Abstract: This article presents the first systematic theoretical and empirical study of high-low agreements in civil litigation. A high-low agreement is a private contract that, if signed by litigants before trial, constrains any plaintiff's recovery to a specified range. In our theoretical model, trial is both costly and risky. When litigants have divergent subjective beliefs and are mutually optimistic about their trial prospects, cases may fail to settle. In these cases, high-low agreements can be in litigants' mutual interest because they limit the risk of outlier awards while still allowing mutually beneficial speculation. Using claims data from a national insurance company, we describe the features of these agreements and empirically investigate the factors that may influence whether litigants discuss or enter into them. Our empirical findings are consistent with the predictions of the theoretical model. Other applications include the use of collars in mergers and acquisitions.