealth v. Matthews, 406 Mass. 380, 390 (1990). Indeed, the judge’s supplemental cautionary language, quoted in note 3 above, is more favorable to the defendant than that in the Kappler case.4 The judge followed the law of the Commonwealth. There was no error.
3. At oral argument, experienced defense counsel said that he would readily accept the burden of proving, by a preponderance of the evidence, a Ghent’s lack of criminal responsibility, if in turn the judge did not give a presumption of sanity instruction. Defense counsel did not make such a proposal to the trial judge. The point deserves serious consideration, however, at least for prospective application, but there was no miscarriage of justice in the judge’s instruction concerning the presumption of sanity.5
4. We have considered other matters referred to in the *870defendant’s brief and conclude that they present no issue that we need discuss. There is no basis on which to provide relief to the defendant pursuant to G. L. c. 278, § 33E.
Judgment affirmed.
The jury also found the defendant guilty on two counts of armed home invasion in violation of G. L. c. 265, § 18C, with Barg and another occupant of the house named as the victims. The defendant does not challenge these convictions on appeal except as may be implicit in his challenge to the judge’s treatment of the insanity defense.
The judge fully and correctly instructed the jury on the consideration they should give to the evidence of the defendant’s consumption of drugs. The defendant does not challenge those instructions here.
The instruction in its fuller form was as follows: “In considering the question of the sanity of the defendant at the time of the murder and armed home invasion, you may consider the fact that a great majority of the people are sane and that [ric] the resulting probability that any particular person, including the defendant, is sane. However, it is for you to decide whether or not to consider this inference about the probability of the defendant’s sanity; and you must carefully weigh any specific evidence of sanity or insanity that has been presented during the course of this trial. I have given you this inference to indicate that you may use your common sense and common experience in deciding whether or not the Commonwealth has met its burden of proving beyond a reasonable doubt that the defendant was criminally responsible at the time of the murder and the armed home invasion.”
The defendant does not argue, as the defendant did in Commonwealth v. Kappler, 416 Mass. 574, 578 (1993), that the evidence was insufficient to support a finding beyond a reasonable doubt that he was sane at the time of the crimes.
When we granted further appellate review in Commonwealth v. Keita, 45 Mass. App. Ct. 550, 558 (1998), we indicated that “the court will consider whether to adopt a rule that the burden is on a criminal defendant to prove lack of criminal responsibility by a preponderance of the evidence, and *870whether, if such a rule were to be adopted, it may properly and should be applied to [that] case.”