The general issues of equity and efficiency are placed at the center of the analysis of resource allocation problems in health care. We examine them using axiomatic bargaining theory. We study different solutions that have been proposed and relate them to previous literature on health care allocation. In particular, we focus on the solutions based on axiomatic bargaining with claims and suggest that they may be particularly appealing as distributive criteria in health policy. Finally, we present the results of a survey that tries to elicit moral intuitions of people about resource allocation problems and their different solutions.