A communication access protocol improves the accessibility of devices operating on an asynchronous network (100), while supporting reduced power consumption. The network (100) includes a mediation device (130) for facilitating communications among network devices. Generally, each network device periodically transmits beacon signals to advertise its presence, and listens for communication signals targeted at the network device (532, 534). A device initiating communication with another operates in one of at least two operating modes in order to establish communications (536, 537, 538). In one mode, the initiating device communicates with the mediation device in order to derive timing information for the other device (537). In another mode, the initiating device listens to receive beacon signals directly from the target device in order to synchronize communications with the device (538). The selection of one of the two operating modes depends on a control parameter established for the initiating device, which in one embodiment is dependent on the urgency of communication, a maximum number of retries for using the mediation device, or the like.