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This paper presents an energy-efficient technique to handle redundant traffic (EEHRT) in the zone-based routing for wireless sensor networks. In this technique, multihop routing is performed based on the remaining energy of the nodes. Afterwards, it performs position-based routing without the need for the nodes to know their respective position. The main objective of this paper is to handle the redundant packets generated in zone-based routing using short beacon messages. Nodes of lower zones route the data of the higher zone to base station (BS) with a minimum number of hops and utilize only those nodes on the path which are energy efficient and located closer to BS. Moreover, the source node is acknowledged by the relaying node using a wireless broadcast advantage (WBA) without sending any special ACK packet to the sender, which reduces the control overhead in the routing process. The EEHRT technique improves the routing against RARZ by ensuring only one copy of the packet is propagated at each hop along the routing path to BS. Simulation results show that EEHRT achieved 28% improvement in energy efficiency, 10% and 25% improvements in data throughput against total and distinct packet reception at BS respectively, 35% increase in overall network lifetime, and 100% reduction in redundant packets generation and propagation in the network against RARZ routing.