Scheduling tasks is one of the most challenging problems in real-time systems. In this paper, we assume that hard deadline periodic tasks are scheduled preemptively according to the Earliest Deadline First algorithm on uniprocessor. This work presents a framework for enhancing predictability in system behavior, when periodic task execution can be postponed. Our analysis first determines a lower bound to the slack defined as the time which may be stolen from hard deadline periodic tasks, without jeopardizing their timing constraints. Second, we show how to implement an efficient method for estimating the slack at run-time. This can be adopted to overcome practical situations where the slack has to be computed dynamically with acceptable time overheads.