For most symmetries the standard parametrization of one-photon electric-dipole transitions between crystal-field levels of the 4f configuration of lanthanide ions gives the same predictions for several quite different parameter sets. An alternative parametrization scheme that provides separate parameters for each of the different polarization directions removes this anomaly. A second problem arises due to the fact that multiple local minima may fit the data nearly equally well. Through a detailed reexamination of the previously well-studied system NdODA, we examine and attempt to resolve this local minima problem. © 2000 Elsevier Science S.A. All rights reserved.