In energy policy, efficiency improvements are conventional means for reducing industrial energy use as well as related environmental and climate externalities. Unfortunately, the effectiveness of energy efficiency improvements in reducing energy use is known to be limited by rebound effects. These rebound effects arise from economic and behavioral responses to the energy efficiency improvements themselves. In this paper, we show that their magnitude critically depends on the substitutability (or complementarity) of energy with different types of capital. These relationships between energy and capital must, hence, be carefully modelled in the context of rebound assessments. To this end, we develop a new, recursively dynamic computable general equilibrium model for Switzerland, which differentiates the capital stock into capital that is substitutable and capital that is complementary with energy. With this model, we simulate average economy-wide rebound effects of 38%; Sector-specific average rebound effects range from negative rebound effects for energy supply sectors to 48% for the energy-intensive manufacturing industry. The sector-specific results crucially depend on the energy and capital intensities of the respective sectors. A sensitivity analysis shows that our more sophisticated representation of capital lowers the simulated rebound effects. Conversely, existing rebound assessments with a homogenous capital stock may overestimate rebound effects. Nonetheless, both economy-wide and industrial rebound effects in Switzerland remain substantial. When devising energy efficiency policies, it is thus essential to evaluate the expected rebound effects and to compensate for them with complementary policies, such as energy and carbon taxes.