When a malleable job is submitted to a space-sharing parallel computer, it must choose often whether to begin execution on a small, available cluster, or wait in queue for more processors to become available. To make this decision, it must predict how long it will have to wait for the larger cluster. We propose statistical techniques for predicting these queue times, and develop an allocation strategy that uses these predictions. We present a workload model based on the environment we have observed at the San Diego Supercomputer Center, and use this model to drive simulations of various allocation strategies. We conclude that prediction-based allocation not only improves the average turnaround time for the jobs; it also improves the utilization of the system as a whole.