  A new model for calculating nuclear level densities is investigated. The
single-nucleon spectra are calculated in a relativistic mean-field model with
energy-dependent effective mass, which yields a realistic density of
single-particle states at the Fermi energy. These microscopic single-nucleon
states are used in a fast combinatorial algorithm for calculating the
non-collective excitations of nuclei. The method, when applied to magic and
semi-magic nuclei, such as $^{60}$Ni, $^{114}$Sn and $^{208}$Pb, reproduces the
cumulative number of experimental states at low excitation energy, as well as
the s-wave neutron resonance spacing at the neutron binding energy.
Experimental level densities above 10 MeV are reproduced by multiplying the
non-collective level densities by a simple vibrational enhancement factor.
Problems to be solved in the extension to open-shell nuclei are discussed
