Based on the classic models developed by Spady and Tinto on the link between social and academic integration and dropout, we propose a refined model to explain dropout intentions–relating to dropout from higher education (HE) and dropout from a specific study programme–that more strongly emphasises individual background characteristics (e.g. gender, social origin, and immigration background). Additionally, we consider students’ satisfaction with the institutional support structures. Using Eurostudent survey data, this conceptual model was tested using structural equation modelling in the international and diverse HE context of Luxembourg. While the fitted model confirmed most of the expected associations of the conventional Spady–Tinto approach, initial study commitment was not linked to social integration (contacts with fellow students). We were able to identify satisfaction with institutional support as a key factor in explaining dropout intention, thus contributing to existing knowledge. In addition, we found that the link between socioeconomic factors and dropout intention from a study programme is not entirely mediated by the Spady–Tinto factors of commitment and integration. © 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.