The major drawback of the slack-stealing based schedulings for aperiodic requests is a high computational complexity to calculate the slack which in consequence makes them not be practical. In this paper, we present a soft-aperiodic task scheduling algorithm, called Alternative Priority Scheduling (APS), which has a simple slack calculation method in dynamic priority systems. The proposed algorithm has extended the EDF-CTI (Earliest Deadline First-Critical Task Indicating) Algorithm developed by the authors. The APS algorithm references the off-line built CTI table and chooses either an EDF or a CEF (Critical Execution time First) algorithm alternatively at run-time. This paper also demonstrates the optimality of the APS algorithm. Our simulation study shows that the APS algorithm, in most cases, is slightly better than the EDF-CTI algorithm and the other soft-aperiodic schedulings in terms of the short response time of aperiodic requests, and considerably improves the previous algorithms in a high workload.