The present calculations were performed on the basis of the Sanchez-Lacombe-Balasz lattice fluid theory. The two system specific parameters epsilon(12)* and delta epsilon* required for that purpose have been obtained from the spinodal temperatures measured (SANS) for mixtures of poly(vinyl methyl ether) (PVME) and deuterated polystyrenes (d-PS) by Schwahn and coworkers. The experimental data reported for atmospheric pressure and six representatives of the present system are well described theoretically, where epsilon(12)* does not depend on molar mass and delta epsilon* decreases only slightly as the chain length of d-PS is raised. The measured pressure influences on the spinodal conditions correspond to an approximately linear reduction of delta epsilon* with increasing P; this observation should reflect the volume changes associated with the formation of specific interactions. According to the present calculations the critical composition shifts markedly towards pure PVME as P is raised. Since experimental data are commonly expressed in terms of the Flory-Huggins theory, the current results were also translated into Flory-Huggins interaction parameters and evaluated with respect to the contributions of enthalpy and of entropy. The agreement between experimental information and that calculated from the Sanchez-Lacombe-Balasz lattice fluid theory is reasonable.