We study a problem of allocating a good among several agents in an environment with asymmetric information, no monetary transfers, and ex-post verifiability. We show that optimal allocation has a number of anti-competitive features: participa- tion might be restricted to a select group of agents; allocation is stochastic, occasionally favoring low-value agents. If the number of agents is high, the optimal mechanism is a shortlisting procedure. Otherwise, the optimal mechanism is a restricted bid auc- tion, augmented by a shortlisting procedure for the agents with minimal bids. From a methodological perspective, the paper provides a solution to an interesting mechanism design problem without transfers that features a nontrivial interaction of incentive and feasibility constraints.