A wireless communications device supports a constant transmission power mode of operation and a time varying transmission power mode of operation for transmitting data, e.g., peer discovery data. The device determines an amount of network congestion and switches between the two modes of operation as a function of the determined amount of network congestion. Various described methods and apparatus are well suited for use in a peer to peer ad hoc wireless communications system in which a limited amount of air link resources are available for peer discovery signaling and the same peer discovery resources are, at times, used concurrently by multiple devices. When network congestion is low, the device operates in the constant transmission power mode. When network congestion is high, the device operates in the time varying power mode. Devices sharing a common peer discovery resource in a local area intentionally select different time varying transmission patterns.