In order to avoid environmental catastrophe we need to move to a post-growth economy that can deliver rapid reductions in environmental impacts and improve well-being, independent of GDP growth. Such a move will entail considerable structural change in the economy, implying different goals and strategies for different economic sectors. So far there are no systematic approaches for identifying the desired shape of structural change and sectoral goals in terms of output, demand and employment. We present a novel analysis that addresses this gap by classifying economic sectors into groups with similar structural change goals. Our framework for the classification considers sectoral characteristics along three dimensions, which are (a) the final energy intensity, (b) the potential and desirability for labour productivity growth and (c) the relationship between labour productivity and the energy-labour ratio. We present empirical evidence on the three framework dimensions for economic sectors in the UK and Germany and derive structural change goals for the four sector groups representing particular combinations of the sector characteristics. Our analysis allows us to discuss the specific role of different economic sectors in the structural change envisioned in the post-growth transition and the most important challenges they might be facing.