The European Emissions Trading Scheme for CO2 established in 2005 is the world's largest emissions trading scheme. Since it covers only some sectors of the European economies it can nevertheless not ensure that the Kyoto targets are reached at minimal cost. This paper first analyzes the conditions for cost efficiency in the current separated carbon markets accounting also for the possibilities of purchasing international carbon credits from outside the EU. A computable general equilibrium model is then used to assess the cost efficiency of current EU climate strategies. Finally, based both on the theoretical as well as the quantitative analysis, recommendations are derived for a better allocation of the reduction burden between the sectors participating in emissions trading, those that do not participate and international carbon purchases.