Many physicians receive a payment for their performance (P4P). This performance is often linked to a health target that triggers a bonus when met. For some patients the target is easily met, while others require a significant amount of care to reach the target (if ever). This study contributes to the literature by providing evidence of how P4P affects allocation of care across patients with low and high responsiveness to treatment compared to a fixed payment, such as capitation and salary, under different degrees of resource constraint. Our evidence is based on a controlled laboratory experiment involving 143 medical students in Denmark in 2019. We find that patients who have the potential to reach the health target, gain care under P4P, whereas patients with no potential to reach it, may receive less care. Redistribution of care between patients under P4P arises when physicians are resource constrained. As many physicians are currently operating under tight resource constraints, policymakers should be careful to avoid unintended inequalities in patients' access to health care when introducing P4P. Risk-adjusting the performance target may potentially solve this issue.