Power management is one of the most important issues in IEEE 802.16e wireless networks. In the standard, it defines three types of power saving classes (PSCs) for flows with different QoS characteristics. It allows a mobile device to turn off its wireless radio when all its PSCs are in sleep states. In this paper, we consider the scheduling of power saving classes of type II in an IEEE 802.16e network with a BS and multiple MSSs (mobile subscriber stations). Previous work proposes to enforce all MSSs to have the same sleep cycle, thus leading to higher energy cost for those MSSs with less strict delay bounds. We observe that if the sleep cycles of MSSs can be assigned according to their delay bounds, MSSs can significantly reduce their duty cycles. We propose an efficient tank-filling algorithm, which is standard-compliant and can allocate resources to MSSs according to their QoS characteristics with the least number of active frames. Simulation results verify that our algorithm incurs less power consumption and leads to higher bandwidth utilization than the previous schemes.