The influence of surface roughness on the performance of bearings and gears operating under Elasto-Hydrodynamic Lubrication (EHL) conditions has become increasingly important over the last decade, as the average film thickness decreased due to various influences. In order to describe the roughness geometry inside an EHL contact, the amplitude reduction of harmonic waviness has been studied over the last ten years. This theory currently allows a quantitative prediction of the waviness amplitude, including wavelength and contact operating conditions. Theoretical analysis has complemented the numerical results indicating the paramount role of the inlet boundary layer. The model has been extended to include general rolling-sliding conditions, general roughness orientation and general contact geometry. However, the current model depends heavily on the characteristic features of Newtonian behaviour in the solution. For line contacts Jacod  has shown that for zero slip the non-Newtonian behaviour coincides with the Newtonian behaviour and Hooke  and  has presented results based on a perturbation approach. The current paper makes a first contribution to the extension of the roughness amplitude reduction for EHL point contacts to include non-Newtonian effects.