EU aspires on being a forerunner in adopting a stringent climate policy. The present paper takes its departure in two observations from the current EU policy. First, the EU has adopted a dual approach in that there is a trading scheme, the EU ETS, covering CO2 emissions from the energy intensive industry, while the remaining emitters, e.g., housing and transportation, are subject to emission taxes. Second, the targets are quantitatively phrased, i.e., there is an upper limit on the total amount of CO2 emissions. Both this observations are of interest under the realistic assumption of abatement costs being uncertain. Then the dual approach is likely not to be ex post cost effective. Furthermore, from earlier literature it is known that an emissions tax outperforms a tradable permit scheme due to the nature of the green house effect. Thus, quantitative targets, which are easier fulfilled by means of a trading scheme, stand in contrast to taxes being the preferable policy instrument. The present paper addresses, by the means of a stylized model, the two observations and shows when and why a dual approach is optimal from an efficiency point of view given an upper limit on total emissions. What determines the characteristics of the optimal solution, e.g., size of the trading vs. taxed sector, tax levels and allocation to the trading sector, is studied in some detail.