Is a witness entitled to be cross-examined on the basis of his own motivation for cooperating with the government?

The dual import of the agreement led us, however, to create an exception to the rule. In United States v. Singh, 628 F.2d 758, 761 (2d Cir.), cert. denied, 449 U.S. 1034, 101 S.Ct. 609, 66 L.Ed.2d 496 (1980), we held that the Government may bring out on direct examination "the circumstances surrounding a witness's motivation for cooperating with the Government or other matters damaging to the witness's credibility." The exception serves to avoid an inference by the jury that the Government is attempting to keep from the jury the witness's possible bias. Id.