This article explores the making of immigrant families as precarious elements in the governing of the population's welfare within the Danish welfare nation-state since the 1970s. The emphasis is on how immigrant families became a problem of welfare governing, and what knowledge practices and welfare techniques emerged as problem-solving responses. The article analyses a diverse set of national and local administrative documents advancing a polyhedron of intelligibility by which the authors discover how problem-solving complexes responsive to immigrant families change and sediment, and ultimately, weave the fabric of a Danish welfare nation-state faced with non-Western immigration after the economic boom in the late 1960s.