Experimentally obtained islands of immiscibility are reported for the systems PS/PVME/THF at 20 degrees C and for PS/PVME/CH at 55 degrees C (PS: polystyrene, PVME: poly(vinyl methyl ether), THE tetrahydrofuran, CH: cyclohexane). THF is a good solvent and CH is a marginal solvent for both polymers. In the case of THF, information on the Flory-Huggins interaction parameters of the three binary subsystems suffices for a qualitative prediction of the phase behavior of the ternary system. Quantitative agreement can be achieved by means of composition-independent ternary interaction parameters. For the marginal solvent CH, the exclusive use of binary interaction parameters wrongly predicts complete miscibility of all three components. In this case, one ternary interaction parameter must be treated as a function of composition in order to match experiment and theory. On the basis of the present results, it can be concluded that the preparation of homogeneous mixtures with arbitrary composition from a pair of compatible polymers and a common solvent is only possible on rare occasions.