The Kyoto Protocol sets national quotas on GHG emissions and allows international trade of these quotas. Taking terms-of-trade effects into account, we argue that this trade is characterized by asymmetric, identity-dependent externalities, and show that bilateral trade of permits may not be sufficient for an efficient allocation of emissions. We derive conditions under which bilateral trade does improve the allocation of permits. The conditions are strong. In this sense, we argue that, for emissions permits, market design matters.