The perfectly coalition-proof Nash equilibrium (PCPN) concept is extended to allow for the emergence of overlapping coalitions in equilibrium. We study the efficiency and stability properties of environmental agreements to control emissions of correlated continental and global pollutants. We show that set of PCPN equilibria includes perfectly strong Nash (PSN) equilibria if the national damage from continental pollution is sufficiently large relative to the national damage from global pollution. We also show that: (i) continental agreements may be perfectly coalition-proof under much less restrictive circumstances; (ii) perfect Nash equilibria for fully overlapped agreements may be superior to the Grand Coalition’s optimal allocation in the presence of coalitional operation costs; and (iii) PSN equilibria may still emerge in a larger world if coalition formation yields R&D spillover benefits.