Sustainable grazing in the nationally iconic southern rangelands of Australia requires landholders to actively manage the grazing pressure from both domestic livestock and non-domestic herbivores. Landholders have primary responsibility for controlling the non-domestic herbivores. In doing so, they must meet the Australian public's expectations for resource conservation (mainly a public good) and animal welfare. Governments are also involved in the management of non-domestic herbivores via native and feral animal legislation and control programs. The Australian public will not accept cruelty to animals, perceived or otherwise. In this paper we explore the challenges faced by landholders in their attempts to manage the grazing pressure from native herbivores, particularly kangaroos, feral goats and feral pigs, while meeting the Australian public's expectations for animal welfare. Landholders typically live on extensive properties and their capacity to manage these is influenced by high climate variability, low labour availability, commodity price fluctuations and limited capital available for investment in new technologies. The additional requirement to reduce the grazing pressure from kangaroos, feral goats and feral pigs is a significant burden on already time-poor landholders. Hence, there is a critical disparity between landholders' capacity and their responsibility to effectively manage the non-domestic herbivores on their properties. We suggest that current expectations of landholders to deliver public benefits by publicly acceptable practices are unreasonable. Further, we suggest that governments should accept more responsibility for managing non-domestic grazing pressure. The concept of duty of care to land management provides a means by which a more appropriate division of responsibilities between landholders and government could be achieved to ensure that valued attributes of this iconic Australian landscape are retained.