In this work, we confirm the somehow previously expressed but not widespread idea that the limitations of cubic equations of state like Soave-Redlich-Kwong equation (SRK) or Peng-Robinson equation (PR) are a consequence of their two-parameter density dependence rather than of their empiric character. Moreover, it is shown that when combined with a simple generalized van der Waals attraction term, the van der Waals repulsion is more capable than the Carnahan-Starling term to follow the PvT behaviour of real fluids and, in particular, that the generalized Redlich-Kwong-Peng-Robinson (RK-PR) equation offers the best performance among cubic three-parameter density functionalities. A simple temperature dependence was developed and a straightforward parameterization procedure established. This simple - and optimized from pure compound data - three-parameter equation of state (3P-EoS) will allow in a later stage, by systematic study and comparison to other types of 3P-EoS, to find out what the actual possibilities and limitations of cubic EoS are in the modelling of phase equilibria for asymmetric systems. (c) 2005 Elsevier B.V. All rights reserved.