Major climate-cum-energy policies and respective impact projections rest on the widespread belief that increased energy efficiency can be equated with savings in energy use and emissions. This belief is flawed. Due to the rebound effect emissions savings from energy efficiency improvements will be generally less than what is technically feasible, or even be reversed. By means of an analytical general equilibrium model we demonstrate the latter to be true in a case that is both stark and relevant: if electricity generation is subject to a cap-and-trade scheme with partial coverage, increased efficiency of electric devices leads unambiguously to increased carbon emissions. The result implies that a proper distinction between the energy rebound and the carbon rebound is warranted, and that public policy must carefully consider the interactions between energy efficiency promotion and carbon pricing.