This article explores how supervisors of teachers preparing dissertations can create a space for the imagination in the tutorial setting. The imagination is seen as "opening up to possibility," where the student is taking a step into the unknown. The article discusses how the tutor can best support this, taking the theme of "holding the space for the student's learning." I consider how the development of a methodological stance that draws on existential and phenomenological perspectives supports inquiry into this aspect of the tutor role. An example of a tutorial is used to discuss this methodological approach, and to highlight key dimensions of the tutor's imaginative capacity in holding this space.