The origins of this paper lie in an article I wrote for a forthcoming volume of the Encyclopaedia of Popular Music of the World on jazz outside the US, which then led me to the question of how and why jazz, a music identified so closely with both 'primitive' blackness and with US modernity, became assimilated to national identities in most of its diasporic destinations by the late twentieth century. In almost all those destinations jazz was initially regarded as deeply disruptive to the traditions, myths and power relations on which local identity was built. Yet within a matter of decades jazz was being made to feel fully at home in these diasporic sites, and by the late twentieth century it is certainly arguable that these sites had overtaken the US as the new 'centres' of jazz innovation. How was this radical reversal achieved? My paper focuses on Australia, but because the pattern is global, it will cast explanatory light on all diasporic jazz.