We consider a model where each agent has an outside option of privately known value. We show that one strategy-proof and individually rational mechanism Pareto-improves another if and only if it expands the set of participants. Corollaries include: a sufficient condition for a mechanism to be on the Pareto-efficient frontier of strategy-proof mechanisms; uniqueness of strategy-proof Pareto-improvements under true preferences over certain normatively meaningful benchmark allocation rules; and a characterization of the pivotal mechanism.