Supervision is generally recognised as playing a crucial role in the quality of a research student's doctoral experience and their academic outcomes and, in common with most areas of higher education, there is an oft-stated desire to pursue excellence in this important area. Excellence in research degree supervision is, however, an elusive concept and on close scrutiny most of the discussions of high-quality supervision, even those that purport to be identifying excellence, refer to competence rather than excellence. This paper examines two potentially national authoritative perspectives from which excellence in research degree supervision might be explicated (codes of practice and learning and teaching awards) from Australia, New Zealand, South Africa and the United Kingdom but concludes that the complex nature of the activity and the complexity of the concept itself mean that rather than identifying excellence in supervision we can only respond to claims for excellence.