The defendant, Diane Farley, was originally convicted of murder in the first degree on a theory of deliberate premeditation in 1994. We reversed that conviction in 2000, holding that her trial counsel was ineffective in failing to develop the defense of a third-party culprit “through evidence, cross-examination or in summation.” Commonwealth v. Farley, 432 Mass. 153, 156 (2000). The defendant was retried, and in 2002, a Superior Court jury again convicted her of murder in the first degree on a theory of deliberate premeditation. The trial judge sentenced her to life in prison.
On appeal, the defendant claims that (1) the third-party culprit jury instruction was erroneous in that it relieved the Commonwealth of its burden to prove beyond a reasonable doubt that no one else could have committed the crime, depriving the defendant of her rights to due process and a trial by jury; (2) the scope of the defendant’s cross-examination of a witness was unfairly restricted to the content of the witness’s testimony at the previous trial and denied the defendant her right to confront the witness; and (3) the judge erred in excluding extrinsic evidence offered by the defendant of a witness’s prior inconsistent statement that went to a central issue in the case. Because we find no merit in the defendant’s claims of error and conclude there is no basis to exercise our power under G. L. c. 278, § 33E, we affirm her conviction.
Facts and procedural background. We summarize the evidence in the light most favorable to the Commonwealth, reserving certain details for our discussion. Commonwealth v. Gilbert, 423 Mass. 863, 864 (1996), citing Commonwealth v. Cordle, 404 Mass. 733, 734 (1989), S.C., 412 Mass. 172 (1992). The defendant went to the home of the victim, Sarah Ann “Sally” Marsceill, on Glancy Lane in Dedham on the evening of April 23, 1993. After drinking some alcohol, the women went to a bar. They both returned to the victim’s house in the early morning hours of April 24, but the victim then left the house alone in her vehicle. The defendant became concerned about the victim’s departure and began knocking on neighbors’ doors in an unsuccessful effort to secure help in locating *742the victim.1 The victim returned home shortly after 3 a.m.
Around that time, the defendant telephoned her own home and asked her friend, David Blatz, to pick her up because “they” were fighting.2 He refused and suggested that she contact him later in the morning if she still wanted a ride.
At approximately 3:14 a.m., Saleem Ghazali, a friend of the victim, arrived at her house.3 Both the defendant and the victim came out of the house. The victim asked Ghazali for some of the pain medication he had been taking for his injured legs. He gave her the medication. Ghazali observed that the victim seemed “uncomfortable” and “upset.” The victim assured him everything was all right and urged him to go, which he did at approximately 3:21 a.m.
At approximately 5:45 a.m., the victim telephoned William T. Armour and they spoke for about fifteen minutes. The victim telephoned him two additional times, the last call ending at approximately 6:15 a.m. Nothing in her words or tone suggested fear.
A neighbor, Amy Cosgrove, telephoned the victim’s house at approximately 8:30 a.m. The defendant answered the telephone and, in a calm voice, informed Cosgrove that the victim was sleeping.
Sometime between 7 and 8:30 a.m., the defendant called Blatz at her home and asked him to pick her up from the victim’s house. Blatz agreed to do so and arrived at the victim’s house at approximately 9:30 a.m. He did not enter the house. The defendant went to Blatz’s car, placed something, on the floor of the back seat, returned to the house, got something else, *743and then they drove away. Blatz, and another one of the victim’s neighbors, noticed that the defendant had a dark, wet stain on the back of her pants. When Blatz questioned the defendant about the stain, she offered him three different explanations on three occasions.4 On the ride home, the defendant informed Blatz that she had had a bad night because “they were up all night, and they were fighting.” When they arrived at the defendant’s home, she dropped a roll of money that “looked like all twenty’s” even though the night before the defendant had told Blatz that she was “broke.”
Later that afternoon, at approximately 2 p.m., the victim’s brother discovered the victim’s body lying in a pool of blood on the floor of her bedroom. She was dressed in a blue nightshirt, which was pulled up to expose her genital area and abdomen. She had been stabbed eleven times and had defensive wounds on her hands and arms, as well as marks on her breast that could have been caused after her death by the tip of a knife.5 Blood consistent with the defendant’s blood was found on the victim’s body, under one of the victim’s fingernails, and on the victim’s bedspread. Blood was also found on several items in the bathroom. Both the victim’s blood and the defendant’s blood were found on a bathrobe that was rolled up on the living room floor near the front door. In addition, semen and sperm cell heads were found in the crotch of the victim’s pantyhose and on a hairbrush in the victim’s bedroom.
Deoxyribonucleic acid (DNA) testing of the sperm yielded a profile matching Michael May.6 In addition, May’s palmprint and fingerprints were found inside the victim’s bedroom and automobile. May testified that he had met the victim at Ghazali’s house a few days before her death. He did not have a car, *744and the victim offered him a ride home. She drove May to her house and the two had sex. May denied killing the victim. The defendant never mentioned that May was at the victim’s house on the night of the murder.
The police questioned the defendant at her home on April 24 and later at the police station. At that time, she stated that a drug dealer called “Raphael”7 had arrived at the victim’s house sometime between 5:30 and 6 a.m. She said that the victim and Raphael had argued. She further stated that when she left with Blatz, Raphael was still in the house with the victim. She described Raphael as a light-skinned Hispanic male with a distinctive haircut. Subsequently, the defendant gave additional statements to the police and testified before the grand jury and at her first trial regarding the events leading up to and immediately after the victim’s death.8 These statements varied significantly. After her arrest, the defendant told police that Raphael had stabbed both her and the victim.9 At trial, the defendant’s sole defense was that a third-party culprit, namely Ronald James (also known as Raphael) or Michael May, had committed the murder.
Discussion. 1. Third-party culprit jury instruction. At trial, the Commonwealth requested a jury instruction stating that the Commonwealth did not have to prove that no one else had committed the crime.10 At trial, the defendant objected to the instruction, arguing that it was prejudicial because the premise of her *745entire defense was that a third person, either May or James, had killed the victim. The defendant now argues that the judge erred in instructing the jury that the Commonwealth did not have the burden of proving that no one else had committed the murder, because it improperly shifted to the defendant the burden of proving that another person committed the murder.
When a timely objection to a jury instruction is made, this court will review the instruction to determine whether there was error and, if so, whether it was reversible error. Commonwealth v. Simpson, 434 Mass. 570, 587 (2001). “[T]he adequacy of instructions must be determined in light of their over-all impact on the jury.” Commonwealth v. Sellon, 380 Mass. 220, 231-232 (1980), and cases cited. As we have previously stated, “ ‘whether a defendant has been accorded his constitutional rights depends upon the way in which a reasonable juror could have interpreted the instruction . . . ,’ and . . . error is avoided if the charge, read as a whole, makes clear the Commonwealth’s burden.” Commonwealth v. Munoz, 384 Mass. 503, 508 (1981), quoting Commonwealth v. Medina, 380 Mass. 565, 578 (1980). We review constitutional errors that were preserved to determine whether they were harmless beyond a reasonable doubt. Commonwealth v. Vinnie, 428 Mass. 161, 163, cert. denied, 525 U.S. 1007 (1998).
The judge’s instruction to the jury that the “Commonwealth does not have the burden of proving that no one else may have committed the murder” is technically correct. The Commonwealth carries the burden to prove each and every element of the crime beyond a reasonable doubt. That burden does not include proof beyond a reasonable doubt that every theory of the case argued by the defendant could not be hue. With respect to the critical issue of identification, the Commonwealth has the *746burden to prove beyond a reasonable doubt that the defendant was the person who committed the murder. See Commonwealth v. Denis, 442 Mass. 617, 624 (2004), citing Commonwealth v. Murray, 396 Mass. 702, 709 (1986). The scope of that burden does not extend to affirmatively proving that another individual, alleged by the defendant to be the true perpetrator, did not commit the crime. See Commonwealth v. Medeiros, 354 Mass. 193, 197 (1968), cert. denied sub nom. Bernier v. Massachusetts, 393 U.S. 1058 (1969) (“It is not necessary to prove that no one other than the accused could have done the act”); Commonwealth v. Fancy, 349 Mass. 196, 200 (1965), quoting Commonwealth v. Leach, 156 Mass. 99, 101-102 (1892) (“In order to convict on circumstantial evidence, it is not necessary to show that it was not in the power of any other person than the defendant to commit the crime”).
Contrary to the defendant’s argument, this is not a case where the murder could only have been committed by either the defendant or a specific alternate suspect, requiring that in order to find beyond a reasonable doubt that the defendant committed the crime the jury had to conclude that the alternate suspect did not commit it. See Commonwealth v. Salemme, 395 Mass. 594, 601-602 (1985) (where only two persons could have murdered victim, and Commonwealth abandoned theory of joint venture, jury could not find defendant guilty unless they found beyond reasonable doubt that defendant and not other person fired shots); Berry v. Commonwealth, 393 Mass. 793, 794-796 (1985) (same). Moreover, this is not a case of “a classic duel of credibility.” Commonwealth v. Ferreira, 373 Mass. 116, 127 (1977). There was no forensic evidence placing James at the victim’s house, nor was there testimonial evidence placing him at the scene other than the defendant’s prior testimony and statements, which the jury were free to discredit. Additionally, while there was trace physical evidence of May’s presence in the victim’s house, it did not prove that he was there at the time of the murder. There was, however, substantial forensic evidence of the defendant’s presence at the scene of the crime. See Commonwealth v. Kalhauser, 52 Mass. App. Ct. 339, 346 (2001) (not “classic duel” where “compelling forensic and strong circumstantial evidence” point to guilt).
*747The instruction is similar to the charge in Commonwealth v. Beldotti, 409 Mass. 553, 562 (1991) (Commonwealth does not have burden of “proving that someone else did not commit the crime”). There, this court noted that, standing alone, this statement could perhaps “be taken as tending to downgrade the Commonwealth’s burden of proof.” Id. However, in the Beldotti case, as in this case, it “certainly did not because the Webster charge[, Commonwealth v. Webster, 5 Cush. 295, 350 (1850),] was given [instructing the jury on the Commonwealth’s burden of proof beyond a reasonable doubt] and, viewing the charge as a whole, we see no such possibility.” Id.
In this case, at the very least, the jury knew from closing arguments that the defendant was presenting a third-party culprit defense, claiming that either May or James killed the victim. The judge instructed the jury several times that, in order to convict the defendant, they had to be convinced beyond a reasonable doubt that the defendant was the person who killed the victim. If any juror had harbored a reasonable doubt that someone other than the defendant killed the victim, the jury would not have convicted the defendant. Although the instruction was unnecessary, it was not error in this case.
2. Limitation of cross-examination. Before trial, the judge allowed the Commonwealth’s motion to compel James to testify at the defendant’s trial. James attempted to avoid testifying by asserting his privilege under the Fifth Amendment to the United States Constitution, and the defendant endorsed James’s efforts to avoid testifying. However, the judge granted the Commonwealth’s motion, finding that James made a full, free and voluntary waiver of his Fifth Amendment privilege at the defendant’s first trial.
At trial, the Commonwealth called James as a witness, and over the defendant’s objection, the judge limited the scope of cross-examination to James’s prior testimony and allowed James to assert his Fifth Amendment privilege on a question-by-question basis. Again, before the cross-examination of James began, the judge directed that any claims of a Fifth Amendment privilege would be determined “question by question” at side bar. During the cross-examination, two specific claims of Fifth *748Amendment privilege were allowed over the defendant’s objection.11
The defendant argues that by restricting the cross-examination of James to the content of James’s testimony in the first trial and allowing James to assert his Fifth Amendment privilege, the judge infringed on her constitutional rights to confront the witness. The defendant further argues that this constitutes reversible error. We disagree.
“Both the Sixth Amendment [to the United States Constitution] and art. 12 [of the Massachusetts Declaration of Rights] guarantee a criminal defendant’s right to confront the witnesses against him through cross-examination.” Commonwealth v. Miles, 420 Mass. 67, 71 (1995), citing Kentucky v. Stincer, 482 U.S. 730, 736-737 (1987). In most cases, that right to confrontation guarantees that a criminal defendant may cross-examine a Commonwealth witness as a matter of right.12 Commonwealth v. Miles, supra, citing Douglas v. Alabama, 380 U.S. 415, 418 (1965). However, “the right to confront and to cross-examine [a witness] is not absolute and may, in appropriate cases, bow to accommodate other legitimate interests in the criminal trial process.” Commonwealth v. Francis, 375 Mass. 211, 214, cert. denied, 439 U.S. 872 (1978), quoting Chambers v. Mississippi, 410 U.S. 284, 295 (1973). When properly invoked, the Fifth Amendment privilege against self-incrimination clearly is one of those interests. Commonwealth v. Francis, supra, citing Davis v. Alaska, 415 U.S. 308, 320 (1974). We apply broad standards in determining whether a claim of privilege is justified. The standards are highly protective of the constitutionally guaranteed right against self-incrimination. It is clear that “[a] witness may *749refuse to testify unless it is ‘ “perfectly clear, from a careful consideration of all the circumstances in the case, that the witness is mistaken, and that the answer[s] cannot possibly have such tendency” to incriminate.’ ” Commonwealth v. Dagenais, 437 Mass. 832, 839 (2002), quoting Commonwealth v. Funches, 379 Mass. 283, 289 (1979) (emphasis in original). “However, a witness’s claim of privilege must be predicated on a ‘real risk’ of incrimination, not just ‘a mere imaginary, remote or speculative possibility of prosecution.’ ” Commonwealth v. Dagenais, supra, quoting Commonwealth v. Martin, 423 Mass. 496, 502 (1996).
With regard to James’s current employment status, that his proffered testimony would tend to incriminate him was far from “imaginary, remote or speculative.” As defense counsel conceded, the purpose of the question was to establish that the witness was currently a drug dealer. While James waived his Fifth Amendment privilege as to his activities as a drug dealer in 1993, this waiver does not extend to his current activities. As testimony regarding any current drug dealings would certainly have a tendency to incriminate James in current criminal conduct, the judge did not err in allowing him to exercise his Fifth Amendment privilege. Moreover, the Commonwealth conceded in closing argument that James was currently a drug dealer. See Commonwealth v. Noeun Sok, 439 Mass. 428, 435-436 (2003) (not reversible error where source of bias “unambiguously demonstrated” through means other than cross-examination of witness).
We agree, however, with the defendant that the judge erred in allowing James to assert his Fifth Amendment privilege when questioned about his relationship to Sarah Zene because it related to his self-incriminating testimony from the first trial. The judge allowed the defendant to ask the witness if he knew Sarah Zene, but then, over the defendant’s objection, permitted the witness to assert his Fifth Amendment privilege when asked who she was because she was not mentioned in any of the testimony at the first trial. However, the proffer was that Zene was a former drug runner for the witness in 1993. The privilege against self-incrimination is waived if the subsequent questioning concerns a fact related to but not necessarily mentioned in *750the prior incriminating statement. See Commonwealth v. King, 436 Mass. 252, 258-259 (2002); Commonwealth v. Francis, supra at 216. As the question would have elicited facts related to James’s prior self-incriminating testimony, the defendant was entitled to question the witness about his relationship with Zene. However, any error was harmless beyond a reasonable doubt as the information was subsequently elicited from Zene herself; she testified that she was a former drug runner for James and provided evidence linking James and May.
3. Exclusion of extrinsic evidence of a witness’s prior inconsistent statement. At trial, James testified that he did not know the victim and had never been to her house. The defendant attempted to impeach James with a statement he allegedly made nine years earlier to defense witness Joanne Harrington. After establishing that the witness would obtain drugs from James, defense counsel attempted to establish that James told the witness he was at “Sally’s” house in the area of Bussey Street.13 The Commonwealth objected to this line of questioning, and the judge sustained the objection. At sidebar, defense counsel offered the testimony as an impeachment of James, who testified that he had never been at the victim’s house. The defendant argues that the judge’s exclusion of this testimony was error because it went to what the defendant considers to be a central issue in the case — whether James knew the victim and had been to her house.
It is well settled that if a witness testifies to a fact that is relevant to the issue on trial, the adverse party, for the purpose of impeaching the testimony, may show that the witness previously made inconsistent or conflicting statements by offering them through other witnesses. Commonwealth v. West, 312 *751Mass. 438, 440 (1942), and cases cited. However, “[e]xtrinsic evidence on a collateral matter may be introduced at trial for the purposes of impeachment only in the discretion of the judge.” Commonwealth v. Chase, 372 Mass. 736, 747 (1977), citing Commonwealth v. Doherty, 353 Mass. 197, 213-214 (1967), cert. denied, 390 U.S. 982 (1968).
At issue in this case was whether a third party, namely James, rather than the defendant, killed the victim. James denied killing the victim. He also denied knowing the victim or ever being at her house. The proffer was merely that James told the witness he was at “Sally’s” house in the area of Bussey Street.14 Thus, the offered impeachment went only to the collateral issue of James’s credibility, and not to a main issue in the case. Accordingly, it was within the judge’s discretion to exclude the evidence, and there was no error. Commonwealth v. Doherty, supra (extrinsic evidence offered to impeach prosecution witness’s claim that she did not know victim before night he was killed was collateral).
4. Review under G. L. c. 278, § 33E. Pursuant to our duty under G. L. c. 278, § 33E, we have reviewed the entire record. We find no reason to exercise our power to disturb the jury’s verdict, either by reducing the verdict or by granting a new trial.
Conclusion. Because we conclude that any error in the defendant’s trial was harmless beyond a reasonable doubt, and we decline to exercise our power under G. L. c. 278, § 33E, we affirm the defendant’s conviction.
So ordered.
Amy Cosgrove, who lived in the duplex across the street from the victim, testified that she saw the victim standing behind the defendant as the defendant was knocking on her door.
The defendant asserts that “they” refers to the victim and an individual other than the defendant. The Commonwealth argues that while that conclusion is possible, it is “hardly inescapable.”
Earlier in the evening, the victim had seen Ghazali at the bar and had given him money to buy cigarettes for her. Ghazali failed to deliver the cigarettes to her at the bar. When he arrived home at approximately 2:30 a.m., there were several messages on his answering machine from the victim, inquiring about the cigarettes. He then purchased some at a convenience store and drove to the victim’s house to give them to her.
The defendant first claimed that her pants were wet from the shower. Later, she claimed that wine was spilled on her pants. Still later, she claimed that she got mud on her pants while she was at a bar.
The murder weapon was never recovered, but a knife appeared to be missing from a block in the kitchen.
Both May and the defendant were possible matches for a minor deoxyribonucleic acid (DNA) profile in blood drops on the victim’s upper right thigh. May was also a possible match for a minor DNA profile in blood drops on the victim’s lower left thigh. The defendant matched the major DNA profile in blood drops on the lower left thigh.
Later identified as Ronald James.
At trial, the Commonwealth read into the record portions of the defendant’s testimony from the first trial, as well as portions of her testimony before the grand jury. The jury also heard testimony as to other statements made by the defendant and listened to the audiotape of the defendant’s interview at the police station.
The Commonwealth presented James as a witness. He testified that he did not know the victim and that he had never been in the victim’s house. Furthermore, he had seen the defendant only once in his life.
Joanne Harrington, a witness for the defense, who had purchased drugs from James, testified that in mid-April of 1993, James pulled a knife out and threatened to kill her because she tried to leave without paying.
Sarah Zene testified that she delivered drugs for James in 1993 and that on one occasion, she delivered drugs for James to May. She further testified that James carried a folding pocket knife.
The judge instructed the jury as follows:
*745“The defendant is presumed to be innocent until and unless you, the jury, decide unanimously that the Commonwealth has proved the defendant guilty of each and every element of the offense charged in the indictment beyond a reasonable doubt. The Commonwealth does not have the burden of proving that no one else may have committed the murder. The Commonwealth does have the burden to prove the defendant’s guilt by proof beyond a reasonable doubt.”
The judge allowed the witness to assert his Fifth Amendment privilege when asked about his current employment status because defense counsel was attempting to establish that the witness was currently a drug dealer. The judge also allowed the witness to assert his Fifth Amendment privilege when asked about his relationship to Sarah Zene, who was a former drug runner for the witness.
While a criminal defendant is entitled to a reasonable cross-examination of the Commonwealth’s witnesses, the scope of the cross-examination rests largely within the discretion of the trial judge, and we will not disturb the judge’s ruling unless the defendant demonstrates that she was prejudiced by the judge’s abuse of discretion. Commonwealth v. Miles, 420 Mass. 67, 71-72, (1995), and cases cited.
The following exchange occurred:
Defense counsel: “|T|n relation to Bussey Street, did you ever have a conversation regarding that area?”
The witness: “Yes, he said he was at somebody’s house.”
The district attorney: “Objection.”
The judge: “Sustained. The conversations would not be admissible. Hearsay.”
The witness only testified that James said he was at “somebody’s” house, not “Sally’s” house. The victim went by the name “Sally.”