Relationships between crystal field invariants and superposition model parameters are established. Various strategies are examined for determining and assessing the reliability of crystal field parameters for lanthanide ions in low‐symmetry sites. In particular, a new method of estimating crystal field parameters is proposed using crystal field invariants in conjunction with the superposition model. The importance of using a fixed reference frame throughout a series of fitting based on approximate symmetries is stressed and this leads us to identify a new simplified parametrization for lanthanide ions in LaF3 which is not related to an approximate symmetry. Copyright © 1985 American Institute of Physics.