This paper considers what has hitherto been a relatively neglected subject in the wage inequality literature, albeit one that has been becoming more important over time, namely the role played by increases in postgraduate education. We document increases in the number of workers with a postgraduate qualification in the United States and Great Britain. We also show their relative wages have risen over time as compared to all workers and more specifically to graduates with only a college degree. Consideration of shifts in demand and supply shows postgraduates and college only workers to be imperfect substitutes in production and that there have been trend increases over time in the relative demand for postgraduate vis-à-vis college only workers. These relative demand shifts are significantly correlated with technical change as measured by changes in industry computer usage and investment. Moreover, the skills sets possessed by postgraduates and the occupations in which they are employed are significantly different to those of college only graduates. Over the longer term period when computers have massively diffused into workplaces, it turns out that the principal beneficiaries of this computer revolution has not been all graduates, but those more skilled workers who have a postgraduate qualification. This has been an important driver of rising wage inequality amongst graduates over time.