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Global warming, as a result of greenhouse gases, is exceeding the planet’s temperature stabilization capacities. Thus, greenhouse gas emissions must be reduced. We analyse a bankruptcy situation aimed at allocating emissions permits of CO₂, the predominant greenhouse gas emitted by human activities. Inspired by the Constrained Equal Awards (CEA) solution for bankruptcy situations, we introduce a new allocation protocol based on the extension of the CEA solution over double-weighted bankruptcy situations, including two exogenous parameters aimed at providing a balance, in the request of emissions permits, between economic activities and the production of renewable energy. In these bi-criteria allocation problems, we focus on a computational approach to find an allocation protocol that does not prioritize any particular parameter. As an application of our method, we first consider CO₂ permit allocation problems in European Union (EU) countries, using real data about the gross domestic product (GDP), the production rate of renewable energies, and countries’ ‘demands’ of CO₂ emissions from 2010 to 2014. Then, we compare our approach with the CEA solution and its single-weighted extension to show the impact of using two weights over the distribution of CO₂ emissions permits; we analyse the correlation between allocations of CO₂ emission permits and the distribution of power within the EU Council to study the acceptability of alternative allocations.