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. (c) 2015 American Institute of Chemical Engineers AIChE J, 61: 2891-2912, 2015