In this study, we show that the inclusion of a short-range part of the total attractive interaction into a reference system allows a natural extension of the traditional first-order perturbation theory of simple fluids to practically all thermodynamic states. This theory is applied to the thermodynamic functions and the liquid–vapor coexistence curve of the Lennard-Jones-like medium range Yukawa fluid and to the Sutherland fluid. Comparison with computer simulation data and the second-order Barker–Henderson perturbation theory is discussed.