A new temperature-dependence is proposed for the depth of the square-well parameter in the Christoforakos-Franck equation of state. A comparison of theory with experiment is reported for the vapour-liquid equilibria of 30 one-component fluids including the noble gases, alkanes, cyclic hydrocarbons, ketones, alkanols and chlorocarbons, which indicates that the modified equation can be accurately employed at sub-critical conditions. The results are also compared with available data for the simplified perturbed hard-chain theory equation of state.