In the framework of the free-volume (FV) theory, a new equation was derived for the evaluation of self-diffusion coefficients of small molecules in polymers above the mixture glass transition temperature. The derivation of the equation turned out to be straightforward once the equivalence between the free volume and the unoccupied volume given by thermodynamic lattice theories is assumed. A parameter evaluation scheme is proposed, which is substantially simpler compared with the conventional Vrentas-Duda approach, even without losing generality. The key assumption is discussed, and its consistency is verified from a numerical viewpoint. A comparison with experimental solvent self-diffusion coefficients for several solvent/polymer binary systems confirmed that the proposed theory presents good correlative ability over wide temperature and composition ranges. Moreover, the introduced thermodynamic foundation allows one to easily include the pressure effect too. In the frame of the proposed lattice free volume theory, the sizes of the polymer jumping units decrease with temperature and increase with pressure. Such behavior converges with theoretical expectations and opens the way for a predictive FV theory. (C) 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 529-540, 2010