The dependence of the optical and spin-Hamiltonian parameters of NiF65- and NiF43- D4h units, with a b1g* (approximately x2 - y2) unpaired electron, upon the equatorial (R(eq)) and axial (R(ax)) Ni+-F- stances has been studied through multiple-scattering Xalpha and self-consistent charge extended Huckel methods. Both methods lead to the following main conclusions: (i) A charge-transfer transition like e(u)(pi + sigma, eq) --> b1g* (approximately x2 - y2) (termed E(u)) is more sensitive than a crystal-field one like b2g* (approximately xy) --> b1g* (DELTA1) or e(g)* --> b1g* (DELTA2) to variations in R(eq). The change experienced by E(u) mainly reflects that of V(el)(M) - V(el)(L), where V(el)(M) and V(el)(L) are the electrostatic potentials experienced by an electron placed on metal and ligands, respectively. (ii) As regards the unpaired spin densities onto n(L)P and n(L)S ligand valence orbitals (termed f(sigma) and f(s) respectively), it is found that f(sigma) much greater than f(s) but f(s) is much more sensitive than f(sigma) to changes in R(eq). The microscopic origin of this relevant fact is explained in detail. (iii) The removal of axial ligands, keeping R(eq) constant, induces a decrease of E(u) as a result of the diminution of the electrostatic repulsion, V(el)(M), and produces a slight increase of DELTA1 and a more important one Of DELTA2. (iv) The dependence of g(parallel-to) - g0 and g(perpendicular-to) - g0 on R(eq) essentially reflects that of DELTA1(-1) and DELTA2(-1), respectively, because of the low covalency (f(sigma) congruent-to 2%). These results on NiF65- and NiF43- explain the main differences displayed by the electron paramagnetic resonance parameters of Ni+(I) and Ni+(III) centres in fluoroperovskites, respectively, only on the basis of the host lattice dependence of R(eq). Furthermore, they support the determination of the true R(eq) through the experimental isotropic superhyperfine constant, A(s). The experimental g-tensor values of Ni+ centres are well understood through our calculations, which involve no adjustable parameters at all, and demonstrate that (i) Ni+(III) and Ni+(I) centres can be distinguished by looking only at the experimental g(perpendicular-to) value, (ii) aside from inducing a decrement of R(eq), the main effects due to axial vacancies are the diminution of the electrostatic repulsion V(el)(M) as well as the breaking of bonds with axial ligands in the e(g)* orbital, and (iii) changes of R(eq) of 0.1 pm can be detected through g(parallel-to) provided an uncertainty of +/-10(-3) is reached. The trends derived from this study are shown to be followed also by Cu2+ and Ag2+ systems, with moderate covalency. In particular, it is now reasonably explained why CdCl2:Cu2+ and (N-mpH)2CuCl4 have the same E(u) value while DELTA1 and DELTA2 are clearly higher for the latter system.