It is plausible that a witness’s credibility is lowered if he testifies to an outcome that has low probability, but this is not always true. If the outcome has a low prior due only to its specificity (as in a fair lottery), witness credibility is not lowered by attesting to it. Even when witness credibility does drop as a result of the testimony, it can substantially confirm its contents, and agreement between independent witnesses can “give back” credibility that one witness lost. Formal modeling and analysis shed light on when each of these situations obtains.