We observe that the state-of-the-art power-saving mechanisms (PSM) for IEEE 802.16e is neither optimal in terms of delay nor in terms of energy consumption. We propose a new PSM which achieves the optimality in terms of the average buffering delay without increasing energy consumption. In order to do so, we derive a formula which relates the average buffering delay to sleep intervals. Simulation results show that our scheme surpasses the BTE algorithm (used by the current IEEE 802.16e Mobile Stations) by 56.75–76% and the PSID algorithm by 8.52–24.39% in terms of the delay-energy consumption product.