Since the 1990s, Swiss immigration policies have placed increasing restrictions on non-European Union (EU) immigrants. However, in 2011, based on the initiative of Jacques Neirynck, the Swiss Parliament approved a law facilitating the admission and integration of non-EU nationals with a Swiss university degree. How can this policy openness in times of closure be explained? Drawing on the narratives of stakeholders during parliamentarian debates, and interviews with key political actors, we propose a unique explanatory approach combining: (1) the convincing "narratives of steering" crafted by parliamentarians, (2) an appropriate "temporal and geographical context," and (3) the "biographical capacity" of the policy initiator to effect policy change. This model will be useful for studies of migration policy change in general.