There is much disagreement in the literature over the extent to which graduates are mismatched in the labour market and the reasons for this. In this paper we utilise the Flexible Professional in the Knowledge Society (REFLEX) data set to cast light on these issues, based on data for UK graduates. We find substantial pay penalties for overeducation for both sexes and for overskilling in the case of men only. When both education and skill mismatch variables are included together in the model only overskilling reduces job satisfaction consistently for both sexes. Using job attributes data it appears that the lower wages of the overqualified may in part simply represent a compensating wage differential for positive job attributes, while for men at least there are real costs to being overskilled. (Contains 6 tables.)