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Unilateral climate policy by the EU can be detrimental for global climate protection. Our purpose is to provide an economic analysis of this policy, to quantify the risk of carbon leakage, and to investigate economic effects related to the potential anti-leakage policy measures. We analyze existing definitions of carbon leakage and propose a new rigorous one. This is then tested using computable general equilibrium analysis for unilateral carbon dioxide abatement programs in the European Union in 2020, adopted under the United Nations Framework Convention on Climate Change (8%, 20% and 30% emission reduction relative to 1990). Our model of the global economy is disaggregated into three regions (the EU, the rest of the Annex I and non-Annex I countries). The analysis includes a decomposition of change in carbon emission using Logarithmic Mean Divista Index. While some anti-leakage measures (such as border tax adjustment on imports) reduce carbon leakage significantly, some of them are less effective. We found that output-based allocation of free emission permits to energy-intensive and trade exposed sectors reduce the leakage rate slightly, and a clean development mechanism -- depending how it is defined -- can either remove or increase carbon leakage. The results crucially depend on technical assumptions adopted in such models. We identified a list of parameters (like intra-import and Armington elasticities) which affect not only the magnitude but also the sign of carbon leakage rate. Manipulating with elasticities of substitution in production function suggests that in reaction to the unilateral action of the EU, the other regions may both increase or decrease their carbon emissions. Even though we are positive about computable general equilibrium models? application in this policy area, their policy simulations cannot be directly treated as policy recommendations without a careful validation of their assumptions.