The melting-pot argument, whereby economically heterogeneous multi-cultural societies, characterised by high levels of immigration from a variety of origins, become more homogeneous over time, has attracted much attention, especially in North America. Australia has similarly experienced major waves of immigration from a wide range of cultural backgrounds. This paper reports successful tests of hypotheses, derived from the melting-pot model, that economic integration of immigrant groups there has also resulted in reduced inter-group occupational and income differences across successive generations, but that the pace of integration can vary across ethnic groups. Using a bespoke tabulation from the 2011 Australian census we explore differences among ten immigrant (ancestry) groups in their educational qualifications, and their occupational and income distributions, using a recently developed method to identify significant patterns within large contingency tables. We find that by the third generation there were no substantial differences either across the ten groups chosen to represent four main waves of immigration to Australia or between these groups and the non-immigrant population.