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. (C) 2008 Elsevier B.V. All rights reserved.