Operation of a mobile voice client utilizing a WLAN for access is enhanced by controlling the rate at which transmission power is changed by the access point with which the mobile voice client is associated. The access point calculates a target transmit power level based at least in-part on the distance to the nearest fixed position wireless device and the distance to the mobile voice client. The access point then determines whether the target transmit power level differs from a current transmit power level. If the target transmit power level is greater than the current transmit power level, the current transmit power level is increased at a first controlled, non-instantaneous rate such as 1 dB per second. If the target transmit power level is less than the current transmit power level, the current transmit power level is decreased at a second controlled, non-instantaneous rate such as 1 dB per second.