We argue that permissibility-based solutions to the paradox of supererogation encounter a nested dilemma. Such approaches solve the paradox by distinguishing moral and rational permissions. If they do not also include a bridge condition that relates these two permissions, then they violate a very plausible monotonicity condition. If they do include a bridge condition, then permissibility-based solutions either amount to rational satisficing or they collapse back into the classical account of supererogation and fail to resolve the paradox.