N-body simulations of collisionless collapse have offered important clues
to the construction of realistic stellar dynamical models of elliptical
galaxies. Such simulations confirm and quantify the qualitative
expectation that rapid collapse of a self-gravitating collisionless
system, initially cool and significantly far from equilibrium, leads to
incomplete relaxation. In this talk we revisit the problem, by making a
direct comparison between the detailed properties of a family of
distribution functions derived from statistical mechanics arguments to
those of the products of collisionless collapse found in N-body
simulations that we have run for the purpose.