The local relaxation around Mn2+ and Ni2+ impurities in K2MgF4 and also in K2ZnF4:Mn2+ has been explored by means of cluster calculations using Density Functional Theory. It is found that the difference between equatorial and axial Mg2+-F distances in the K2MgF4 (K2ZnF4) when Mg2+ (Zn2+) is replaced by Mn2+ increases from 1.5 (-0.2) pm to 5 (3.5) pm. This surprising behaviour, consistent with the available EPR experiments, is shown to arise from the elastic anisotropy of the host lattice. From the present analysis it emerges that results which are valid for a transition-metal complex in a cubic lattice cannot in general be transferred to host lattices of lower symmetry. The results of this work confirm that the local distortion around a d(9) ion in a layered compound cannot necessarily be associated with the Jahn -Teller effect. (C) 2009 Elsevier B. V. All rights reserved.