In a tree-based ZigBee network, ZigBee routers (ZRs) must schedule their beacon transmission times to avoid beacon collisions. The beacon schedule determines packet delivery latency from the end devices to the ZigBee coordinator at the root of the tree. Traditionally, beacon schedules are chosen such that a ZR does not reuse the beacon slots already claimed by its neighbors, or the neighbors of its neighbors. We observe however that beacon slots can be reused judiciously, especially when the risk of beacon collision caused by such reuse is low. The advantage of such reuse is that packet delivery latency can be reduced. We formalize our observation by proposing a node pair classification scheme, that classifies pairs of nodes that are at most two hops apart. Based on this scheme, we can easily assess the risk of slot reuse by a node pair. If the risk is high, slot reuse is disallowed; otherwise, slot reuse is allowed. This forms the essence of our ZigBee-compliant, distributed, riskawa...