The European Council is the highest political body of the European Union and the main venue for setting the agenda on high politics. Using a new dataset of all content-coded European Council Conclusions issued between 1975 and 2010, we analyze the policy agenda of the European Council and test hypotheses on agenda change and diversity over time. We find that the theory of punctuated equilibrium applies to the agenda of the European Council, which exhibits a degree of kurtosis similar to that found in policy agendas of other institutions located at the juncture between input and output of the policy process. Throughout the 36-year period, agenda-setting dynamics involved both small changes and major shifts but also more frequent medium-sized negative changes than found elsewhere. Given capacity limits to the agenda, large expansions of attention to topics involved large cuts in attention. Cuts were more often medium in size in order to maintain some level of attention to the topics affected, even though issue disappearance from the European Council agenda has been frequent too. This relates to the functions of the European Council as venue for high politics, with expectations about issue attendance rising with increasing policy jurisdictions throughout the European integration process. Studying dynamics over time, we measured entropy to show how the agenda became more diverse but also displayed episodic concentration in an oscillating pattern. This can be accounted for by the nature of the European Council as a policy venue: increasing complexity of this institution pushed the members to produce a more diverse agenda, but capacity limits and the need to be responsive to incoming information led to concentration at specific time-points.