International bargaining depends not only on the negotiators but also on the domestic political system in which they find themselves. Knowing this, countries often change domestic political institutions to influence the outcomes of international negotiations and/or to shape the domestic distributional consequences of those negotiations. This institutional change generally occurs in an already-rich institutional environment, where many different actors must jointly agree to modify existing institutions. To examine these, this paper develops a thirteen-actor model of U.S. trade policy institutions over the past century. Whereas the existing literature emphasizes the role of the median legislator in delegating to or constraining the executive, I find that changes in nonmedian procedural actors drive institutional reform in trade policy. Some of these procedural actors do not have veto authority and yet they play decisive roles, taking this analysis beyond veto player theory. The president can sometimes present these procedural actors with a choice that they can only make in a way favorable to him. As a result, small changes in the relative preferences of different nonmedian actors, such as the House Rules Committee or the key filibuster member of the Senate, can lead to large policy or institutional changes. These make a big difference in bargaining outcomes involving the United States and dramatically restrict the bargaining leeway enjoyed by negotiators.