Pairing correlations have a strong influence on nuclear level densities. Empirical descriptions and theoretical models have been developed to take these effects into account. The present article discusses cases, where descriptions of nuclear level densities are inconsistent or in conflict with the present understanding of nuclear properties. Phenomenological approaches consider an energy-shift parameter. However, the absolute magnitude of the energy shift, which actually corresponds to the pairing condensation energy, is generally not compatible with the observation that stable pairing correlations are present in essentially all nuclei. It is also shown that in the BCS model pairing condensation energies and critical pairing energies are inconsistent for light nuclei. A modification to the composite Gilbert-Cameron level-density description is proposed, and the use of more realistic pairing theories is suggested.