It has been argued by some (e.g. the Confederation of British Industry [CBI]) that graduates lack the skills that render them employable. In particular, graduates of science, technology, engineering and mathematics (STEM) subjects are often portrayed as being unready for the world of work. This study uses three large-scale national data-sets from the UK to explore this assertion, including the results of the Destinations of Leavers from Higher Education surveys. It reports analysis of 22,207 individuals who graduated from their first degree in 2007, and works from the hypothesis that those entering the workforce and then returning for taught postgraduate study are primarily doing so due to underemployment in the period following graduation. The study uses binary logistic regression and finds that a range of educational, demographic and employment-based variables have a significant relationship with the propensity to return for taught postgraduate study. Of particular note, those returning tend to be high achievers from elite universities in low-skill work after graduation, as well as women and those from minority ethnic communities; this suggests a mix of individual and structural factors at work. In addition, STEM graduates were significantly less likely to return, apparently challenging the argument advanced by the CBI.