Tolerance of uncertainty is crucial in creative practice-led PhD projects. This paper draws on our combined experiences as an Iranian born candidate and a German born supervisor negotiating their supervisory relationship in Aotearoa/New Zealand. We argue for the vital role of negotiated territories, threshold spaces of potentiality, in PhD supervision. While we take this to be crucial in all PhD projects exploring a research topic creatively, it is even more important for candidates who are not what Taylor & Beasley (2005) call “traditional candidates”. They and their supervisors often have to confront tensions resulting from different world views. The field of difference and differential power between them can be imagined as a threshold, limiting and divisive at times, but also providing possibilities for change, dialogue and discovery.