We develop a model of waiting lists for public hospitals when physicians deliver both private and public treatment. Public treatment is free but rationed, i.e., only cases meeting some medical criteria area admitted for treatment. Private treatment has no waiting time but entails payment of a fee. Both physicians and patients take into account that each patient treated in the private practice schedule reduces the waiting list for public treatment. We show that physicians do not necessarily select the mildest cases from the waiting list. We provide su±cient conditions on the rationing policy under which cream skimming is always partial. We show that, to a large extent, one can bypass the analysis of doctors' behavior in the characterization of patient selection.