This paper analyzes the interactions between a number of key energy characteristics of German industrial plants in 2006, using an exceptionally rich dataset comprising more than 44 000 plants. Already by using basic descriptive statistical techniques we find that larger energy users tend to use energy less efficiently. This correlation is particularly prevalent in sectors with high energy intensity. We identify an energy mix effect as the main driver of this interrelation, since larger energy consumers tend to use less electricity in relation to other fuels, and electricity can be deployed more efficiently. The energy mix effect is also one of the reasons behind a negative correlation between energy intensity and the emission factor. From the correlation between plant-level energy intensity and gross output, we infer on the existence of increasing and decreasing returns to energy. We identify increasing returns to energy in most sectors, but decreasing returns to energy in some of the particularly energy intensive sectors.