Pulsed detonation engines have recently received increasing attention. Various advantages claimed for the pulsed detonation engines depend on performance estimates. A review of previous computational studies of pulsed detonation engines shows a wide variation in the predicted performance of even an idealized system. In this paper, detailed, time-dependent numerical simulations are used to explore some plausible reasons for the observed differences. The system simulated consists of a tube closed at one end and open at the other. The relaxation of the pressure at the exit of the tube to the ambient value is found to be a critical factor determining the specific impulse. Higher specific impulse can be attained with a gradual relaxation of the pressure at the exit of the tube. Numerically, different specifications of the outflow boundary conditions result in different relaxation rates and hence different values for the specific impulse. Experimentally, different effective rates of relaxation can be attained with different exhaust nozzle designs. The initial conditions used in simulations to initiate detonations are also found to contribute significantly to the overall performance. The results from these studies are used to reconcile previous performance estimates.