For most symmetries the standard parametrization of one-photon electric-dipole transitions between crystal-field levels of the 4fN 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 has been shown to remove 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 a series of lanthanide oxydiacetate (LnODA, Ln=Nd, Sm, Eu, Dy, and Ho) systems using the new parametrization, we examine the multiple local minima problem, and attempt a determination of the robustness of the global parametrization minimum.