We reassess the well-known “narrow-but-deep” versus “broad-but-shallow” trade-off in international environmental agreements (IEAs), taking into account the principal–agent relationship induced by the hierarchical structure of international policy. To this end, we expand the modest coalition formation game, in which countries first decide on whether to join an agreement and then decide on emissions by a strategic delegation stage. In the weak delegation game, principals first decide whether to join an IEA, then delegate the domestic emission choices to an agent. Finally, agents in all countries decide on emissions. In countries not joining the IEA, agents choose emissions to maximize their own payoff, while agents of countries joining the IEA set emissions to internalize some exogenously given fraction γ of the externalities that own emissions cause on all members of the IEA. In the strong delegation game, principals first delegate to agents, who then decide on membership and emissions. We find that strategic delegation crowds out all efforts to increase coalition sizes by less ambitious agreements in the weak delegation game, while in the strong delegation game the first-best from the principals’ point of view can be achieved.