A new combinatorial activity coefficient model, based on the Staverman-Guggenheim (SG) one, is developed in this study. It involves a system-dependent exponent, determined from the size ratio of its components only, and is useful for group-contribution models. The model, referred to as R-UNIFAC, is applied to the prediction of activity coefficients in the following nearly athermal mixtures : (a) alkane/alkane mixtures; (b) alkane/polymer mixtures; (c) polymer/solvent mixtures, where the activity coefficient data were obtained by constant-pressure Monte Carlo simulations. For all these mixtures the residual contribution to the activity coefficient is expected to be close to zero. The new model yields satisfactory predictions for all systems considered, independently of system asymmetry, comparable to those obtained with free-volume models such as the Entropic-FV and p-FV ones. It has the advantage, however, that it does not require pure-component liquid molar volumes and, thus, is directly applicable to systems containing compounds where such volumes are not accurately known or supercritical fluids.