[en] Recent calculations show that ratios of exciton level densities in one- and two-fermion formulations vary with both excitation energy U and exciton number n. This means that the exciton level density in the two-fermion formulation, which is the correct one, cannot be simulated by a normalization of its one-fermion counterpart to the total level density in the two-fermion formulation, which is only a function of U. Such a normalization has been adopted in several unified Hauser-Feshbach and pre-equilibrium model codes. Some of the resulting problems are studied and clarified in this paper. It is shown that all three exciton level densities (one fermion, two fermion, and normalizations lead to very different cross sections and neutron emission spectra if a fixed set of model parameters are used. However, close agreements of calculated neutron emission spectra with data for all three options can be obtained by adjusting a parameter that controls the pre-equilibrium strength. A fourth option of an exciton level density that contains only bound final states in the two-fermion formulation yields the best results for incident energies lower than 15 Mev