The EU has proposed four flexibility mechanisms for the regulation of greenhouse gas emissions in the period 2013-2020: (1) the Emissions Trade Scheme (ETS), a permit market between selected companies; (2) trade in non-ETS allotments between Member States; (3) the Clean Development Mechanism (CDM) to purchase offsets in developing countries; and (4) trade in CDM warrants between Member States. This paper shows that aggregate abatement costs fall as flexibility increases. However, limited flexibility creates rents so that increasing flexibility raises costs in some Member States. Costs are reduced more by the CDM than by non-ETS trade. The CDM warrants market reduces costs by a small amount only; market power is a real issue. However, the warrants market is obsolete in case there is non-ETS trade. The CDM leads to price convergence between the ETS and non-ETS market. There would be one price for carbon in the European Union if the proposed limits on CDM access are relaxed slightly. © 2009 Elsevier Ltd. All rights reserved.