This article modifies the conventional two-stage DEA model to construct an analytical model for energy-related efficiency with undesirable outputs. Our proposed model relaxes the constraint that the inputs of the second process must come from the first process. As a result, our proposed model is more flexible than the original model in terms of the application of energy-related efficiency measurement analysis, and more policy implications may thus be provided by the decomposition of efficiencies for different processes. For demonstration purposes, the proposed model is applied to measure the energy use efficiency and the economic efficiency of 28 OECD countries during 2005 to 2007. The demonstration results reveal the following three findings. First, the average values of energy use efficiency are smaller than those of the average economic efficiency during the three-year period. It is shown that the OECD countries are only interested in economic development and are not concerned about energy use efficiency. Second, a tradeoff relationship exists between energy use efficiency and economic development for the OECD countries. Third, the differences of the initial carbon dioxide (CO2) emissions from the optimal CO2 emissions as well as the average economic efficiency increase year by year. These results indicate that the OECD countries still discharge too much CO2. Finally, this article establishes a managerial decision-making matrix to divide 28 OECD countries into different positions according to their energy use and economic efficiencies, and provides improvement suggestions to policy makers.