The influence of the form of the interaction potential on the thermodynamic properties of fluids is investigated. Differences in the potential profile of nonconformal interactions are taken into account by the steepness of the potential functions and used to define a relative softness between interactions. In the dilute gaseous phase, the system of interest is characterized by a relative softness relating its virial coefficient B(T) with respect to that of a reference system B-0(T). For constant softness S, B(T) is obtained directly from B-0(T) by linear relations involving only S. The conditions on which S is exactly or approximately constant are analyzed and shown to hold in a wide range of cases. Furthermore, it is shown how to invert B(T) to construct potentials whose form and parameters reproduce accurately the thermodynamic properties of the gas.