In the computer aided engineering environment, exceptionally smooth but irregular surfaces are often required, such as car bonnets. It is often a lengthy process to design these surfaces to the degree of smoothness and aesthetic beauty that is required by the designer. Smoothing these surfaces is known as fairing and a variety of techniques exist to tackle the problem in different ways. A new method of surface fairing is proposed and demonstrated in this thesis. Many conventional fairing methods use an agreeable curvature plot across the surface as proof of fairness, the method documented here takes the more holistic approach of constructing the improved surface from an agreeable curvature plot.