Priority setting in healthcare is a highly contentious area of public decision making, in which different values often support incompatible policy options and compromise can be elusive. One promising approach to resolving priority-setting conflicts divides the decision-making process into two steps. In the first, a set of eligible options is identified; in the second, one of those options is chosen by a deliberative process. This paper considers the first step, examining proposals for identifying a set of options eligible for deliberation. (...) It focuses on the approach proposed by Anders Herlitz, which limits deliberation to options that are on a par; neither better or worse than, nor strictly equal to the alternatives. Once these “maximal” options are identified, the choice among them is made though a deliberative process that acknowledges the difficult tradeoffs which must be made. While parity and kindred notions are clearly useful in resolving some priority-setting conflicts, this paper argues that the conflicts that arise in setting priorities make it as difficult to decide which options are on a par as it is to decide among those options. The paper draws on priority-setting debates that occurred during the recent pandemic to illustrate the challenges in identifying eligible options: There may be sharp disagreement about how to understand and individuate relevant values; about whether certain values are relevant in a priority-setting context; about how to establish parity between “consequential” and “deontic” options, and about whether one option remains on a par with others after it is modified in various ways. (shrink)