In this paper we re-examine the relationship between global Gross Domestic Product (GDP), Primary Energy Use (PEU) and Economic Energy Efficiency (EEE) to explore how investment in energy efficiency causes rebound in energy use at the global scale. Assuming GDP is a measure of final useful work, we construct and fit a biophysics-inspired nonlinear dynamic model to global GDP, PEU and EEE data from 1900—2018 and use it to estimate how energy efficiency investments relate to output growth and hence economy-wide rebound effects. We illustrate the effects of future deployment of enhanced energy efficiency investments using two scenarios through to 2100. The first maximizes GDP growth, requiring energy efficiency investment to rise ~ twofold. Here there is no decrease in PEU growth because economy-wide rebound effects dominate. The second scenario minimizes PEU growth by increasing energy efficiency investment ~ 3.5 fold. Here PEU and GDP growth are near fully decoupled and rebound effects are minimal, although this results in a long run, zero output growth regime. We argue it is this latter regime that is compatible with the deployment of enhanced energy efficiency to meet climate objectives. However, while output growth maximising regimes prevail, efficiency-led pledges on energy use and emissions reduction appear at risk of failure at the global scale.