While the time-honoured one-to-one supervisory model of higher research degree training has its advantages, recent research suggests that the model also has significant drawbacks, including its hierarchical nature. Nevertheless, this pedagogical model remains the default for higher research pedagogy. Using the discipline of music as a case study, where growing interest in practice-based research has lately demanded considerable fluidity in supervisory practices, this research explores the benefits and challenges of one-to-one models of supervision. Drawing on semi-structured interviews, dialogue forums, survey data, the extant literature and observations of practices at selected higher music education institutions in Australia, the UK, Belgium and the Netherlands, it recommends and suggests ways to implement more "horizontal" approaches to research pedagogy. The findings of this research may improve teaching and learning experiences and outcomes in higher research degrees in music and the creative arts, and stimulate a reflection of supervisory approaches more generally across the sector.