This paper proposes three energy efficient scheduling approaches for 802.16e broadband wireless networks. Instead of considering a single Mobile Subscriber Station (MSS) as most of the current researchers do, multiple MSSs are considered in our work. The constant bit rate traffic with QoS delay constraint is considered in this paper. The proposed approaches address both energy efficiency and bandwidth utilization. We reuse the idle fragmentation of the allocated OFDM frames to balance power saving and bandwidth utilization. Simulation results show that our proposed approaches benefit with more sleep time and higher bandwidth utilization. Furthermore, we give a QoS scheduling mechanism to find the maximum sleeping time for single MSS, called Minimum Wakeup Time (MWT) scheduler. Even though we don't know whether exists a feasible scheduling to satisfy all MSSs with MWT, it will serve as an upper bound for the power-saving scheduling in IEEE 802.16e.