Conventional wisdom holds that negotiators who are under time pressure should avoid revealing their final deadlines to the other side, especially if they are in a weak position. The present study questions this conventional wisdom. The experiment manipulates time pressure on the negotiators, knowledge of that time pressure, and each side’s power at the bargaining table. Power is manipulated by varying the quality of each side’s alternatives to negotiated agreement (BATNAs). Results show that negotiators benefited from revealing their final deadlines, regardless of the strength of their BATNAs. The discussion explores why this simple lesson is counterintuitive and why negotiators mistakenly believe they ought to keep their deadlines secret.