Detailed comparisons are made of the results of two approaches to the problem of non-linear refraction at frequencies just below the band edge of a semiconductor. The magnetic field case discussed is shown to give potentially larger non-linearities than the zero-field situation. The physical origin of the non-linear dispersion is taken to be direct saturation of T2 broadened band states in the first model. In the second the refraction associated with a dynamic Burstein-Moss shift of the absorption edge is considered. Both models predict an extremely large non-linearity, of importance in the field of dispersive optical bistability. The results are also consistent with experimental observations of non-linear Faraday rotation and interband saturation in InSb.