Health outcomes, such as mortality and readmission rates, are commonly used as indicators of hospital quality and as a basis to design pay-for-performance (P4P) incentive schemes. We propose a model of hospital behaviour under P4P where patients differ in severity and can choose hospital based on quality. We assume that risk-adjustment is not fully accounted for and that unobserved dimensions of severity remain. We show that the introduction of P4P which rewards lower mortality and/or readmission rates can weaken or strengthen hospitals´incentive to provide quality. Since patients with higher severity have a di¤erent probability of exercising patient choice when quality varies, this introduces a selection bias (patient composition ef...