A wireless station (114) is within range of more than one access point (120, 124) transmitting on the same channel. The wireless station is associated with one access point and not the other. Consequently the wireless station may receive undesired beacons (304) and desired beacons (302) on the channel. To optimize power save operation the wireless station arbitrates between a scan and shut down scanning procedure (708) and a timed window channel scanning procedure (724), depending on whether the desired beacon is the first received beacon upon waking up from a low power state at a target beacon time.