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Security is of critical importance for many potential applications of wireless sensor networks. Broadcasting from base station to nodes is very important in the cases such as distributing secure keys in the network or delivering control commands to nodes. However, the sparse distribution and limited resource of nodes bring difficulties to the efficient and reliable broadcast in wireless sensor networks. A lightweight energy-efficient reliable broadcast tree, or LERBT, is proposed to provide a framework by which to support reliable broadcast while reducing the broadcast coverage overlap and power consumption. Additionally, LERBT can configure itself quickly, allowing the base station to begin broadcasting commands shortly after deployment. Simulation results show the protocol can save significant energy over SBA and LKDT without sacrificing the coverage and reachability.