We study nonmonetary markets where objects that arrive over time are allocated to unitdemand agents with private types, such as in the allocation of public housing or deceased-donor organs. An agent’s value for an object is supermodular in her type and the object quality, and her payoff is her value minus her waiting cost. The social planner’s objective is a weighted sum of allocative efficiency (i.e., the sum of values) and welfare (i.e., the sum of payoffs). We identify optimal mechanisms in the class of direct-revelation mechanisms. When the social planner can design the information disclosed to the agents about the objects, the optimal mechanism has a simple implementation: a first-come first-served waitlist with deferrals. In this implementation, the object qualities are partitioned into intervals; only the interval containing the object quality is disclosed to agents. When the planner places a higher weight on welfare, optimal disclosure policies become coarser.