Since Van der Waals, the attractive term a(T) of any cubic equation of state is expressed as the product of its value at the critical temperature (a(c)) by the so-called alpha function. Our recent investigations made it however possible to conclude that to get accurate and physically meaningful behaviors in both the subcritical and supercritical domains, it was necessary to work with a consistent alpha-function, i.e., with an alpha-function which is positive, decreasing, convex and with a negative third derivative. This paper aims at quantifying the gain of accuracy resulting from the use of a consistent alpha-function when a cubic equation of state is used to calculate the properties of a pure compound in the supercritical region. As a key conclusion, embedding a consistent a-function in a cubic equation of state instead of an inconsistent one entails a division by a factor 9 of the deviations between calculated and experimental data. (C) 2017 Elsevier B.V. All rights reserved.