We investigate a central issue in the climate change debate associated with the Kyoto Protocol: the likely performance of international greenhouse gas trading mechanisms. Virtually all design studies and many projections of the costs of meeting the Kyoto targets have assumed that an international trading program can be established that minimizes the costs of meeting overall goals. This conclusion rests on several simplifying assumptions. We focus on one important issue that has received little, if any, attention: the interaction between an international trading regime and a heterogeneous set of domestic greenhouse policy instruments. This is an important issue because the Protocol explicitly provides for domestic sovereignty regarding instrument choice, and because it is unlikely that most countries will choose tradable permits as their primary domestic vehicle. It is true that costs can be minimized if all countries use domestic tradable permit systems to meet their national targets (allocate permits to private parties) and allow for international trades. But when some countries use non-trading approaches such as greenhouse-gas taxes or fixed quantity standards -- which seems likely in the light of previous experience -- cost minimization is hardly assured. In these cases, achieving the potential cost savings of international trading will require some form of project-by-project credit program, such as joint implementation. But theory and experience with such credit programs suggest that they are much less likely to facilitate major cost savings, because of large transactions costs, likely government participation, and absence of a well functioning market. Thus, individual nations' choices of domestic policy instruments to meet the Kyoto targets can limit substantially the cost-saving potential of an international trading program. There is an important trade-off between the degree of domestic sovereignty and the degree of cost effectiveness. Moreover, there is a need to analyze the likely cost-savings from feasible, as opposed to idealized, international policy approaches to reducing emissions of greenhouse gases.