This article investigates the relevance of spatial assimilation theory in Copenhagen, Helsinki, Oslo, and Stockholm. An important backdrop is the "Nordic model of welfare": We assume that welfare generosity decreases the speed of spatial integration. The study uses non-Western immigrants as a target group and natives as a reference group. We register location in 2000 and 2008, and analyze integration in terms of neighborhood status and residential segregation. The results show, in all cities, a lack of aggregate upward mobility in the spatial hierarchy. We also find a negligible effect of upward earnings mobility on upward spatial mobility. Upward spatial mobility increases integration in ethnic terms, but other factors work in the opposite direction and contribute to prevailing segregation. The results as a whole strengthen the purported association between welfare state characteristics and spatial integration. Deviant outcomes, particularly in Helsinki, are explained by immigration history and housing market structure.