This paper raises a number of issues in thinking about and addressing the intergenerational transmission of disadvantage. Starting with choice subject to constraints by parents as determining outcomes for children, the paper identifies sequences of interventions to relieve “binding constraints” in the expansion of education. But the fact that parents choose for children is shown to raise a number of questions on normative aspects of inequality measurement. The main conclusions are as follows: (i) A key analytical task is to identify whether education is supply constrained or demand constrained; (ii) The cost-benefit analysis of identifying the “most binding constraint” requires the estimation of an education quality production function; (iii) The recent focus on “quality as opposed to quantity” in education is not self-evidently pro-poor; (iv) The intergenerational links inherent in education between parental choice and children’s outcomes, raise serious conceptual and empirical questions on attempts to separate out inequality of opportunity from inequality of outcomes.