This paper presents an optimization of MPI communications, called CoMPI, based on run-time compression of MPI messages exchanged by applications. A broad number of compression algorithms have been fully implemented and tested for both MPI collective and point to point primitives. In addition, this paper presents a study of several compression algorithms that can be used for run-time compression, based on the datatype used by applications. This study has been validated by using several MPI benchmarks and real HPC applications. Show that, in most of the cases, using compression reduces the application communication time enhancing application performance and scalability. In this way, CoMPI obtains important improvements in the overall execution time for many of the considered scenarios.