*173Judgment, Supreme Court, New York County (Richard D. Carruthers, J.), rendered April 5, 2000, convicting defendant, after a jury trial, of murder in the second degree, and sentencing him to a term of 25 years to life, unanimously affirmed.
The verdict was not against the weight of the evidence. Issues of credibility, including the weight to be given the backgrounds of the People’s witnesses and inconsistencies in their testimony, were properly considered by the jury and there is no basis for disturbing its determinations (see People v Gaimari, 176 NY 84, 94 [1903]). Two eyewitnesses, along with a third witness who overheard defendant’s admission of guilt, independently implicated the same person.
The court properly exercised its discretion in permitting cross-examination of defendant’s alibi witness concerning his knowledge of defendant’s whereabouts, including defendant’s incarcerations, at time periods made relevant by the witness’s testimony (see People v Vasquez, 88 NY2d 561, 577-578 [1996]). Under the circumstances of the alibi testimony, the challenged evidence was highly probative, particularly where the fact of defendant’s incarceration on a particular date significantly contradicted the witness’s testimony and cast doubt on his credibility. The court minimized any prejudicial effect by delivering an appropriate limiting instruction.
During the testimony of the witness who overheard defendant’s admission, the court properly exercised its discretion in permitting a brief allusion to defendant’s involvement with a drug dealing operation. The witness quoted defendant as telling the other party to the conversation that the instant murder was one of the things he had done for that person. Therefore, in order for the jury to understand what defendant meant, it was necessary to establish that he was talking to his associate in the drug trade about things he had done for him in furtherance of *174that activity. Concomitantly, the challenged evidence was relevant to motive, and explained why defendant was making this admission (see People v Ortiz, 238 AD2d 213 [1997], lv denied 90 NY2d 862 [1997]). Defendant’s remaining arguments on this issue are unpreserved and we decline to review them in the interest of justice.
We perceive no basis for reducing the sentence. The court properly exercised its discretion in directing that defendant’s sentence be served consecutively to a sentence imposed for an unrelated murder conviction. Concur—Mazzarelli, J.P., Williams, Friedman, Gonzalez and Catterson, JJ.