How should scarce health-related resources be allocated? This paper argues that values that apply to these decisions fail to always fully determine what we should do. Health maximization and allocation-according-to-need are suggested as two values that should be part of a general theory of how to allocate health-related resources. The “small improvement argument” is used to argue that it is implausible that one alternative is always better, worse, or equal to another alternative with respect to these values. Approaches that rely (...) on these values are thus incomplete. To deal with this, it is suggested that we ought to use incomplete theories in a two-step process. Such a process first discards ineligible alternatives, and, second, uses reasons grounded in collective commitments to identify a unique, best alternative in the remaining set. (shrink)