The equilibrium impurity-ligand distance, R-e, in six fluoroperovskites of the AMF(3) series (A: K, Rb, Cs; M: Mg, Zn, Cd, Ca) doped with Mn2+ has been explored through density functional calculations for MnF(6)A(8)sM(6)(16+) clusters where the effects of the electrostatic potential due to the rest of the lattice are included. The R-e-values obtained coincide, within the experimental uncertainties, with those derived from the analysis of the experimental isotropic superhyperfine constant, A(s), and the 10Dq-parameter and also with available extended x-ray absorption finestructure results. This important result is shown to be practically independent of the quality of the basis set employed. From the analysis of recent electron paramagnetic resonance data for AIF(3):Mn2+ it is concluded that, for this system, R-e approximate to 197 pm which is 7% smaller than the average distance for pure compounds involving MnF64- complexes. The latter figure is shown to be consistent with the substitution of Mn2+ for a trivalent cation in AlF3:Mn2+. The present theoretical scheme has also been applied to Tl+ impurities in NaI. First results indicate an outwards relaxation of ligands which is equal to, at least, 5% and thus is much higher than the figure (1%) calculated by Aguado et al.