A major advance in the statistical associating fluid theory (SAFT) for potentials of variable range (SAFT-VR) has recently been made with the incorporation of the Mie (generalized Lennard–Jones [LJ]) interaction between the segments comprising the molecules in the fluid (Lafitte et al. J. Chem. Phys. 2013;139:154504). The Mie potential offers greater versatility in allowing one to describe the softness/hardness of the repulsive interactions and the range of the attractions, which govern fine details of the fluid-phase equilibria and thermodynamic derivative properties of the system. In our current work, the SAFT-VR Mie equation of state is employed to develop models for a number of prototypical fluids, including some of direct relevance to the oil and gas industry: methane, carbon dioxide and other light gases, alkanes, alkyl benzenes, and perfluorinated compounds. A complication with the use of more-generic force fields such as the Mie potential is the additional number of parameters that have to be considered to specify the interactions between the model molecules, leading to a degree of degeneracy in the parameter space. A formal methodology to isolate intermolecular-potential models and assess the adequacy of the description of the thermodynamic properties in terms of the complex parameter space is developed. Fluid-phase equilibrium properties (the vapor pressure and saturated-liquid density) are chosen as the target properties in the refinement of the force fields; the predictive capability for other properties such as the enthalpy of vaporization, single-phase density, speed of sound, isobaric heat capacity, and Joule–Thomson coefficient, is appraised. It is found that an overall improvement of the representations of the thermophysical properties of the fluids is obtained using the more-generic Mie form of interaction; in all but the simplest of fluids, one finds that the LJ interaction is not the most appropriate.