A base station (LBS) (110) in a wireless network (100) establishes power levels for transmitting messages acknowledging receipt of packet data from a mobile communications device (MAD) (114). In one implementation, the LBS infers whether the MAD received a given acknowledgement message by considering whether (306, 316) the next communication from the MAD comprises new packet data, and whether (310, 320) that data comprises re-transmitted data. The LBS adjusts (312, 314, 322, 324) transmit power level for future acknowledgement messages according to whether the MAD received past acknowledgement messages. In a different implementation, actual/estimated transmit power from a serving base station to a given MAD is averaged (404), and increased (406) by a prescribed amount to yield a target level. Whenever the non-serving base station transmits messages acknowledging receipt of packet data from the MAD, the non-serving base station transmits (408) at the target level.