We consider a distributed server system model and ask which policy should be used for assigning tasks to hosts. In our model each host processes tasks in First-Come-First-Serve order and the task's service demand is known in advance. We consider four task assignment policies commonly proposed for such distributed server systems: Round-Robin, Random, Size-Based, in which all tasks within a give size range are assigned to a particular host, and Dynamic-Least-Work-Remaining, in which a task is assigned to the host with the least outstanding work. Our goal is to understand the innuence of task size variability on the decision of which task assignment policy is best. We nd that no one of the above task assignment policies is best and that the answer depends critically on the variability in the task size distribution. In particular we nd that when the task sizes are not highly variable, the Dynamic policy is preferable. However when task sizes show the degree of variability more characteristic of empirically measured computer workloads, the Size-Based policy is the best choice. We use the resulting observations to argue in favor of a speciic size-based policy, SITA-E, that can out-perform the Dynamic policy by almost 2 orders of magnitude and can outperform other task assignment policies by many orders of magnitude, under a realistic task size distribution.