Pressure-volume-temperature measurements in phenylphthalein-dimethylether (PDE) are reported, in combination with recently published dynamic light scattering data obtained under high pressure. We discuss the role that volume and thermal effects play in controlling the dynamics in the vicinity of the glass transition. Although volume is not the unique thermodynamical parameter characterizing the relaxation dynamics in PDE, its contribution to the super-Arrhenius behavior of the relaxation times in the vicinity of the glass transition is remarkable. The contribution of volume to the temperature dependence of the relaxation times has been characterized by means of the ratio of the activation energy at constant volume to the enthalpy of activation at constant pressure, E-V/H-P. We point out that this quantity is correlated with the temperature behavior of the nonexponentiallity parameter, beta(KWW). Moreover, the tau(T,P) values were analyzed in terms of an extension of the Adam-Gibbs model. It was shown that this model gives a satisfactory interpretation of the pressure sensitivity of the dynamics (d log(10)(tau)/dP)\(T) in terms of thermodynamic properties of the material.