In the direct democratic arena, the consensus of voters is required to deliberate policies; without that consent policies are blocked. When bills that support cultural diversity or foreigners’ integration are put into referendums, voters may or may not exert their veto power over the proposed policies. In order to determine under which circumstances these types of bills are successful in referendum, I have undertaken a fuzzy-set qualitative comparative analysis of 39 referendums about the extension of political rights to foreigners at the Swiss cantonal level. My analysis identified a total of five theoretically-informed conditions that explain citizenship liberalization and the success of popular votes. I then located these conditions within two configurational hypotheses which postulate how referendum proponents might overcome direct democratic hurdles. The analysis of the success of referendums reveals that the only sufficient path that leads to the popular vote’s success is to insert the sensitive issues into a multi-faceted bill. As demonstrated by a more in-depth case analysis, the sensitive object is successful because it is hidden from voters during the referendum campaign or because other priority objects inside the bill reduce its salience.