While the literature concerning doctoral students has looked at institutional setup and socialisation of students within higher education structures and across disciplinary boundaries, so far, little attention has been given to the socialisation of PhD students in the intersections between strategic interdisciplinary research projects and monodisciplinary institutional structures, which is the aim of this article. The study is based on interviews with 32 PhD students and principal investigators affiliated with five research projects in the Excellence Programme for Interdisciplinary Research at University of Copenhagen, Denmark. In analysing this empirical material, the analytical concept of the 'implied student' has worked as a sensitising concept, highlighting the expectations of PhD students, principal investigators, the institutions, the educational system, and the encounter between them. In the interviews, the PhD students emphasise the conundrum of having to fit into a confined disciplinary role, while simultaneously being expected to cross boundaries and deliver on predefined goals in the interdisciplinary research projects. The findings show that students cope with these expectations by limiting the scope for improvisation and experimentation; in other words, suppressing what MacLure points towards as education's 'other'. This calls for greater attention to be paid to the accumulation of expectations heaped upon such PhD students and how this affects the education of the future generation of researchers.