We study the dynamics of equilibrium membership of an international environmental agreement aimed at increasing the stock of a global public good such as climate change mitigation. In contrast with previous studies, we assume partial cooperation among signatories, and show that the coalition size can be large and increasing over time even when the initial coalition size is small. We highlight a novel trade-off between agreements that are narrow but deep and long-lived versus those that are broad and shallow but short-lived. We show that loose cooperative agreements, which are broad but shallow and short-lived, are both welfare superior and Pareto superior to tight cooperative agreements, which are narrow but deep and long-lived. We also show that conditions exist under which the equilibrium coalition size is efficient.