In general, competition enhances efficiency. On the market for health insurance free market competition, however, has unwanted side-effects. The existence of asymmetrical information can lead to adverse selection and cream skimming. Adequate risk-adjustment removes the incentives for cream skimming and balances the negative consequences of adverse selection. In an attempt to enhance efficiency, the Dutch government in 1992 introduced price competition between social health insurers in combination with risk-adjusted capitation payments. Our estimation results indicate that this has not resulted in altering market shares. Relatively cheap insurers did not enlarge their market share at the expense of their relatively expensive competitors. The introduction of competition among social health insurers has not been the success the Dutch government hoped for. Experiences in Belgium and Germany show that the Dutch difficulties are not exceptional. When equity considerations are high valued features of a health insurance system, it is difficult to introduce competition. To enhance efficiency, we recommend that the current capitation formula should be refined and that the insurers should be given more room for selective contracting of health care providers.