Abstract: This case study is constructed from an anthropological perspective. An anthropological analysis has a particular kind of contribution to make in a situation such as a census enumeration, in which members of an encapsulated cultural minority are interacting with the institutions of the encapsulating state. I want to convey how the census enumeration appears to the Yolngu—particularly the Community Coordinators (CCs) and collector-interviewers (CIs)—in order to understand some of the problems that arise and what their possible solutions might be. The census, being a dwelling-based count, is founded on assumptions about the characteristics of populations that fit sedentary settler societies such as mainstream Australia, but which do not fit populations such as the Yolngu, who, as I have argued elsewhere (Morphy 2007), behave in ‘radically uncontained’ ways. I am concerned to explore the consequences of this for the Indigenous Enumeration Strategy (IES) in general, and its impact on the role of the Census Field Officer (CFO) in particular. I have also chosen to structure the major part of this case study as a chronological narrative of the count in four phases, to convey a sense of just how difficult a task it is to ‘capture’ this mobile population, and as a background to what might sometimes appear to be critical comments about how the 2006 enumeration was managed. There is no self-evident and easy strategy; however, in the way in which it is currently constituted, the CFO’s job is all but impossible. I am not asserting necessarily that the current collection methodology results in a significant over or under-count, rather that the expectations put on the CFO are unrealistic and unattainable, and this makes the job unnecessarily stressful. I also want to demonstrate that the mobility of the population, although radical, is not random; it takes place within particular parameters. Once these are understood, it becomes easier to devise more efficient enumeration strategies. I will argue that such strategies will depend crucially on making best use of local knowledge, not only of the CCs and CIs, but of the staff—Indigenous and non-Indigenous—of local organisations whose primary task it is to provide local populations with services and infrastructure. The patterns of mobility that I describe below are peculiar to this particular region and cannot necessarily be generalised to others. In each region, however, there are organisations that are repositories of knowledge about the characteristics of local population mobility. I will be suggesting that the Australian Bureau of Statistics (ABS) needs to engage in long-term relationships with these organisations and help them build their capacity to better understand the local dynamics of mobility. This in turn will deliver to the ABS, come census time, key individuals who will be in a position to help in significant ways with the organisation of the census enumeration.