A detailed study is carried out of the accuracy of molecular equilibrium geometries obtained from least-squares fits involving experimental rotational constants B-0 and sums of ab initio vibration-rotation interaction constants alpha(r)(B). The vibration-rotation interaction constants have been calculated for 18 single-configuration dominated molecules containing hydrogen and first-row atoms at various standard levels of ab initio theory. Comparisons with the experimental data and tests for the internal consistency of the calculations show that the equilibrium structures generated using Hartree-Fock vibration-rotation interaction constants have an accuracy similar to that obtained by a direct minimization of the CCSD(T) energy. The most accurate vibration-rotation interaction constants are those calculated at the CCSD(T)/cc-pVQZ level. The equilibrium bond distances determined from these interaction constants have relative errors of 0.02%-0.06%, surpassing the accuracy obtainable either by purely experimental techniques (except for the smallest systems such as diatomics) or by ab initio methods.