The aspiring composer's development is commonly described using the metaphor of finding one's own composer voice. A central goal for teaching composition in higher music education is to guide students toward finding such a voice--toward personal expression and creativity. In order to shed light on the teaching strategies associated with this goal, we analyzed composition teachers' views on their students' typical problems and how they deal with them. We conducted semistructured interviews with higher education composition teachers in Germany and Sweden. By means of thematic analysis, we identified two recurring problem situations. First, students might be insecure about what they want to achieve musically. To address this issue, teachers reported engaging students in self-reflection regarding their aesthetic preferences or specific compositional decisions. Second, students' work might not seem original enough. Teachers reported addressing this problem by providing new perspectives on students' music, for example, by prompting students to engage with their materials, acquire new experiences, or consider different musical parameters. Despite an ideal of creative freedom, the teachers thus retain authority over the aesthetic learning process by requiring adherence to a second ideal--that of originality. The findings could strengthen pedagogical practitioners' efforts to foster the creativity of young composers.