We consider the problem of task assignment in a distributed server system, where short jobs are separated from long jobs, but short jobs may be run in the long job partition if it is idle (cycle stealing). Jobs are assumed to be non-preemptible, where short and long jobs have generally-distributed service requirements, and arrivals are Poisson. We consider two variants of this problem: a central queue model and an immediate dispatch model. This paper presents the first analysis of cycle stealing under the central-queue model. (Cycle stealing under the immediate dispatch model is analyzed in [9]). The analysis uses a technique which we refer to as busy period transitions. Results show that cycle stealing can reduce mean response time for short jobs by orders of magnitude, while long jobs are only slightly penalized. Furthermore using a central queue yields significant performance improvement over immediate dispatch, both from the perspective of the benefit to short jobs and the penalty to long jobs.