Article 17 of the Kyoto Protocol allows Annex B parties to meet their commitments by trading greenhouse gas emissions reductions "supplemental" to domestic emissions control. We demonstrate that implementing supplementarity by imposing concrete ceilings on imports of allowances in a market for tradable emissions rights gives rise to monopsonistic effects, even with price-taking behavior by both buyers and sellers. We assess the importance of this finding for Annex B emissions trading, in the context of the import and export provisions of the recent EU Proposal on supplementarity. Our results show that the proposal would reduce efficiency, and could significantly alter the distribution of the gains from trade in an Annex B tradable permits market.