The scenario approach is a key tool in futures analysis. The likelihood of scenarios is evaluated by subjective judgment of analysts. In order to assert futures with higher certainty this article explores the notion of bounding scenarios. Making an analogy to the notion of mathematical bounds, bounding scenarios aim to exclude what will not occur rather than guess what will. The hope is that bounds established with a high degree of confidence can constrain the future in a useful way. We develop bounding scenarios through a case study of the potential for plant-level efficiency improvements to reduce net energy demand in the Chinese steel sector from 2008-2027. A lower bound is developed which reflects slow growth in industry output and rapid adoption of an idealized technology. The result is 0.9% annual average increases in energy use to 2027. The upper bound reflects dramatic growth in industry output and static technology, resulting in 9.5% average growth in net energy demand. Even rapid deployment of an idealized technology does not result in net reductions in energy demand. This suggests that managing climate and other energy issues should encompass strategies beyond plant level efficiency, such as efficiency of steel use. © 2012 IEEE.