Most systems of health care financing in EU member states currently include elements of income redistribution. The paper analyzes the effects of shifting income redistribution entirely to the tax system, while confining public health systems to their insurance role. We argue that this reform could create two types of efficiency gains. On the expenditure side, it would allow to offer insured persons an improved menu of choices - for example through co-payment schemes - that would help to reduce the gap between the social costs of health care and the perceived private costs. On the revenue side, social security contributions represent a specific type of wage taxation that may imply a shadow price of public funds above that of the general tax system.