This paper brings attention to the fact that the energy demand frontier model introduced by Filippini and Hunt (2011, 2012) is closely connected to the measurement of the so-called rebound effect associated with improvements in energy efficiency. In particular, we show that their model implicitly imposes a zero rebound effect, which contradicts most of the available empirical evidence on this issue. We relax this restrictive assumption through the modelling of a rebound-effect function that mitigates or intensifies the effect of an efficiency improvement on energy consumption. We illustrate our model with an empirical application that aims to estimate a US frontier residential aggregate energy demand function using panel data for 48 states over the period 1995 to 2011. Average values of the rebound effect in the range of 56-80% are found. Therefore, policymakers should be aware that most of the expected energy reduction from efficiency improvements may not be achieved.