The paper examines the demand for a privately supplied good, private medical insurance, in a market dominated by a large public supplier. It is argued that the high political visibility of the public alternative means that individual demand for private medical insurance is the outcome of two processes. The first process is one of choice set generation. The second process is that of the choice between the insurance and the no-insurance prospects. The factors affecting these processes are discussed and an econometric specification suggested. The estimation results indicate the importance of political belief in determining choice sets and of income and health in determining choice between the two prospects.