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One of the significant applications of Wireless Sensor Networks (WSNs) is threat surveillance, where events are rare and the sensing nodes are idle most of the time. Sleep is essential for conserving energy in such applications, since, for sensor technology, the energy consumption rate during idle state is in the same order of magnitude as during radio communications. This paper proposes Topology and Energy Adaptive, Non-synchronous (TEAN) sleep, a network-level sleep coordination scheme for WSNs that exploits the neighborhood connection redundancies to achieve longer durations of continuous node sleep, while ensuring uniform (close to 100%) network coverage and connectivity for reliable threat surveillance. The main objective of TEAN-sleep is to maximize lifetime without degrading the connection reliability of a network. In that perspective, this work adopts sensor-oriented α-metrics, a unified representation of energy conservation, coverage and connectivity efficiency, to quantify the performance of TEAN-sleep. Simulations predict 70% average α-performance improvement when employing TEAN-sleep as compared to the sleep deprived WSNs, under variety of monitoring scenarios.