Promoting energy efficiency is generally assumed to be an effective strategy to reduce energy use and tackle climate change. However, an extensive literature has shown that rebound effects reduce its effectiveness and can even be counterproductive. We show how a more complex policy strategy, with coordinated measures, could provide the desired results by offsetting energy and carbon rebound effects. Along with the energy-efficiency improvement, we separately implement five different policies: carbon taxes, energy production taxes, an emissions trading system, and changes in consumption patterns (away from energy and toward services consumption). These policies are assessed using an economy–energy–environment dynamic Computable General Equilibrium (CGE) model developed for Catalonia, and compared in economic, energy, and environmental terms. The simulations show that all the strategies tested are able to offset rebounds at a low cost, with a proper design. All of them improve GDP in relation to the no-efficiency improvement base case. If tax revenues from the parallel policies are used to encourage investment, the long-term effect on GDP may even be positive. Jaume Freire-González received the support of the Beatriu de Pinós postdoctoral program of the Government of Catalonia's Secretariat for Universities and Research of the Ministry of Business and Knowledge. Mun Ho is supported by the Harvard Global Institute.