How are political issues institutionalized? When do new ministries come into being? We content that once political issues regularly appear on the agenda, political actors, who are invested in solving an issue, construct permanent institutional venues to address them. Our argument on how new policy venues materialize fuses literature in public policy and coalition politics. The former claims that political agenda-setting occurs when political issues are processed and resolved by political systems, often disrupting a previous policy equilibrium. Here, agenda-setting is a political process. In contrast, governance literature holds that both incoming governments allocate and ministers use their portfolios for setting their legislative agenda. We call this second process institutional agenda-setting. Venue-making is the process by which political agenda-setting congeals into institutional agenda-setting. Instead of resolving issues only on the political agenda, venue-making happens when interest groups and government jointly benefit from the persistence of an issue on the legislative agenda. Our research design provides a probability probe that process-traces how political issues emerge and become institutionalized in three policy domains -- energy, environment, and digitalization -- across three countries -- Denmark, Germany, and Netherlands. We show that political issues first get on the agenda and provoke ministerial reorganization. Once institutionalized, more regular legislative output in that domain transpires. As such, political agenda-setting precedes institutional agenda-setting in parliamentary systems.