A principal has to allocate a good among a number of agents, each of whom values the good. Each agent has private information about the principal's payoff if he receives the good. There are no monetary transfers. The principal can inspect agents' reports at a cost and penalize them, but the punishments are limited. I characterize an optimal mechanism featuring two thresholds. Agents whose values are below the lower threshold and above the upper threshold are pooled, respectively. If the number of agents is small, then the pooling area at the top of value distribution disappears. If the number of agents is large, then the two pooling areas meet and the optimal mechanism can be implemented via a shortlisting procedure.