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 which 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 re-examination of the previously well-studied lanthanide oxydiacetate (LnODA) systems, where Ln = Nd, Sm, Eu, Dy, Ho and Er, we examine 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 experimental intensities and rotatory strengths. Inclusion of circular dichroism rotatory strengths in the calculation is shown to greatly reduce the total number of local minima which must be considered, resulting in much better determination of the overall intensity parameter values.