Correspondence tests on ethnic discrimination in the labor market usually focus on how often native majority candidates and ethnic minority candidates are invited for job interviews on an aggregated level. Cases in which only minority candidates are invited for an interview have mostly been disregarded as noise and not analyzed further. In this paper, we argue that employers who prefer minority over majority candidates may have good reasons to do so. We propose several theoretical mechanisms that explain why it would be desirable to hire individuals with a non-native background and test these expectations quantitatively with correspondence test data that was collected in Switzerland between October 2017 and December 2018. We find partial support for our expectations: in particular, in urban and thus likely more international firm settings; and among owners doing the recruitment themselves in the context of small enterprises, where close supervision is possible, we identified employers who are more willing to “take the risk” and to invite only minority applicants for a job interview. We argue that employer behavior is likely to be complex and that research should analyze instances of minority preferences more systematically.