The defendant, Darrin E. Smiledge, appeals from his conviction of murder in the first degree and from the denial of his motion for a new trial. He also asks that we exercise our power under G. L. c. 278, § 33E (1992 ed.), and grant him a new trial or reduce the verdict to a lesser degree of guilt. We affirm both the conviction and the trial judge’s denial of the defendant’s motion for new trial and decline to exercise our power under G. L. c. 278, § 33E.
There was testimony from which the jury could have found the following: On May 31, 1988, George J. Rollo, the victim, drove the defendant and Kenneth Tarantino to Brace’s Cove in Gloucester. After arriving at Brace’s Cove, Tarantino saw the victim touching the defendant in the groin area. The defendant responded by brutally beating the victim. The defendant then tied the victim’s hands and feet, placed the victim in the trunk of the victim’s car, and drove with Tarantino to a deserted parking lot at a theater in Beverly. After removing the victim from the trunk of the car, the defendant strangled him to death. The defendant and Tarantino then threw the victim’s body down an embankment, covered the body with branches, and fled the area.
Shortly thereafter, Tarantino called his girl friend, Jennifer Valle, from a public telephone and told her about the murder. After spending the morning of June 1, 1988, together, Tarantino and Valle went to the Gloucester police department and told the police that Tarantino had witnessed a murder. After relating the prior evening’s events to the police, Tarantino led the police to the victim’s body. The police then arrested the defendant and charged him with the mur*158der of the victim. Tarantino, however, was granted immunity from prosecution for the murder in exchange for his cooperatian and his testimony at the defendant’s trial.
In June, 1989, prior to trial, the defendant requested the probation records of the Commonwealth’s principal witnesses, Tarantino and Valle. According to the commissioner of probation neither Tarantino nor Valle had criminal records. However, in December, 1989, in the course of the trial, the probation department disclosed that Tarantino had been convicted and sentenced for three violations of a restraining order pursuant to G. L. c. 208, § 34C (1992 ed.), and that there was an additional complaint pending. Although the defendant was permitted to use these convictions to impeach Tarantino at trial, the defendant was not allowed to ask whether Valle was the person who had obtained the restraining order. The judge ruled that the information could not be disclosed because Valle was a minor when the restraining order was obtained. G. L. c. 209A, § 8 (1992 ed.).
On appeal, the defendant claims error arising from the fact that: (1) the prosecution failed to provide the defendant with exculpatory evidence of Tarantino’s convictions in a timely manner; (2) the defendant’s right of confrontation was violated when the judge denied inquiry into the details of Tarantino’s convictions; (3) the judge failed to declare a mistrial because of the prosecutor’s question concerning the defendant; (4) the prosecution improperly vouched for the credibility of one of its witnesses; and (5) the jury instructions given by the judge contained several errors.
1. Failure to provide exculpatory evidence. The defendant argues that the Commonwealth failed to make a timely disclosure of exculpatory evidence consisting of Tarantino’s criminal records, and that this failure mandates reversal. We disagree. When dealing with a delayed disclosure of exculpatory evidence, “it is the consequences of the delay that matter, not the likely impact of the nondisclosed evidence, and we ask whether the prosecution’s disclosure was sufficiently timely to allow the defendant ‘to make effective use of the evidence in preparing and presenting his case.’ ” Common*159wealth v. Wilson, 381 Mass. 90, 114 (1980), quoting Commonwealth v. Adrey, 376 Mass. 747, 755 (1978).
On receiving an accurate record, defense counsel carried out a thorough and searching cross-examination of Tarantino, and was able to impeach him by using the record. We conclude that the defendant failed to demonstrate that he was prejudiced by the delayed disclosure of Tarantino’s criminal record.
2. Right of confrontation. The defendant claims that the judge erred by ruling that the defendant could not introduce evidence that Valle was the person who had obtained the restraining order against Tarantino. According to the defendant, the evidence would have established Valle’s fear of Tarantino, and therefore, that she corroborated his story to avoid being harmed. The defendant claims the judge’s ruling denied him his right to confront witnesses against him. We disagree. Where, as here, there has been extensive inquiry into a witness’s bias and credibility in general, it was within the judge’s discretion to exclude a specific inquiry. Commonwealth v. Donahue, 369 Mass. 943, 951, cert. denied, 429 U.S. 833 (1976).
The right to cross-examine a witness on bias is not infringed on by curbing such inquiry if the matter has been sufficiently aired. Commonwealth v. Hicks, 377 Mass. 1, 8 (1979). In this case, defense counsel was allowed to establish Valle’s inherent bias toward Tarantino by exploring several issues including that Valle had been in a long-term relationship with Tarantino, and that, when she made her initial statements to the police, she was pregnant with Tarantino’s child. Based on the depth of defense counsel’s examination into areas which probed Valle’s credibility and raised the possibility of her bias, we conclude that the judge’s ruling was within the proper exercise of his discretion.
The defendant also claims that the judge erred by refusing to permit the identification of the attorney who represented Tarantino in these cases. He claims that knowledge of this relationship would have permitted the jury to infer that Tarantino had help in concocting a self-serving story about *160the murder. The fact that Tarantino consulted an attorney before talking to the police was known to the jury. The attorney’s identity was irrelevant, especially where there was no evidence that the attorney behaved unethically or illegally.
3. Failure to declare a mistrial. The prosecutor’s question concerning the defendant’s conduct at trial did not violate the defendant’s right not to testify. The jury may consider the defendant’s courtroom demeanor when the defendant’s sanity is an issue at trial. Commonwealth v. Louraine, 390 Mass. 28, 34 (1983). In the present case, the defendant’s expert testified that the defendant suffered from a mental disease characterized by hyperactive behavior and the inability to focus his attention or to control his impulses. After the issue of criminal responsibility had been raised, the prosecutor asked the defendant’s expert whether he found it surprising that the defendant was able to sit quietly and to pay attention through nine days of trial. We hold that this question was merely an attempt to alert the jury to inconsistencies between the defendant’s conduct at trial and his alleged mental disease, and therefore, the prosecutor’s reference to the defendant’s courtroom demeanor was not improper.
4. Vouching. Although we recognize that prosecutors may not submit their own personal opinions regarding a witness’s credibility, a prosecutor may fairly respond to an attack made on the credibility of a government witness. Commonwealth v. Chavis, 415 Mass. 703, 713 (1993). In the present case, in her closing argument, the prosecutor made reference to the testimony of Lieutenant Thomas E. Spartichino, who stated that he had “believed” Tarantino’s story. After reviewing the prosecutor’s closing, we hold that the prosecutor’s statements were made in the context of discussing the Commonwealth’s decision to grant Tarantino immunity, and were not made for the purpose of vouching for the credibility of Tarantino.
5. Jury instruction. The defendant claims that the judge did not adequately instruct the jury to use caution when evaluating the testimony of an immunized witness. After reviewing the judge’s charge, we hold that the judge properly in*161structed the jury on issues of credibility including the possibility of witness bias as well as the need to scrutinize the testimony of an immunized witness.1
The defendant also argues that the judge’s instructions impermissibly shifted the burden of proof on key elements of the crime charged. We must first note that, because defense counsel did not object at trial to the now challenged instructions, we review the alleged error pursuant to G. L. c. 278, § 33E, solely to determine whether it created a substantial likelihood of a miscarriage of justice. Commonwealth v. Adorno, 407 Mass. 428, 430 (1990). In doing so, we view the instructions in their entirety, to determine the impact on the jury’s function. Id. In this case, the judge gave accurate instructions on the permissive nature of drawing inferences, on the presumption of innocence, and on the Commonwealth’s burden of proof. Therefore, viewing the instructions in their entirety, we conclude that the instructions did not impermissibly shift the burden of proof or confuse the jury on the quantum of proof necessary to support a conviction.
Furthermore, we hold that the defendant’s argument that the judge’s instructions improperly restricted the jury’s power to determine the degree of murder is meritless. The instructions accurately informed the jury that, although they could return a verdict of murder in the second degree, it was their duty to return a verdict for the highest crime proved beyond a reasonable doubt.
6. Review under G. L. c. 278, § 33E. The defendant contends that we should exercise our power to reduce his conviction to murder in the second degree. As a basis for this contention, the defendant argues that the judge’s instructions failed adequately to guide the jury in applying evidence of his mental disease to the issue of extreme atrocity or cruelty. He also contends that the reduction is justified by the evi*162dence that he suffered from a severe mental disease. After careful review of the record, we conclude that the issue of the defendant’s mental disease was fully presented to the jury and that the jury were fully instructed on the impact of the defendant’s mental disease on his ability to commit murder with extreme atrocity or cruelty. For these reasons, we decline to exercise our power under G. L. c. 278, § 33E.
Judgment affirmed.
Order denying motion for new trial affirmed.
On the issue of credibility, the judge instructed the jury that “you are the sole judges of the credibility of the witnesses. . . . We have had one witness that was granted immunity . . . [and] you may take that into consideration. You may also take into consideration whether or not a witness has been given some promises that have induced him to testify.”