In precise real-time systems, scheduling algorithms without considerable complexity are more effective to be applied. Virtual release advancing for shorter response times is a technique that is valuable for the Earliest Deadline First (EDF) scheduling, but not adaptive to precise systems due to its high time complexity. A new scheduling algorithm, called enhanced virtual release advancing, that mitigates the time complexity, is presented in this paper. Applied in the Total Bandwidth Server (TBS) context, the new algorithm significantly improves the time complexity while guaranteeing the responsiveness and schedulability. Simulation results show that the runtime overhead is apσproximately 56% lower than that of the original algorithm under the periodic processor utilization of 95%.