Consider a dilute gas composed of identical, isotropic molecules in which the potential energy of interaction between pairs of particles is an analytic function of the distance of separation with either a monomial or a normal binomial Laurent expansion. It is shown that the complete iterative inversion method inverts second virial coefficient data in one step to obtain the pair potential. In particular, the CIIM inverts second virial coefficient data in one step for gases with a Lennard-Jones pair potential.