The authors present pseudopotential calculations of the conduction and valence mini-band non-parabolicity in GaAs-Ga_1-xAl_xAs superlattices of period approximately 80 AA with various well widths. They find an order of magnitude difference between the non-parabolicity in structures with very narrow approximately 5 AA and wider approximately 40 AA wells and relate this effect to the competition between quantum-size effects and zone-folding enhanced momentum mixing involving higher levels of X character. The authors show that the variation of the non-parabolicity of the electron energy with respect to its wave-vector across the small Brillouin zone takes on a complicated form which arises due to the anti-crossing behaviour of the higher conduction and lower valence mini-band states. Their results show that non-linear properties of semiconductor superlattices are a sensitive function of the form and position of the higher lying mini-bands which are normally ignored in simple models.