This article explores how schools with below average attainment can support high-attaining learners in their decision-making about university. We report on a project involving longitudinal case studies of 43 high-achieving learners from a range of backgrounds across five institutions, during their sixth form career in 2013/14 and 2014/15, focusing on ways in which aspirations towards university develop. To understand schools' roles in supporting learners, we draw on Hart's analytical framework which sees the development of aspiration for higher education as a capability--the development of the opportunity freedoms of young people to pursue future trajectories that they have reason to value. We draw attention to the factors that facilitate or hinder this development, and highlight the key crunch points at which this feeds into young people's decision-making about university. We suggest that policy and practice should move beyond a traditional focus on the role of schools in raising aspirations amongst learners from non-traditional backgrounds. Instead, there should be a focus on how schools can support young people to develop a more comprehensive understanding of the university landscape, so that young people do not rule out options without fully understanding them. This will in turn lead to young people being able to make informed choices linked to future trajectories they have reason to value. 'Learning to play the game' of attending Russell Group universities needs to be seen as part of the development of this wider capability to aspire.