The effect of low-dose cation doping (0.005 <x <0.08) of magnetite single crystals, Fe3-xMxO4 (M = Ni, Mg, Co, Al, Ti, Ga), was studied by the magnetic after-effect (MAE) spectroscopy with respect to (i) the Verwey transition, (ii) the low-temp. (4 K <T <125 K .simeq. TV) charge transport mechanisms and (iii) the zero-crossing of the crystal anisotropy. The obsd. low-temp. shifting of the transition (TV) is in fair agreement with previous cond. measurements. Variations of the MAE spectra clearly indicate the low-temp. tunnelling (4 K <T <35 K) to be far more affected by smallest impurity doping than variable long-range hopping (50 K <T <125 K) - this outstanding sensibility of the tunnelling processes against impurities or any other defects is also true when compared with the corresponding TV shifting. All samples undergo a doping-induced temp. splitting, DTVC, between the Verwey transition (spontaneous jump of the susceptibility at TV) and the zero-crossing of the crystal anisotropy (giving rise to a delayed susceptibility max.) - in contrast to perfectly stoichiometric Fe3O4 single crystals where both effects are coincident. This range of temp.-splitting DTVC, extremely large in the case of Co2+ doping, is characterized by destabilized magnetic domain structures due to locally disordered anisotropy distribution in the lattice.