We investigate the use of data compression to reduce the battery consumed by handheld devices when downloading data from proxy servers over a wireless LAN. To make a careful trade-off between the communication energy and the overhead to perform decompression, we experiment with three universal lossless compression schemes, using a popular handheld device in a wireless LAN environment and we find interesting facts. The results show that, from the battery-saving perspective, the gzip compression software (based on LZ77) to be far superior to bzip2 (based on BWT) and compress (based on LZW). We then present an energy model to estimate the energy consumption for the compressed downloading. With this model, we further reduce the energy cost of gzip by interleaving communication with computation and by using a block-by-block selective scheme based on the compression factor of each block. We also use a threshold file size below which the file is not to be compressed before transferring.