Putnam revived interest in the “Schelling conjecture” that in international bargaining, a domestic ratification constraint provides a negotiator with a bargaining advantage. However, existing formal analyses of the Schelling conjecture generally allow only one side in the bargaining to be constrained. In this article, a model is analyzed in which both negotiators are constrained. A generalized version of the Schelling conjecture holds that if one negotiator’s constraint is high and the other’s is only low or medium, the former gets a better deal than if neither side were constrained, and the latter is worse off. With incomplete information, however, the complete opposite of what the Schelling conjecture predicts can occur, and there is an equilibrium in which delay in reaching an agreement results in both sides being worse off than if neither side were constrained. Incomplete information can but does not always completely eliminate the advantage of having a high constraint.