This paper examines the public provision of health insurance for high severity illness. Besley (Journal of Public Economics, 1989, 39, 141-156) argues that public coverage of high severity illness may interact with private coverage for low severity illness so as to increase welfare. The possibility of interaction between public and private coverage raises important questions for mixed systems, as in the United States. Nevertheless, even within the more general framework presented in this paper there are no welfare gains of the sort Besley envisions.