Owing to the rapid increase in data demand, the need for power saving in mobile communication is of great importance. This study proposes a combination of a zone-based technique, also known as the Zonal Based GrEEn (ZBGrEEn) algorithm, with the Lempel Ziv Welch (LZW) data compression algorithm in order to produce significantly more energy- efficient device-to-device (D2D) communication network. The system is modeled as a device- to-device communication between one primary transmitter (PT) and many primary receivers (PRs) located in various zones around the PT. The ZBGrEEn algorithm ensures that power allocation is optimally performed so that the target rate of each application needed by PRs is met. Both the transmission time and transmission power computed in the ZBGrEEn algorithm are minimized due to the reduced data size achieved by applying the LZW algorithm on the data. Simulation results show an increase in battery lifetime of mobile devices from 46.28% (achieved when ZBGrEEn algorithm is used alone) to 51% when ZBGrEEn is combined with LZW algorithm.