An alternative four-parameter cubic equation of state (CES) and a new form for a temperature dependent coefficient alpha(T-r) of the attractive energy parameter were examined. As a consequence a three-parameter CES is proposed. A critical reduced volume beta(c), an apparent critical compressibility factor zeta(c), and the coefficient alpha(T-r) are compound-specific. The abilities to describe the vapour-liquid equilibrium for sixteen representative pure compounds and p, nu, T behaviour along critical isobar for six selected compounds are reported. For the best known CES the percentage deviations of the vapour pressure, saturated volumes, and densities above critical temperature on the critical isobar are compared.