  The variation ranges of the axial B_{k0} crystal-field parameters, for
k=2,4,6, of tetragonal including cubic crystal-field Hamiltonians H_{CF} for
all possible orientations of the relevant reference frame are studied. The
distinguished z-axis directions fixed by the maximal absolute values of B_{k0}
are analyzed. The diagrams for any tetragonal H_{CF} parametrization depicting
the maximal values of |B_{k0}|/M_{k}, where M_{k} is the 2^{k}-pole modulus, as
a function of the x=B_{k4}/B_{k0} or B_{64}/B_{60} ratios, together with the
distinguished directions are presented. The max|B_{k0}|/M_{k} magnitudes and
the relevant distinguished directions are the discriminants of all the
equivalent parametrizations. They vary within the intervals (0.7395,1],
(0.6074,1] for tetragonal k=4 and tetragonal k=6 H_{CF} components,
respectively. Such specified directions determine the mutual spatial
orientation of the component 2^{k}-poles of the H_{CF}, and due to their rigid
coupling in the H_{CF}, they also refer to the global H_{CF} parametrization.
This approach demonstrates the difference in fitting capability between the
real and complex isomodular H_{CF} parametrizations.
