Convicted of deliberately premeditated murder, Christopher R. Fletcher appeals from that judgment and the denial of his motion for a new trial. He argues that trial counsel provided him with ineffective assistance in failing to investigate his mental state and in failing to present certain evidence at trial, prejudicing his defense that he could not deliberately premeditate or form the requisite intent for murder because of his intoxication and insanity.1 For the first time on appeal he also claims that the judge erroneously instructed the jury regarding the intent required for a conviction of premeditated murder. There being no basis for ordering a new trial or for granting the defendant relief under G. L. c. 278, § 33E, we affirm the judgment and the order denying the defendant’s motion for a new trial.
1. Background. The jury could have found as follows. On the night of the murder — April 12-13, 1995 — the defendant was homeless. He went to look for the victim, whom he knew through his estranged girl friend, because he thought he might be able to stay with her. At about 8 p.m., the defendant located the victim at the Captain’s Lounge in Leominster, where she worked. Throughout the evening the defendant had several drinks and talked with the victim. He asked the victim if he could stay with her, but she refused. There was evidence that, at the time, the defendant was extremely angry that he had been rejected by both his parents and his former girl friend.
At closing, the victim tidied up, ran some errands, and then headed home. The defendant, meanwhile, had proceeded directly from the bar to the victim’s house, even though the victim had told the defendant he could not stay with her. According to a statement he later gave to the police, he drove by the house and “scoped it out,” and then parked in a neighbor’s driveway. The defendant removed a light bulb from the fixture next to the victim’s front door, then went behind the house and cut a *560telephone line. He returned to the front of the house and slashed the tires of the two automobiles in the driveway.
When the victim arrived home some time later, the defendant approached and told her to come with him. She resisted. The defendant put a utility knife to her neck “so she could see it,” and ordered her to get into his automobile. When she continued to resist, the defendant sliced the victim’s throat with the knife, then plunged the knife into her neck so deeply that it severed her carotid artery and sliced part of a bone on her spine. Expert evidence at trial established that either wound could have been fatal.
State police investigators located the defendant two days later. After some preliminary inquiries during which the defendant received Miranda warnings, the defendant told two troopers that he had killed the victim, and he gave a statement detailing his activities on the night of April 12 and 13.
Prior to trial the defendant moved to suppress statements he had made to law enforcement authorities, including his confession, and evidence seized from his person and automobile, on the ground that his statements were involuntary because of intoxication and insanity and that his arrest was without probable cause. Following a three-day evidentiary hearing, the defendant’s motion was denied.
At trial, the Commonwealth proceeded on theories of deliberate premeditation and extreme atrocity or cruelty. The defendant admitted killing the victim, but argued that he could not be held criminally responsible because, at the time of the killing, he was insane and intoxicated. In support of these defenses, trial counsel introduced evidence of the defendant’s regular use of powder and crack cocaine, recent homelessness, and rejection by his girl friend and parents. Counsel also argued that the defendant’s actions at the time of the killing were irrational and senseless, and demonstrated his inability to act with malice, to premeditate deliberately, or to confess voluntarily to the murder. Trial counsel pointed out that the defendant cut only one of two telephone lines at the victim’s house; he removed the light bulb from only one of three porch lights near the entryway to her house; he waited for the victim outside her house despite the noise of barking dogs and his suspicion that someone had *561detected his presence; he washed his hands and automobile with the neighbor’s hose following the killing; he returned to the scene to retrieve belongings that the victim dropped, but not the numerous utility knife blades that had scattered about the property; he drove to a nearby store to remove the victim’s clothing and to let the falling rain rinse the blood from her body; and then he returned the victim’s body to his vehicle. Trial counsel also introduced evidence of the defendant’s confusion during his interrogation at the State police barracks where he wrote the wrong year in the date on the Miranda warning card, necessitating repetition of the warnings. Trial counsel sought and obtained jury instructions on legal insanity and intoxication; however, no expert testified for either the defense or the prosecution on the defendant’s mental state. The jury found the defendant guilty of murder in the first degree on a theory of deliberate premeditation.
2. Erroneous jury instruction on malice. As the defendant correctly claims, the judge’s instructions to the jury were erroneous because he failed to inform the jury that only the first prong of malice can support a conviction of deliberately premeditated murder. See Commonwealth v. Jenks, 426 Mass. 582, 585 (1998). Rather, the judge improperly instructed the jury that either the first or the second prong of malice could support a conviction of deliberately premeditated murder. He intermingled the second prong of malice within his definition of deliberate premeditation, and erroneously instructed the jury on several occasions that, to convict a defendant of deliberately premeditated murder, the Commonwealth must prove that the defendant unjustifiably killed the victim and that he specifically intended to kill her or to do grievous bodily harm to her. We conclude that the error did not create a substantial likelihood of a miscarriage of justice entitling the defendant to a new trial. See Commonwealth v. Wright, 411 Mass. 678, 681 (1992).2
First, the jury were correctly and repeatedly instructed that deliberate premeditation requires “a conscious and a fixed purpose to kill continuing for a length of time,” and that any *562“decision to kill was the product of cool reflection.” The judge also instructed the jury:
“The word deliberately, in the expression ‘deliberately premeditated malice aforethought,’ has reference to the prior formation of a purpose to kill rather than to any definite length of time. . . . It is not so much a matter of time as of logical sequence: First the deliberation and premeditation, then the resolution to kill, and lastly the killing in pursuance of the resolution . . . .”
The judge’s instructions on deliberate premeditation therefore focused the jury on the requirement that they must find a specific intent to kill in order to find the defendant guilty of deliberately premeditated murder. Where the judge makes clear that premeditated murder contains as a necessary condition of guilt a finding by the jury beyond a reasonable doubt of a specific intent to kill, an error in instructing the jury on the second prong of malice does not create a substantial likelihood of a miscarriage of justice. See, e.g., Commonwealth v. Simpson, 434 Mass. 570, 588 (2001); Commonwealth v. Vinton, 432 Mass. 180, 192-193 (2000); Commonwealth v. Squailia, 429 Mass. 101, 107 (1999); Commonwealth v. Jiles, 428 Mass. 66, 71-72 (1998); Commonwealth v. Nolan, 427 Mass. 541, 544-545 (1998); Commonwealth v. DiBenedetto, All Mass. 414, 425 (1998). Cf. Commonwealth v. Johnson, ante 113, 121-122 (2001).
Second, the evidence in this case was overwhelming that the defendant planned to kill the victim. He waited for her at her home. He took steps to conceal his presence and to prevent anyone who might become alerted to the impending struggle from summoning help. Almost immediately after confronting the victim, the defendant slashed her throat, leaving a four-inch gash, and thrust the knife into her neck, penetrating to the spine. The evidence would not warrant a jury finding that the defendant intended to cause the victim grievous bodily harm, rather than death. Cf. Commonwealth v. Murphy, 426 Mass. 395, 401 (1998); Commonwealth v. Fryar, 425 Mass. 237, 248, cert, denied, 522 U.S. 1033 (1997) (“The evidence showed that the victim was stabbed in the chest with a knife. This evidence does not warrant a finding of a risk of harm less than a strong likelihood of death”).
*563The defendant points to Commonwealth v. Johnson, supra, in which we recently ordered a new trial where the judge gave erroneous jury instructions on the intent necessary to support a conviction of murder in the first degree. There are critical distinctions between Commonwealth v. Johnson, supra, and this case. In Johnson, “the judge did not clearly inform the jury [that to find deliberate premeditation] they must find the plan, the decision to kill after a period of deliberation, and then the resolution to kill,” id. at 121, as he did here. Moreover, during their deliberations, the Johnson jury requested that the judge clarify the distinction between murder in the first degree and murder in the second degree. See id. at 121-122. The judge repeated the erroneous instructions, and did so when the jury were most focused on the issue. “The last definition the jurors heard was . . . wrong.” Id. at 122. No such request occurred here. Last, in Commonwealth v. Johnson, supra, the judge gave an incorrect instruction on the third prong of malice, expressly permitting the jury to convict the defendant in that case of premeditated murder if they found he did an act “creating a plain and strong likelihood that death or grievous bodily harm would follow.” Id. at 121. Because “an erroneous definition of the third prong of malice ... is similar to the proof required for involuntary manslaughter,” id., we pointed to that error in the charge as one of several that “relieved the Commonwealth of its burden to prove deliberate premeditation beyond a reasonable doubt.” Id. at 122, quoting Commonwealth v. Lennon, 399 Mass. 443, 448 (1987). In this case, the judge correctly instructed the jury that the “so-called third prong of malice” does not support a finding of premeditated murder.
The jury rejected the defense that either his intoxication or his insanity prevented him from forming the requisite intent for murder.3 In view of the judge’s clear and forceful instructions that, to convict the defendant of premeditated murder, the jury “must find a conscious and a fixed purpose to kill continuing *564for a length of time,” there was no substantial likelihood of a miscarriage of justice from the erroneous portions of the judge’s instruction.
3. Ineffective assistance of counsel, a. Failure to adduce expert testimony on the defendant’s mental state. The defendant claims that his trial counsel was ineffective in failing to investigate his mental capacity and ability to premeditate deliberately, or to offer expert testimony on these issues. Counsel’s failure to investigate the defendant’s mental state can, of course, constitute ineffective assistance “if facts known to, or accessible to, trial counsel raised a reasonable doubt as to the defendant’s mental condition.” Commonwealth v. Doucette, 391 Mass. 443, 458-459 (1984). Our review of the record establishes beyond cavil that trial counsel thoroughly investigated the defendant’s mental condition, and that his decision not to proffer in evidence the expert opinions he did obtain was sound.
The defendant was examined by two experts at the request of trial counsel. He was first examined by a board certified forensic psychiatrist who concluded that the defendant had no defense of insanity or “diminished capacity” and that the defendant was “a malingerer and a liar.” Undeterred, trial counsel had a psychologist examine the defendant. After the psychologist spent fourteen hours with the defendant on six separate occasions, he opined that there was insufficient evidence to conclude that the defendant was not criminally responsible for the killing. He also concluded that the defendant’s actions were “inconsistent with what one would expect from someone who was sufficiently intoxicated to be incompetent to intelligently and knowingly waive his privilege against self-incrimination.”
It was reasonable for trial counsel not to present either expert to the jury, just as it was reasonable for counsel not to seek further expert evaluations of the defendant. See Commonwealth v. Cormier, 427 Mass. 446, 451 (1998) (“Defense counsel sought the opinions of several experts. That he did not present those opinions is consistent with the proposition that they would not have been helpful to the defendant”). Their testimony would *565not have helped the defendant, and indeed would have been highly detrimental to the defense. Nor was counsel’s decision a unilateral one: he discussed with the defendant the decision not to offer expert testimony on the defendant’s mental condition. The defendant agreed with that strategic choice. Finally, trial counsel did not leave the defendant without a defense, nor did he abandon the defense. See Commonwealth v. Mello, 420 Mass. 375, 394 (1995). Trial counsel pursued a defense of insanity and intoxication by cross-examining the Commonwealth’s witnesses, requesting and receiving jury instructions on insanity and intoxication, and arguing those issues forcefully to the jury.
As detailed above, there was overwhelming evidence that the defendant formulated the intention to kill the victim and carried out that intention knowing the consequences of his actions. In these circumstances, expert testimony that was so damaging to the defendant “would not likely have affected the jury’s conclusion that at the time of the murder he had the mens rea necessary for a conviction of murder in the first degree.” Commonwealth v. Hardy, 426 Mass. 725, 730 (1998).
b. Failure to introduce evidence. The defendant argued in his motion for a new trial that trial counsel was constitutionally ineffective in failing to introduce evidence that would have demonstrated that he lacked the ability to act with malice, to premeditate, or to confess voluntarily to the victim’s killing. The defendant claims trial counsel should have introduced evidence that, at the time he confessed to killing the victim, he also confessed to twelve other murders. The defendant argues that he did not in fact commit those other murders, and that no sane person would confess to numerous murders he did not commit. The defendant also contends that trial counsel should have introduced in evidence a conversation he had “made up” between himself and two Leominster police officers on the morning following the murder, which he later related to the police during his confession. We review the defendant’s claims of ineffective assistance to determine whether error, if any, by his counsel “was likely to have influenced the jury’s conclusion.” Commonwealth v. Wright, 411 Mass. 678, 682 (1992). We discern no such error.
In his four-page, single-spaced affidavit submitted at the mo*566tion for a new trial, trial counsel stated that he discussed at length with the defendant the benefits and risks of introducing the evidence of his “false” confessions and that the defendant agreed with the strategy not to do so. Among the many considered pitfalls was that, at the time of trial, all twelve murders to which the defendant confessed were still under investigation by the police. While one of the confessions was demonstrably false (because deoxyribonucleic acid [DNA] tests definitively ruled the defendant out as a suspect), the status of the remaining eleven was less clear.4 Having the jury hear a confession to multiple homicides that the jury might not view as false was of obvious concern.
Trial counsel also informed the motion judge that he was concerned that introducing the “false confessions” might prejudice the jury because many of their details paralleled the circumstances of the victim’s killing. In his confessions, the defendant described slitting victims’ throats, transporting bodies in his vehicle, going back for victims’ belongings that had been left behind at the site of the killing, and cutting the clothes off a female victim. Trial counsel’s explanations, discussed at length with his client, were eminently reasonable. See Commonwealth v. Bousquet, 407 Mass. 854, 863-864 (1990). The judge, who was also the trial judge, was fully warranted in not crediting the defendant’s self-serving affidavit to the contrary. See Commonwealth v. Grace, 370 Mass. 746, 752-753 (1976).
The same result obtains concerning the “failure” to introduce evidence of the defendant’s imagined conversation with the Leominster police officers following the murder.5 Trial counsel investigated whether the conversation ever took place, and was unable to locate any Leominster police officer who had any recollection of any conversation with the defendant on April 13. *567Counsel apprised the defendant of the use that could be made of the evidence and the drawbacks that such use might entail. The defendant agreed with the decision not to offer the evidence at trial. We agree with the judge that the utility of the fictitious conversation evidence was marginal. Our review of the record satisfies us that counsel’s strategic decisions not to introduce the false confessions or the imagined conversation would not have played an important role in the jury’s conclusions. See Commonwealth v. Plant, 417 Mass. 704, 715 (1994); Commonwealth v. Wright, supra at 682.
c. Other claims of ineffective assistance. Pursuant to Commonwealth v. Moffett, 383 Mass. 201, 216 (1981), the defendant raises additional claims of his trial counsel’s ineffective assistance. He contends that (1) counsel failed competently to argue the motion to suppress and to prepare adequately for the hearing; and (2) counsel permitted a State trooper to testify in place of a key witness. The defendant also claims that the prosecutor’s conduct was improper throughout the trial.
There is no merit to the defendant’s claim that his counsel was ineffective in challenging his statements made to the police. After a three-day hearing on the defendant’s motion to suppress, the motion judge concluded that the defendant was not under arrest when State police first approached him and requested that he accompany them to the State police barracks to talk about the victim’s death. Even had he been under arrest at that time, the motion judge correctly found there was probable cause for the arrest. Defense counsel thoroughly cross-examined the witnesses and forcefully argued the issues of probable cause and voluntariness. See Commonwealth v. Satter-field, 373 Mass. 109, 111 (1977) (“the basic trouble from the defense standpoint was weaknesses in the facts rather than any inadequacy of counsel”).
Contrary to the defendant’s contention that, during the hearing on the motion to suppress, counsel sat idly by while a State trooper testified to what a witness had seen outside the victim’s house in the early morning hours of April 13, counsel did object to the testimony. Information given to the State trooper bore directly on probable cause and therefore was not hearsay. See Commonwealth v. Weiss, 370 Mass. 416, 418 (1976).
*568Finally, our review of the record belies the defendant’s claims that counsel inadequately prepared for the motion hearing or that the prosecutor engaged in improper argument or conduct during the trial. We are satisfied that the motion judge’s conclusions were correct in denying the defendant’s motion to suppress.
4. Relief under G. L. c. 278, § 33E. We have reviewed the entire record6 and conclude that there is no reason to exercise our power under G. L. c. 278, § 33E, either to order a new trial or to reduce the verdict.7
Judgment affirmed.
Order denying motion for a new trial affirmed.