Physicians are supposed to serve patients' interests, but some are more inclined to do so than others. This paper studies how the system of health care provision affects the allocation of patients to physicians when physicians differ in altruism. We show that allowing for private provision of health care, parallel to (free) treatment in a National Health Service, benefits all patients. It enables rich patients to obtain higher quality treatment in the private sector. Because the altruistic physicians infer that in their absence, NHS patients receive lower treatment quality than private sector patients, they optimally decide to work in the NHS. Hence, after allowing for private provision, the remaining (relatively poor) NHS patients are more likely to receive the superior treatment provided by altruistic physicians. We also show, however, that allowing physicians to moonlight, i.e. to operate in both the NHS and the private sector simultaneously, nullifies part of these beneficial effects for the poorest patients.