A wireless mesh network includes a mesh of continuously-powered devices (CPDs) and a mesh of battery-powered devices (BPDs). The BPDs are organized into hop layers based on hopping distance to the mesh of CPDs. In a medium latency communication mode, a given BPD receives data during a receive window that is scheduled to occur within either the first half of a communication window or the second half of the communication window, depending on the parity of the hop layer where the BPD resides. With this approach, a data packet can traverse one hop of the BPD mesh per communication window. In a low-latency communication mode, a given BPD receives and transmits data according to an alternating pattern that depends on the parity of the hop layer where the node resides. With this technique, a data packet can traverse multiple hops of the BPD mesh within a single communication window. These techniques also are applicable to CPDs and other types of nodes as well.