We look at the consequences of allowing public health insurance (PuHI) to be voluntary when its coverage can be supplemented in the market. PuHI redistributes with respect to risk and income, and the market is affected by adverse selection. We argue that making PuHI voluntary does not lead to its collapse since there are always individuals participating in it. Additionally, in some cases, a voluntary PuHI scheme creates an increase in market efficiency because participation in it becomes a sign of an individual's type. The welfare consequences depend on the status quo. If in the status quo there is no political support for a compulsory PuHI, making it voluntary constitutes a Pareto improvement, and in some cases all individuals are strictly better off. If, instead, the status quo implements compulsory PuHI, making it voluntary then results in less redistribution.