Analysis of data on civil litigation claims reveals two puzzles. First, despite the large costs of nonbargaining, only a fraction of claims receive more than one offer before settlement or adjudication. Second, the size of this fraction seems to depend on the type of parties involved in the claim. This paper develops a theory to explain these observations. The basic model describes bargaining between a risk-neutral defendant who plays the litigation game repeatedly and a risk-averse plaintiff who is involved in litigation only once. (This set-up, it is argued, is a good description of the parties in many civil litigation cases.) The paper shows that (under certain circumstances) the defendant will commit to withholding offers partially: In a two-period game, the optimal strategy is to make a second offer to the plaintiff with a probability between zero and one. The dependence of this probability on the characteristics of the plaintiff is described. A unique data set, collected from the files of the Taxing Masters in the United Kingdom, allows specific testing of the model’s predictions. Regression analysis and comparison with U.S. studies provide support for the theory.