  In a realistic application of the SPA + RPA theory for calculation of the
nuclear level densities we find that quantal fluctuation corrections (RPA) are
important even up to temperature $T = 2.0 MeV$. This leads to a good agreement
between calculated numbers and the available experimental data for $^{104}Pd$
and $^{114}Sn$, particularly the excitation energy ($E^*$) dependence.
Furthermore, we also argue that $a=S^2/4E^*$ is the only correct definition of
the level density parameter in the present context which is also consistent
with the Bethe like level density formula.
