We study the link between illness severity and the use of public health care services by the privately insured under a public health system. Our theoretical model shows that this relationship will depend on the prioritization established by the public health authorities, the cost of waiting and the private sector's risk selection behavior. In our empirical exercise, based on the British Household Panel Survey data, we find the consistent pattern that both the most severe cases and the least severe cases are more likely to be treated under the public system, leading to a U-shaped relationship between severity and public use. As our theoretical model points out, this is not necessarily a consequence of risk selection by private health providers, but it could be just a consequence of prioritization by the public sector.