We develop a model to analyze parallel public and private health-care financing under two alternative public sector rationing rules: needs-based rationing and random rationing. Individuals vary in income and severity of illness. There is a limited supply of health-care resources used to treat individuals, causing some individuals to go untreated. Insurers (both public and private) must bid to obtain the necessary health-care resources to treat their beneficiaries. Given individuals' willingnesses-to-pay for private insurance are increasing in income, the introduction of private insurance diverts treatment from relatively poor to relatively rich individuals. Further, the impact of introducing parallel private insurance depends on the rationing mechanism in the public sector. We show that the private health insurance market is smaller when the public sector rations according to need than when allocation is random. Copyright © 2010 John Wiley qqqamp; Sons, Ltd.