This paper focuses on an area of privatisation that has not to date received significant attention in educational research: the privatisation of infrastructure, facilities and maintenance, and in particular the labour of cleaning. Analysing the case of Victoria, Australia, we demonstrate how successive governments have defended the privatisation of cleaning labour on the basis that it allows schools to concentrate on the 'core' business of teaching and learning. Tracing the evolution of private contracts and public-private partnerships, we argue that the bracketing of cleaning work divides the types of labour carried out in the school, and thus the meaning and practice of public education. Thus, we suggest that controversies regarding the underpayment of cleaning staff, for instance, signal a deep problematic for public education as a whole.