We describe a model of international, multidimensional policy coordination where countries can enter into selective and separate agreements with di®erent partners along di®erent policy dimensions. The model is used to examine the implications of negotiation tie-in|the requirement that agreements must span multiple dimensions of interaction|for the viability of multilateral cooperation when countries are linked by international trade °ows and transboundary pollution. We show that, while in some cases negotiation tie-in has either no e®ect or can make multilateral cooperation more viable, in others a formal tie-in constraint can make an otherwise viable joint multilateral agreement unstable.