In today's mobile devices, the battery reservoir remains severely limited in capacity, making power consumption a key concern in the design and implementation of mobile applications. In this paper, we closely examine one widely adopted approach to improve the energy efficiency of mobile applications-adaptively offloading the computation to the remote cloud. In particular, we measure the power consumption of computation offloading for two representative real-world mobile cloud applications under various wireless network conditions and identify the unique features of data transmission for computation offloading. We then formulate the power-aware scheduling problem for computation offloading and present a scheduling algorithm that makes adaptive offloading decisions according to the dynamic network conditions. Simulation results show that our proposed method can achieve better battery performance, which also reveal that computation-intensive and delay-tolerant tasks are more likely to benefit from offloading.