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In wireless networks, maximizing throughput and minimizing energy consumption are two conflicting objectives. For elastic traffic, it is important to enhance the throughput since it directly affects the quality-of-service (QoS) of users. At the same time, the energy consumption should be minimized in order to prolong the battery lifetime of the mobile station. In this paper, we propose several adaptive energy saving schemes that consider throughput and energy saving simultaneously. The proposed schemes are designed for an efficient tradeoff between throughput and energy saving when transferring elastic traffic. Through extensive simulations, we compare the proposed schemes with the conventional scheme where a mobile terminal stays awake until all the pending packets are completely serviced. Our schemes outperform the conventional one in terms of utility, i.e., user satisfaction, which is defined as inversely proportional to the weighted multiplication of service completion time and energy consumption.