This paper presents a model of a competitive health insurance market with two risk types and two health benefits. In the benchmark case, community rating insurers (CRIs) are only allowed to offer the basic benefit. The additional benefit is sold by risk rating insurers (RRIs). It is shown that low risk types can only be better off at the expense of high risk types if CRIs are allowed to offer the additional benefit and no additional measures are taken. However, high risk types can be made better off if CRIs must offer the additional benefit or if community rating health insurers offering the additional benefit are subsidized while those selling only the basic benefit are taxed.