We present the calculation of nuclear magnetic resonance shielding constants using a range of different methods. In particular we examine two new methods proposed by Yang and Wu which are based on the Kohn-Sham potential. The first is a method which reproduces an accurate input density (WY) and the second is an implementation of the optimised effective potential method. We find that these methods give results which are very similar to each other and when the methods are applied to a hybrid functional (e.g. B3LYP) we obtain good agreement with experiment. (C) 2004 Elsevier B.V. All rights reserved.