Despite the wide variety of agendas used in legislative settings, the literature on sophisticated voting has focused on two formats, the so-called Euro-Latin and Anglo-American agendas. In the current paper, I introduce a broad class of agendas whose defining structural features, history-independence and persistence, are common in legislative settings. I then characterize the social choice rules implemented by sophisticated voting on agendas with these two features. I also characterize the rules implemented by more specialized formats (called priority agendas and convex agendas) whose structure is closely related to the prevailing rules for order-of-voting used by legislatures. These results establish a clear connection between structure and outcomes for a wide range of legislative agendas.