Elbro et al. [Macromolecules 23 (21) (1990) 4707] proposed a simple but successful entropic expression for polymer and other size-asymmetric solutions. The expression is similar to the Flory-Huggins model, but free-volume (FV) fractions are used instead of segment or volume fractions and much better results are obtained. The FV is simply defined as V-f = V - V-W,V-where V-W is the van der Waals (vdW) volume, essentially a measure of molecule's hard-core volume. In this work we adopt the statement by Bondi that due to the packing of molecules, a higher than V-W inaccessible volume represents more adequately the hard-core volume. Using experimental phase equilibrium data for athermal polymer (and other asymmetric) solutions, we show that the optimum V*/V-W ratio is equal to 1.2, which is very close to the value expected based on the packing density at 0 K for organic systems. Using the entropic expression by Elbro et al. [Macromolecules 23 (21) (1990) 4707] and V* = 1.2 V-W yields improved results of activities for athermal polymer solutions and alkane-alkane systems over an extensive database. The results are better compared to other existing entropic expressions, e.g. those of Oishi-Prausnitz (Unifac-FV) and of Zhong-Masuoka.