By using the statistical methods originally due to Bethe, the predictions for the densities of nuclear energy levels at excitation energies around 8 Mev are examined for two different versions of the shell model. A crude method is used to take into account the effects of shell structure. The assumed form of the theoretical expression for the density of nuclear energy levels is employed to analyze the data from slow-neutron resonance experiments and from fast ($n, \ensuremath{\gamma}$) cross sections. In contrast to earlier results, for the necessary potential radius, it is found that either the static diffuse potential with a radius of $\ensuremath{\sim}1.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\ifmmode\times\else\texttimes\fi{}{A}^{\frac{1}{3}}$ cm, or the diffuse velocity-dependent potential based on the Johnson-Teller model with a radius of $\ensuremath{\sim}1.4\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\ifmmode\times\else\texttimes\fi{}{A}^{\frac{1}{3}}$ cm, leads to fair agreement with the above experiments. In each case the values of the thickness of the surface layer on the nuclear potential and the magnitude of the spin-orbit coupling are taken to be those previously found to give close agreement with the experimental shell-model level sequences.The level-density expressions used here lead to an energy dependence which is in even stronger disagreement with those derived from various excitation function and inelastic scattering experiments than the empirical formula of Blatt and Weisskopf. It is argued that this anomaly may cast more light on the use of the statistical theory of nuclear reactions than on the validity of the expression for nuclear level densities.