Co-supervision of doctoral theses is on the rise worldwide, but we know little of the relational dynamics of the co-supervisory team and doctoral student. These teams often must work together for several years, during which supervisors may come and go. We interviewed 19 doctoral students about their experiences of co-supervision and found a complex team climate characterised by prior relations, merit- and network-gaining activities, and 'cushioning' adopted by supervisors to support the student during stressful periods. Doctoral students viewed themselves as passive and dependent -- as pawns in a bigger game -- suggesting that co-supervision might uphold the traditionally strong hierarchical structure of academia. We therefore suggest that all co-supervision teams discuss the roles and structure of supervision before commencing a research project.