We present an optical potential analysis of the antiproton-proton interactions at low energies. Our optical potential is purely phenomenological, and has been parametrized on data recently obtained by the Obelix Collaboration at momenta below 180 MeV/c. It reasonably fits annihilation and elastic data below 600 MeV/c, and allows us for an evaluation of the elastic cross section and rho-parameter down to zero kinetic energy. Moreover we show that the mechanism that depresses antiproton-nucleus annihilation cross sections at low energies is present in antiproton-proton interactions too.