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In a wireless sensor network, energy efficiency is one of the primary concerns since typically the sensor nodes rely on small battery to operate. Non-Cooperative events refer to such events that they are not easily monitored as they come and go. As a result, they can be observed only if the sensors are constantly monitoring the environment. However, energy efficiency is a serious concern if the sensors are always ON. In this work, the tradeoff between energy efficiency and non-cooperative events coverage in a wireless sensor network is studied. We begin with fixed listen and sleep time schemes for a single sensor node and quantify the performance results in terms of event miss rate and normalized average power consumption. If the statistics of the event is unknown, an adaptive scheme based on a "additive increase/multiplicative decrease" rule is proposed to adapt the sleep schedule with the sensing data. Both fixed and adaptive schemes are extended to multiple nodes and the coverage of the entire area of a network is taken into consideration in addition to energy efficiency. Discrete-event simulations are carried out to demonstrate the effectiveness of the proposed scheme.