This Paper uses coincidence analysis (CNA) to examine the pattern of contributions to the 2011 military intervention in Libya and the air strikes against the self-proclaimed Islamic State. More specifically, CNA is used to examine the complex relationship between military deployment decisions, external threats, public opinion and domestic institutions. The extensive body of academic literature that examines the relation between public opinion and foreign policy offers competing hypotheses on the link between military interventions and public opinion. While some scholars argue that mass publics have a consistent influence on foreign policy decisions, others suggest that public support itself is a function of the rallying around the flag effect that follows a military intervention. Given these competing views, it is not possible to categorize the variables into possible causes and possible effects prior to the analysis. Moreover, both mass publics and decision makers might support military intervention when national interests are threatened. The variable “Threat” might thus cause both the intervention itself and public support for the intervention. Finally, some variables can be both cause and effect. Military deployment might, for example, be the effect of “Threat” and the of cause public support. CNA should be the most appropriate method to examine the complex causal structure under investigation. Baumgartner, who introduced the method in 2009, argues that CNA’s ability to identify causal structures that involve multiple effects and mutually dependent causes, such as causal chains and common cause structures constitutes a distinct advantage over Qualitative Comparative Analysis. However, CNA has so far barely been applied in empirical research. Next to uncovering the causal model behind the pattern of contributions to the two operations under investigation, this paper therefore aims to shed light on the distinctive advantages of CNA in applied research.