This paper examines the effect of substitution of water by heavy water in a polymer solution of polystyrene (molecular weight=13000) and acetone. A critical double point (CDP), at which the upper and the lower partially-miscible regions merge, occurs at nearly the same coordinates as for the system [polystyrene+acetone+water]. The shape of the critical line for [polystyrene+acetone+heavy water] is highly asymmetric. An explanation for the occurrence of the water-induced CDP in [polystyrene+acetone] is advanced in terms of the interplay between contact energy dissimilarity and free-volume disparity of the polymer and the solvent. The question of the possible existence of a one-phasehole in an hourglass phase diagram is addressed in [polystyrene+acetone+water]. Our data exclude such a possibility.