Agenda-setting theory has a long tradition within policy studies but took a major leap forward with the work of Baumgartner and Jones and their formulation of punctuated equilibrium theory (PET). Since then, an extensive literature has developed, both evaluating the notion of punctuated equilibria from a comparative perspective and providing ideas for a broader theoretical development on political processes. The original formulation of the theory was based on the US political system, whose institutional elements make it a likely case to observe the type of political processes that PET highlights. Subsequent comparative studies have demonstrated that the theory’s idea is of general relevance in two regards. First, factors, such as issue characteristics, operate similarly across political systems. Second, political institutions shape agenda-setting processes. This paper expands on the political institutional features that are particularly important when applying PET to a West European context. We illustrate the interplay of these institutional characteristics with the political process regarding the German debate on digitalization.