The alpha-relaxation process in polymethylphenylsiloxane was studied over a broad temperature and pressure range by dielectric spectroscopy. In the vicinity of the glass temperature, the shape of the dielectric loss peak is independent of both temperature and pressure. The steepness index (fragility), describing the temperature dependence of the relaxation times, is also independent of pressure (and of molecular weight as well). Thus, the correlation between fragility and nonexponentiality of the relaxation function is maintained under conditions of high compression. The combined temperature and pressure dependences of the relaxation time conformed to the Avramov equation. This model offers a means to relate the relaxation behavior to thermodynamic properties of the material.