Many commentators have seen the growing gap in earnings and income between those with a college education and those without as a major cause of increasing inequality in the United States and elsewhere. In this article we investigate the extent to which increasing the educational attainment of the US population might ameliorate inequality. We use data from NLSY79 and carry out a three-level decomposition of total inequality into within-person, between-person and between-education parts. We find that the between-education contribution to inequality is small, even when we consider only adjusted inequality that omits the within-person component. We carry out a number of simulations to gauge the likely impact on inequality of changes in the distribution of education and of a narrowing of the differences in average incomes between those with different levels of education. We find that any feasible educational policy is likely to have only a minor impact on income inequality.