A detailed model is developed for calculating the local distortion near Eu²⁺ impurity sites in the alkali halides. The ionic positions obtained using this model are then used to carry out a superposition model analysis of the spin-Hamiltonian parameters. The results are consistent with results obtained for Eu²⁺ and Gd³⁺ in other systems and provide a significant extension of the understanding of the properties of S-state ion spin-Hamiltonian parameters. Although the predictions of the local distortion model do not provide detailed agreement with the experimental spin-Hamiltonian parameters, it is shown that very small corrections in the ionic positions produce excellent agreement, thus demonstrating the viability of the approach. Copyright © 1988 IOP Publishing Ltd.