Simulations of phase changes provide a way to investigate nucleation at a depth of supercooling so far not accessible to laboratory experiments. One helpful aspect of this regime is that deficiencies of theory are substantially magnified, helping to call attention to the weaknesses of existing treatments, In the present molecular dynamics simulations, a system of small liquid clusters of SeF6 spontaneously froze to single body-centered cubic (bcc) crystals when cooled to 120 K. The transition was mediated by homogeneous nucleation rather than by spinodal decomposition. Its nucleation rate of 6.6 x 10(35) m(-3) s(-1) was analyzed in both terms of classical nucleation theory (to derive the interfacial free-energy parameter) and Granasy＇s diffuse-interface theory (to derive the interface thickness parameter). In each case, both the classical prefactor and the Grant-Gunton (GG) prefactor were applied. Large differences between the various treatments were found. Derived interfacial free energies of 13-17 mJ/m(2) were roughly in accord with Turnbull＇s empirical relation. Granasy＇s interface thickness agreed in order of magnitude with the estimated interface correlation length of the GG prefactor and the interfacial breadth implied by a capillarywave model. Simulations provided no criterion for deciding among prefactors, but several severe flaws were found in the classical theory. Intrinsic in this theory is the attribution of bulk properties to critical nuclei and a neglect of the thickness of the interfacial region between the old phase and the new. It was found that the heat which evolved into clusters as the bcc nuclei grew was considerably less than that implied by the bulk heat of fusion. This was due to the excess interfacial enthalpy, the less efficient packing of molecules in the minute nuclei than in the bulk, or a combination of these factors. Critical nuclei contained approximately 30 molecules rather than the 5 predicted by the classical theory. Finally, the simulations revealed a transition layer around the critical nuclei of appreciable thickness.