Single-pool systems as defined in this article may be accompanied by two forms of voluntary health insurance (VHI): gap coverage for benefits not included in the statutory arrangement and parallel coverage through which individuals pay extra for ostensibly superior versions of the statutory benefits. In all cases the markets for this coverage are much smaller than the market for private insurance in the United States. In each case, the market for VHI depends on perceived inadequacy in the statutory system. With gap coverage, the extent of the statutory benefit package is a more basic issue than the gap coverage itself. Parallel coverage raises more significant independent issues. It is particularly related to the dynamics and politics of waiting lists in the statutory system. Waiting lists appear to be a greater concern in single-pool systems than in social insurance systems due to the effects of having spending on a government's budget and some perverse incentives for physicians. Single-pool approaches are less politically plausible in the United States than adaptation of social insurance models because they leave less room for private insurance and thus will be less attractive to advocates of the private sector; yet leaving any room at all requires that the statutory system be less attractive than advocates of national health insurance could probably justify politically.