Many countries have introduced competitive mechanisms in health insurance along with regulations to avoid risk selection and guarantee solidarity between the sick and the healthy. The “regulated competition” model is applied to basic health insurance in Switzerland, the Netherlands, Germany, and Israel. It has inspired healthcare reform in the United States. To analyze how the system operates, we use Switzerland as a case study, looking at the potential interference between the supplementary-insurance and basic-insurance markets. France's current health-insurance system differs from the Swiss model, but the regulation of the supplementary-insurance market may eventually become an issue. Twelve years after the introduction of “regulated competition”, the results observed in Switzerland are disappointing. For the same policy, premium gaps between insurance companies are very wide, but the proportion of insureds who switch companies remains small. The figures imply that the insureds are not using competition to their advantage. Our analysis shows that the low mobility of the insureds is due to the coexistence of two health-insurance markets operating under different rules: the basic-insurance market, where risk selection is banned, and the supplementary-insurance market, where it is allowed. The estimates show that the propensity to change insurers is much weaker among supplementary-insurance policy-holders who do not regard their health as excellent. Because of the practical advantage of using the same provider for basic and supplementary insurance, the two markets are effectively linked. The right to select applicants for supplementary insurance harms competition in basic insurance.