In one aspect thereof the invention provides a method that includes transmitting from a first (beaconing) mesh point at least one multicast or broadcast frame; and transitioning the first mesh point to a lower power mode of operation state after expiration of a specified post groupcast time from a last multicast or broadcast frame that was transmitted by the beaconing mesh point after expiration of an awake window, or when the awake window expires, whichever occurs later. In another aspect thereof the invention provides a method that includes operating a peer mesh point in an awake state; and maintaining the peer mesh point in the awake state for no more than a specified post groupcast time after a last target beacon transmission time, or a last received beacon frame, or a receipt of multicast or broadcast frame having an indication that another multicast or broadcast frame will be transmitted. A computer-readable medium storing program instructions to implement the methods is also disclosed, as are corresponding apparatus.