Social health insurance traditionally imposes mandatory membership in a single pool in the aim of improving the welfare of high risks. However, this creates two problems, inefficiency of a monopolistic scheme and insufficient adaptation to individual preferences. Competition combined with a risk adjustment scheme can be used to improve efficiency. In the presence of preference heterogeneity, risk selection may improve adaptation to individual preferences, resulting in Pareto improvement over the pooling contract. This is shown to be possible both under perfect and imperfect risk adjustment.