Summary: A revised fuzzy-set interpretation of possibility theory is introduced in this paper. Contrary to the standard fuzzy-set interpretation of possibility theory, which is coherent only for normal fuzzy sets, the revised interpretation is shown to be coherent for all fuzzy sets. It is also argued that the revised interpretation, which coincides with the standard one for normal fuzzy sets, is more meaningful on intuitive grounds. Prior to the introduction of the revised interpretation, previous efforts to overcome the well-known difficulties of the standard interpretation are critically examined, and it is demonstrated that none of them results in a coherent and meaningful interpretation of possibility theory.