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The development of ICT following Moore's Law has resulted in a situation where mobile users are able to make use of a wealth of versatile services. Yet, battery and electronics technology has not followed this development as well, which has resulted in a situation where a mobile user's battery can only enable a few hours of active use. Therefore, we need to focus increasingly on energy efficient wireless and mobile communication to reduce energy consumption, but also to cut down greenhouse emissions and improve business competitiveness. Due to significant energy consumption of transmitting data over wireless networks, data compression techniques are one simple way to trade the overhead of compression for less communication energy. This paper investigates the usages of data compression to reduce the energy consumption in a modern hand-held device. By conducting various experiments, we analyze content-aware compression schemes that can reduce energy consumption significantly. Yet, blind or careless use of compression results in a huge energy loss. We also discuss the deployment issues of data compression.