Integration has become a keyword across texts and genres, and is often uncritically embraced not only by politicians and journalists but also by academic researchers. This paper explores how integration is used in reference to people categorized as “migrants“ or “foreigners“. It discusses intertextual links between a wide range of texts from different European countries, including official policy documents, print media texts and academic publications. It has deliberately chosen liberal and progressive texts rather than the texts of the extreme right, since the objective is to show how even in liberal texts, the use of the concept of integration is frequently informed by illiberal assumptions and ideologies. This study aims to lay bare the cultural or discourse models underlying the use of the concept of integration. It compares and contrasts three discourse models of integration, which were labelled as the centre-periphery, mathematical game and statistical correlations models. It is shown how one particular text shuttles between models and examines the pernicious consequences of the linguistic choices made in the text. The paper concludes with a call for greater awareness of the potentially discriminatory ideological frameworks within which the term “integration“ functions.