In the study being reported here, heads of composition at a selection of music conservatoires (n = 6) in the UK were invited to share their experiences of teaching composition. Arising from the analysis of interview data, three main themes, termed 'pedagogical goals', emerged as important for undergraduate and postgraduate students to progress as composers. These included: becoming independent learners; developing one's own compositional voice; and building confidence. Findings revealed that these three themes and the pedagogical tools used to achieve them could create tensions between student expectations of what they believed traditional composition teaching to be. On top of this, the interviewees reported having to navigate increasingly neoliberal higher education policy and performativity measures such as the emphasis on student satisfaction, employability and the rising sense of competition between institutions, causing them to reflect on their role as professional educators. Implications for practice are highlighted, particularly around how conflicting priorities and expectations within creative subjects such as composing can in turn create pedagogical conflict. This calls for further research on how composers learn and develop, especially within higher music education contexts.