A modification of an existing correlative equation for self-diffusion coefficients is presented. A free-volume theory for liquids has been corrected to reproduce diffusivities of hard-sphere and Lennard-Jones fluids from low-density limit to melting points, and has been applied to correlate a wide database of non-polar, polar, quantic and hydrogen-bonding substances, although it is unable to fit helium, water and hydrogen fluoride. The adjustable parameters are generalized with available fluid properties, and the three resulting predictive formulas present lower deviations than other correlative equations used in a predictive way for non-quantic and non-associated fluids. (c) 2008 Elsevier B.V. All rights reserved.