The study on which this article is based shows that, in the context of the growing diversity of the Swiss population, linguistic resources related to regional variation are beginning to signify new ethno-national boundaries. This indexical change consists in excluding from the social meaning of a local variant the trait of majority ethnicity when alongside with foreign accent features, which cancels out the added value that migrant people might derive from the use of local variants. This result points to a paradox: the appropriation of linguistic resources by people with a migrant background that allow for social integration does not contribute to reducing their minorization.