In this paper we present a new scheduling approach for servicing soft aperiodic requests in a hard real-time environment, where a set of hard periodic tasks is scheduled using the Earliest Deadline First algorithm. The main characteristic of the proposed algorithm is that it achieves full processor utilization and optimal aperiodic responsiveness, still guaranteeing the execution of the periodic tasks. Another interesting feature of the algorithm is that it can easily be tuned to change its performance and complexity according to the application requirements. Schedulability issues, performance results, and implementation complexity of the algorithm are discussed and compared with other classical methods, such as Background, the Total Bandwidth Sewer (TBS), and the optimal EDL server. Extensive simulations show that a substantial improvement can be achieved with a little increase of complexity, ranging from the TBS performance up to the optimal behavior.