This paper uses a model with Directed Technical Change to theoretically analyse observable heterogeneous energy intensity developments. Based on the empirical evidence, we decompose changes in aggregate energy intensity into structural changes in the economy (structural effect) and within-sector energy efficiency improvements (efficiency effect). The relative importance of these effects is determined by energy price growth and sectoral productivities that drive the direction of technical change. When research is directed to the labour-intensive sector, the structural effect is the main driver of energy intensity dynamics. In contrast, the efficiency effect dominates energy intensity developments, when research is directed to energy-intensive industries. Increasing energy price generally leads to lower energy intensities and temporal energy price shocks might induce a permanent redirection of innovation activities. We calibrate the model to empirical data and simulate energy intensity developments across countries. The results of our very stylised model are largely consistent with empirical evidence.