Our present economy is high-energy and demand-intensive, demand met through the use of high energy yield fossil fuels. Energy efficiency and renewable energy sources are proposed as the solution and named the ‘twin pillars’ of sustainable energy policy. Increasing energy efficiencies are expected to reduce energy demand and fossil fuel use and allow renewables to close the ‘replacement gap’. However, the simple fact is that fossil fuel use is still rising to meet increasing global demand and even when demand is stabilised, the substantial energy efficiencies achieved are not delivering the expected reductions in energy demand. The net effect is that efficiencies are gained and renewable energy use is increasing, even though the replacement of fossils is not an immediately plausible possibility. This points to the under-theorised problems in the ‘efficiency and replacement’ formula. We argue the need to pay closer attention to the ‘systemicity’ of the problem and to the technical and practical systems involved in energy demand. There are a number of detailed reasons why the ‘efficiency and replacement’ equation has become problematic (‘globality’, energy yield, ‘rebound’ and ‘momentum’ effects) and we include a short review of these and relate them to our ‘systemicity’ argument. We argue there is a need for better thinking, but also for a new primary instrument to drastically reduce energy demand and fossil fuel use. Attention should be urgently shifted from gains in energy efficiency to substantial year-over-year reductions in demand.