The coexistence of IEEE 802.16 (WiMAX) and IEEE 802.11 (WiFi) in shared radio spectrum is an acute problem. In license-exempt frequency bands, the frame-based medium access of 802.16 requires rigorous protection against interference from wireless local area networks in order to operate properly when sharing spectrum. We focus here on the unlicensed U-NII frequency band at 5 GHz and consider therefore the distributed medium access of 802.11(a) as competitor for spectrum utilization. We expect 802.16 systems to be available in laptops soon and then to provide wireless VoIP services that 802.11 cannot support satisfactorily well. Therefore, this paper describes approaches for enabling a reliable operation of 802.16 when sharing unlicensed spectrum with 802.11. We propose software upgrades to the medium access control of the 802.16 BS. Thereby, no 802.11 frame transmissions are required by an 802.16 system. Coexistence between 802.16 and 802.11 is enabled without any data exchange between both standards. Our solution of the described coexistence problem implies the possibility to guarantee quality-of-service within the 802.16 system although operating in unlicensed frequencies