The high-end telecom terminal and PDAs, sometimes called Personal Trusted Devices (PTDs) are programmable, have tens of megabytes memory, and rather fast processors. In this paper we analyze, when it is energy-efficient to transfer application data compressed over the downlink and then decompress it at the terminal, or compress it first at the terminal and then send it compressed over up-link. These questions are meaningful in the context of usual application code or data and streams that are stored before presentation and require lossless compression methods to be used. We deduce an analytical model and assess the model parameters based on experiments in 2G (GSM) and 3G (FOMA) network. The results indicate that if the reduction through compression in size of the file to be downloaded is higher than ten per cent, energy is saved as compared to receiving the file uncompressed. For the upload case even two percent reduction in size is enough for energy savings at the terminal with the current transmission speeds and observed energy parameters. If time is saved using compressed files during transmission, then energy is certainly saved. From energy savings at the terminal we cannot deduce time savings, however. Energy and time consumed at the server for compression/decompression is considered negligible in this context and ignored. The same holds for the base stations and other fixed telecom infrastructure components.