Equilibrium structures have been determined for 19 molecules using least-squares fits involving rotational constants from experiment and vibrational corrections from high-level electronic-structure calculations. Equilibrium structures obtained by this procedure have a uniformly high quality. Indeed, the accuracy of the results reported here likely surpasses that reported in most experimental determinations. In addition, the accuracy of equilibrium structures obtained by energy minimization has been calibrated for the following standard models of ab initio theory: Hartree-Fock, MP2, CCSD, and CCSD(T). In accordance with previous observations, CCSD(T) is significantly more accurate than the other models; the mean and maximum absolute errors for bond distances of the 19 molecules are 0.09 and 0.59 pm, respectively, in CCSD(T)/cc-pCVQZ calculations. The maximum error is obtained for R-OO in H2O2 and is so large compared with the mean absolute error that an experimental reinvestigation of this molecule is warranted.