Over the past two decades there has been a considerable increase in the number of referendums worldwide. The existing literature on direct democracy has so far failed to explain this phenomenon by delivering a consistent theory on the causes of referendums. This explorative study aims at undertaking steps toward closing this gap by focusing on the specific type of facultative government-initiated referendums (FGIR) and their use in presidential systems. Using QCA (a case-sensitive technique based on the formal logic of Boolean algebra), this study systematically compares the political opportunity structures of 49 presidential systems from 12 Latin American countries to detect the factors that spurred or obstructed the occurrence of FGIR. It concludes that FGIR are closely linked to high levels of party system fragmentation and divided government, i.e. two factors which have long been deemed problematic in the context of presidential systems, while their obstruction is mainly owed to the specific constitutional provisions regulating the referendum device.