The dissertation is a highly valued form of teaching and learning in higher education, yet the practice of undergraduate supervision is understudied and under-theorised. Effective supervision is regarded as essential to student success -- by students and supervisors alike, although training, resources and support for supervisors is limited. Drawing on data from qualitative questionnaires with eleven supervisors, this paper utilises the concept of teaching dilemmas to explore tensions and challenges within supervision. Three dilemmas were identified regarding 'taking ownership', 'driving supervision' and 'challenging and encouraging'. Underpinning all of these was a tension between an ideal model of supervision (characterised by high levels of engagement from students and supervisors), and the need to flexibly adapt supervisory practice to suit students' learning styles, needs and abilities. We suggest ways in which conceptualising supervision as a dilemmatic space could inform future research and training in supervisory practice.