This article analyses the obstacles faced by graduates who benefited from a positive discrimination scheme at an elite French higher education institution. It adopts a Bourdieusian perspective enriched by research on the barriers encountered by socially mobile individuals from disadvantaged and stigmatised categories and studies the experiences of graduates who lack the economic, cultural, and social capital necessary to compete with traditional holders of elite positions and who, due to their ascribed characteristics and/or the positive discrimination label itself, are prone to self-eliminate from elite positions or be subjected to discriminatory practices. Using data collected through interviews with 42 beneficiaries of this scheme still in the early stages of their professional careers, the article shows that the graduates' disadvantages and ways of coping with them, as well their chances of being stigmatised and reactions to this process, vary considerably. This variation can be explained by different family backgrounds and ethnoracial characteristics but also by axiological positions towards employability and social mobility, with 'purists' more likely to invest in increasing their technical cultural capital to make up for 'handicaps' and 'players' more likely to put forward 'soft skills' including, in some cases, those associated with their 'diversity'.