Parametrizations of one-photon electric-dipole transitions between crystal-field levels of the 4fn configuration of lanthanide ions often result in multiple local minima that fit the data nearly equally well. This is especially true for structurally complex systems containing lanthanide ions, such as the oxydiacetate single crystals Na3[Ln(oda)3]·2NaClO4·6H2O (commonly abbreviated as LnODA). Through a detailed reexamination of the previously well-studied EuODA system, we investigate the seriousness of the multiple local minima problem. Parameter robustness is determined by means of an analysis of the sensitivity of the local minima with respect to perturbation of the energy-level wavefunctions and intensity strengths. Inclusion of rotatory strengths is shown to greatly reduce the number of local minima that must be considered.