Has Australian colonisation tended to ‘eliminate’ the Indigenous presence? The Australian government did not enact the logic of elimination—by ceasing to enumerate people as Indigenous Australians—when the referendum in 1967 showed popular support for the ‘inclusion’ of ‘Aborigines’. No longer distinguishing ‘Aborigines’ in the results of the census, thus ending the ‘Aboriginal population’, was a possible road to inclusion, but it was not taken. Rather, census policy 1961–1971 effectively enlarged the ‘Aboriginal population’. We argue that ‘the logic of elimination’ was resisted by a combination of Indigenous demand (for recognition), technical considerations (the unreliability of self-reported ‘caste’), and social scientists' and bureaucrats’ demand for better knowledge of Indigenous Australians.