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The IEEE 802.16-2004 standard (formerly 802.16d) has been approved to provide last-mile connectivity to fixed locations by radio links. Although the IEEE committee is working on a future 802.16e standard to support terminal mobility, we believe that adding mobility support to the present standard will offer a significant business opportunity for service providers by enabling them to serve a large pool of potential users whose laptops and PDAs are 802.16-2004 enabled. In our prior work, we have shown how to reuse commands from the 802.16-2004 standard to support handoff between access points without any change to the standard. However, given that the mobile terminals will be severely constrained by battery life, it is essential that new protocols and control mechanisms be devised to save terminal energy, based on the existing 802.16-2004 standard. To achieve this objective, in the present paper we propose protocols and use existing 802.16-2004 commands to put mobile terminals to "sleep" (to save energy) when they are idle, and "wake them up" when there is traffic destined for them. We also demonstrate how this "sleep/wakeup" cycle can is compatible with the handoff process.