We develop a positive model of waiting lists for public hospitals when physicians are able to divert patients from the public to the private sector. Public treatment is free but rationed, i.e., only cases meeting some medical criteria are admitted. Private treatment has no waiting time but entails payment of a fee. Physicians and patients take into account that each patient treated in the private practice reduces the waiting list for public treatment. We show that physicians do not necessarily end up treating the mildest cases from the waiting list. Our analysis is valid for a wide class of doctors' utility functions.