This research aims at clearing up misunderstandings about the distributive impacts of carbon taxes, which proved to be a decisive obstacle to their further consideration in public debates. It highlights the gap between partial equilibrium analyses, which are close to the agents' perception of the costs of taxation, and general equilibrium analyses, which better capture its ultimate consequences. It shows that the real impact on households' income inequality is not mechanically determined by the initial energy budgets and their flexibilities but also depends upon the way tax revenues are recycled and its general equilibrium consequences. The comparison of five tax-recycling schemes highlights the existence of trade-offs between maximizing total consumption, maximizing the consumption of the low-income classes and reducing income inequality.