Many immigrants are overqualified in their first job after arrival in the host country. Education-occupation mismatch can affect the economic integration of immigrants and the returns to education and experience. The extent of this problem has been measured in recent years by means of micro level data in Australia, North America and Europe. However, these papers have typically ignored the importance of allowing for heterogeneity, in particular by qualification level and years in the destination country. In this paper, we use data from the 1996, 2001 and 2006 New Zealand censuses to examine differences between each migrant’s actual years of education and the estimated typical years of education in the narrowly defined occupation in which they work. We find that migrants living in New Zealand for less than 5 years are on average overeducated, while earlier migrants are on average undereducated. However, once accounting for heterogeneity, we find that both overeducated and undereducated migrants become, with increasing years of residence in New Zealand, more similar to comparable native born. Convergence from overeducation is stronger than from undereducation.