The main subject of the paper is to show how the shape and thickness of an α-layer and the amplitude of the α-effect influence the solution of model Z, especially the magnetic field energy (MFE). Solution of model Z with different input parameters allows us to conclude that the larger the thickness of the α-layer, the greater the ratio of the MFE of the meridional to the MFE of the azimuthal field and, therefore, the greater the efficiency of the α-effect, although the appropriate value of the amplitude of the α-effect is more difficult to find. The MFE tends to oscillate for a sufficiently thick α-layer if the amplitude of the α-effect is changed, but the oscillations are suppressed and MFE is again stabilized. If the thickness of the α-layer does not vary, the MFE of the azimuthal field relative to the MFE of the meridional field decreases with increasing amplitude of the α-effect in certain narrow limits. The geostrophic shear does not change its character, and its maximum follows the maximum of α-effect in the layer.