We consider a general framework where each agent has an outside option of privately known value. First, we show that if a strategy-proof mechanism is required to (weakly) Pareto-improve an individually rational and participation-maximal benchmark mechanism, there is at most one choice. A consequence is that many known mechanisms are on the Pareto frontier of strategy-proof mechanisms. Second, we characterize the Pareto-improvement relation over strategy-proof and individually rational mechanisms: one of these mechanisms Pareto-improves another if and only if it weakly expands the set of participants at each profile of preferences. Third, for settings with transfers, we provide a characterization of the pivotal mechanism and a revenue equivalence theorem.