Any buyer that depends on suppliers for the delivery of a service or the production of a make-to-order component should pay close attention to the suppliers’ service or delivery lead times. This paper studies a queueing model in which two strategic servers choose their capacities/processing rates and faster service is costly. The buyer allocates demand to the servers based on their performance; the faster a server works, the more demand the server is allocated. The buyer’s objective is to minimize the average lead time received from the servers. There are two important attributes to consider in the design of an allocation policy: the degree to which the allocation policy effectively utilizes the servers’ capacities and the strength of the incentives the allocation policy provides for the servers to work quickly. Previous research suggests that there exists a trade-off between efficiency and incentives, i.e., in the choice between two allocation policies a buyer may prefer the less efficient one because it provides stronger incentives. We find considerable variation in the performance of allocation policies: Some intuitively reasonable policies generate essentially no competition among servers to work quickly, whereas others generate too much competition, thereby causing some servers to refuse to work with the buyer. Nevertheless, the trade-off between efficiency and incentives need not exist: It is possible to design an allocation policy that is efficient and also induces the servers to work quickly. We conclude that performance-based allocation can be an effective procurement strategy for a buyer as long as the buyer explicitly accounts for the servers’ strategic behavior.