Abstract The major part of the difference between the zero-point and equilibrium moment of inertia of a molecule is a homogeneous function of degree 1 2 in the atomic masses. The use of explicit mathematical models of is studied here as a means of determining near-equilibrium molecular structures from the zero-point moments of inertia of a range of isotopomers. It is found that models with more than two parameters per axis generally give strongly correlated fits for the number of isotopomers typically available. The two-parameter model , where N is the number of atoms, m i are the atomic masses, and M is the molecular mass, usually gives well-conditioned fits with standard deviations in the parts-per-million range, and structures called that are often close to equilibrium structures. Laurie-type corrections for hydrogen atoms and parameters to describe isotopic rotations of the ϵ tensor can also be included.