and a general hexadecapole nonaxiality, when accounted for within the [*nonexact*]{} method of constrained minimization (used generally in all selfconsistent studies), may reach 2.5 MeV for some superheavy even-even nuclei, see Fig. 5 in [@Kow]. Here, we extend our previous discussion of its role to the odd and odd-odd nuclei and, at the same time, improve the treatment by employing the exact IWF method in potentially most interesting cases.

By using the original 5D mesh (4) we have obtained saddles with [*quadrupole*]{} nonaxiality for about 900 nuclei, what constitutes more than 70 % of all fission barriers. We illustrate this conspicuous effect in Fig. \[nonaxial\] on the example of two isotopic chains, Z=103 and 113.

![ Effect of the non-axiallity on the fission barrier heights (see text for further explanations).[]{data-label="nonaxial"}](nonaxial.EPS){width="1.2\linewidth" height="3.5in"}

We show the difference between axial and nonaxial barriers in these nuclei. One can see that for lighter Lawrencium isotopes the effect of nonaxiality is quite considerable. Starting with $N=$164, it is weakening quickly and finally vanishes for $N\geq$ 176. Somewhat different dependence of the effect on the neutron number occurs in $Z=113$ isotopes. The maximum lowering of the barrier of more than 1.5 MeV occurs for $N\approx 165$, 