The downlink transmit powers of base stations involved in a diversity handover communication with a mobile station are controlled to minimize base station power "drift." A downlink reference power level is determined based on detected, current transmit power levels of the diversity handover base stations. One or more power offsets is determined for one or more of the base stations based on signal quality measurements made by the mobile station. The reference power level and power offset(s) are used to selectively regulate an adjustment to the transmit power levels of the diversity handover base stations. The general reference power is transmitted at a first, relatively high frequency to the diversity handover base stations by embedding it in a user data frame. In that way, the signal processing load is kept to a minimum despite the higher transmission rate. Individual power offsets are sent to associated individual base stations in a control signalling channel identifying the one base station at a second frequency lower than the first frequency. The control channel signaling permits individual base station power offsets, but the lower frequency at which the offsets are transmitted reduces the associated signaling load.