We consider a general model of allocating discrete resources when agents have unit demand. We show that if a pair of individually rational and non- wasteful allocations are Pareto-comparable, then they leave the same agents unmatched and allocate each object to the same number of agents.

For strategy-proof rules, we show the following results: 1. If distinct individually rational rules leave the same agents unassigned at each profile of preferences, then at most one of them is strategy-proof. 2. If one strategy- proof rule Pareto-dominates another, then the former leaves no more agents unassigned than the latter at every profile and strictly fewer at some profile. 3. No pair of distinct strategy-proof, non-wasteful, and individually ratio- nal rules is Pareto-comparable. 4. At most one strategy-proof rule Pareto- dominates any given individually rational and non-wasteful benchmark rule. 5. No strategy-proof and non-wasteful rule is Pareto-dominated by another strategy-proof rule.

We specialize the model to handle exogenous constraints captured through a choice correspondence for each object. When these choice correspondences are size monotonic and idempotent, we show that each stable rule is Pareto- dominated by at most one strategy-proof rule. We also show that the question