Recently as smart phones have merged into heavy applications like video editing and face recognition. These kinds of applications need intensive computational power, memory, and battery. A lot of researches solve this prob-lem by offloading applications to run on the Cloud due to its intensive storage and computation resources. However, none of the available solutions consider the low bandwidth case of the networks as well as the communication and net-work overhead. In such case, it would be more efficient to execute the applica-tion locally on the Smartphone rather than offloading it on the Cloud. In this paper, we propose a new framework to support offloading heavy applications in low bandwidth network case, where a compression step is proposed for the fa-vor of minimizing the offloading size and time. In this framework, the mobile application is divided into a group of services, where execution-time is calcu-lated for each service apart and under three different scenarios. An offloading decision is then smartly taken based on real-time comparisons between being executed locally, or compressed and then offloaded, or offloaded directly with-out compression. The extensive simulation studies show that both heavy and light applications can benefit from the proposed framework in case of low bandwidth as well as saving energy and improving performance compared to the previous techniques