Dielectric loss spectra are reported for alpha -tocopherol acetate (an isomer of vitamin E) in the supercooled and glassy states. The alpha -relaxation times, tau_{alpha} , measured over a 190 degrees range of temperatures, T , at pressures, P , up to 400MPa can be expressed as a single function of TV3.9 ( V is specific volume, measured herein as a function of T and P ). At ambient pressure, there is no dynamic crossover over eight decades of measured tau_{alpha} . The relaxation spectra above the glass transition temperature T_{g} show ionic conductivity and an excess wing on the high-frequency flank of the alpha -relaxation loss peak. Temperature-pressure superpositioning is valid for the alpha process; moreover, the peak shape is constant (stretch exponent equal to 0.65). However, application of pressure changes the shape of the dielectric spectrum at higher frequencies due to the shift of the excess wing to form a resolved peak. Additionally, another relaxation process, absent at atmospheric pressure, emerges on the high-frequency side of the alpha -process. We propose that this new peak reflects a more compact conformation of the alpha -tocopherol acetate molecule. Drawing on the coupling model, the experimentally determined relaxation times, activation energy, and activation volume for the Johari-Goldstein process are compared to values calculated from the properties of the alpha relaxation. The agreement is generally satisfactory, at least for T<T_{g} .