[en] Griffin's exciton model of pre-equilibrium emission and Blann's hybrid model have proven extremely successful in describing the energy dependence and, to a certain extent the angular dependence, of nucleon and composite particle emission in pre-equilibrium reactions. However, the conceptual basis of these models was called into question by Bisplinghoff already some time ago. Numerical calculations of our own corroborate his doubts. In response to Bisplinghoff, Blann proposed the hybrid Monte Carlo simulation model (HMS), which uses only the densities of available states for creation and decay of single particle-hole pairs. The model was later extended, in collaboration with Chadwick, to the double-differential HMS, which we call the DDHMS. This extension is based on Chadwick and Oblozinsky's prescription for approximating the energy-angular distribution of available two-particle-one-hole states. Here, we show how this distribution can be calculated exactly and compare the exact result to the approximate one, both directly and in calculations within the DDHMS model. (author)