In this article, we analyze the rationale for introducing outlier payments into a prospective payment system for hospitals under adverse selection and moral hazard. The payer has only two instruments: a fixed price for patients whose treatment cost is below a threshold and a cost-sharing rule for outlier patients. We show that a fixed-price policy is optimal when the hospital is sufficiently benevolent. When the hospital is weakly benevolent, a mixed policy solving a trade-off between rent extraction, efficiency, and dumping deterrence must be preferred. We show how the optimal combination of fixed price and partially cost-based payment depends on the degree of benevolence of the hospital, the social cost of public funds, and the distribution of patients severity. [Authors]