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This article studies energy-aware design strategies in the context of wireless sensor networks. Sensor networks provide an efficient means to collect, analyze, and transmit environmental data. Since wireless sensor nodes are normally powered by small batteries, the performance and viability of such systems rely strongly on energy conservation. In this work, an energy-efficient scheme by which sensor nodes go to sleep periodically is proposed. The duration of a sleep interval is determined dynamically based on past observations and prior knowledge about the statistics of the stochastic process being observed. For the problem of detecting level crossings in a Poisson arrival process, dynamic programming is employed to obtain an optimal average power versus detection delay tradeoff curve. This problem serves as an illustrative example to show how a small increase in expected detection delay can result in substantial energy savings.