The maximum wait time for callers in a call center (FIG. 10) is lowered by selecting, for an agent (25) who has just become available to handle a call, a highest-priority waiting call that would most likely wait the longest if it were not selected at this time. Anticipated wait times are computed for the calls at the heads of the non-empty highest-priority call queues that correspond to the agent's skills or splits (202-210). The anticipated wait time of a call is computed as the call's present (elapsed) wait time plus the average rate of advance of calls in the call's queue (210). The call with the longest anticipated wait time is then selected first and is assigned to the available agent for handling (212-216). The process is repeated each time that any agent becomes available.