A number of litigated Australian native title cases concern lands located within the area of Australia known as the Western Desert. In these cases, legal arguments concerning the nature of the land-owning group and the 'society' at the time of colonisation have inevitably drawn on anthropological writings about Western Desert local and social organisation. The impetus for this paper was provided by the Yulara case, a compensation claim over the township of Yulara near Mum, in which the trial judge concluded that land tenure systems in the Western Desert are based on patrilineal principles. One of the significant factors in the Court's decision was an apparently uncritical acceptance of early anthropological models and data, which had reported supposedly patrilineal socio-territorial organisation in the Western Desert. Researchers currently working in this region and Indigenous peoples themselves, however, reject this model. In this paper, we question the validity of some of the earlier investigations, and propose an alternative understanding of Western Desert territorial organisation based on data gathered from one of the Pitjantjatjara-speaking people's neighbouring dialectal groups, which is also consistent with most of the other recent and extensive work done in this cultural bloc.