Most OECD countries use choice and competition within their education system. They give students and their families a choice of school and university, and ensure that funding follows these choices. The same is often true of pre-school and adult learning and skills services. They increasingly give state owned schools and universities operational autonomy to compete to be chosen, sometimes against rival not-for-profit providers. This creates incentives for schools and universities to become more efficient so that they can invest those savings in improving the quality of the education they provide. In this context, and given the huge importance of the sector, both in terms of productivity and inclusive growth, competition agencies may increasingly see education markets as a priority area in which to advocate for more effective competition. They may, for instance conduct market studies, provide opinions or advise education departments (in addition to taking enforcement action). This paper identifies that excessive deregulation risks incentivising competition on wasteful aspects of the service, and can generate outcomes that directly contradict important policy goals which can make policymakers reluctant to use competition to improve efficiency. Competition agencies will therefore need to instead advocate for markets that complement, and not contradict those policy goals, if they are to be successful. This paper was prepared as a background note for a discussion held at the OECD in June 2019 on publicly-funded education markets.