If in a game with multiple proper coordination equilibria there is a single one that is best for all participants, it is rational for each participant to choose the strategy that has the best equilibrium as one of its possible outcomes. This seems so obvious that any plausible theory of rationality should be expected to be applicable to such situations. However, this is not true for the “orthodox” theory of rational choice, as Robert Sugden has convincingly shown. In this paper, I shall argue that this failure is due to an implicit individualistic understanding of intentionality. John R. Searle’s concept of collective intentionality (as put forth in his Construction of Social Reality) and his more recent theory of Rationality in Action provides important conceptual tools pertaining to a more comprehensive theory of rationality. The account I shall develop differs from Searle’s own, as for reasons to be found in his overall project, Searle’s departure from the orthodox view of rationality gets stuck half-way.