We analyze the regulation of a single health care provider (e.g. a hospital). According to several payment rules used in different countries, we consider a mixed linear payment in which the hospital is paid a fixed price per DRG (diagnosis related group) for most patients (inlier patients) and is reimbursed by a cost sharing payment for patients with exceptionally costly stays (outlier patients). Given this form of payment, we determine the optimal threshold above which to consider a patient as an outlier patient, as well as the optimal payment per DRG and the optimal cost sharing parameter. For the case where the regulator can use a two part tariff, we also determine the fixed charge the regulator has to impose in order to extract hospital rents. [Authors]