The free-volume theory for solvent self-diffusion coefficients in polymer-solvent systems is modified to include a more general analysis of the effects of solvent size. The predictions of the theory are compared with self-diffusion data for a diverse set of solvents and four polymers, polystyrene, poly(vinyl acetate), poly(methyl methacrylate), and poly(p-methylstyrene). The new prediction of size effects is based on the consideration of the asymmetry of solvent molecules.