This paper focuses on the switching behaviour of sickness fund enrollees in the Swiss health insurance system. Even though the new Federal Law on Social Health Insurance (LAMal) was implemented in 1996 to promote competition among health insurers, there still remains large premium variations within cantons. This indicates that competition has not been able so far to lead to a single price, and reveals some inertia among consumers who seem reluctant to switch to less expensive funds. We investigate one possible barrier to switching behaviour, namely the influence of the supplementary insurance on the choice for basic insurance plan in Switzerland, which has not been studied so far. Our aim is to analyse the two decisions (choice of health plan, subscription to supplementary insurance contracts). We use the data of the OFAS survey conducted in 2000 on health plan choice and import some additional data on the sickness funds (number of enrollees, premiums). The decision to switch is estimated by both logit and a fixed-effects logit models; two main explanatory variables are studied: premiums (for basic insurance contracts) and supplementary insurance. The results suggest that holding a supplementary insurance contract substantially decreases the propensity to switch. The switching decision is positively influenced by the expected gain of switching, measured by the premium differential. The expected gain of switching is higher for switchers with no supplementary insurance (CHF 19.44) than for switchers with supplementary insurance (CHF 13.06). The income level has a direct positive influence on the propensity to buy a supplementary insurance. This finding suggests that the purchase of supplementary insurance is influenced, not only by risk aversion, but also by the willingness to pay for the goods covered by the supplementary insurance, which would be higher for rich people. Bad health has a negative influence on the subscription to a supplementary contract, but is no longer significant when the income is introduced into the specification. All the information about health is captured by the income level, a low income being strongly correlated with a bad health status. Income and a supplementary insurance contract are observable by the insurance company, and can be used as tools for selection.