This paper deals with selecting a heuristic rule for concurrent scheduling of mixtures of due-date and non-due-date jobs. The measure of performance for the mixture of jobs is chosen to be mean flowtime subject to the constraint that due dates are satisfied. To handle varying levels of due-date tightness, three types of schedules are introduced. Dispatching rules for two of the three types of schedules were selected by simulation. Decision rules for determining the best schedules in appropriate situations are suggested.