While the sustainable development goals (SDGs) are most challenging for developing countries, they apply equally to OECD member countries and are important to consider during these countries’ energy transition. Low energy demand (LED) scenarios, modelled with energy system optimisation models (ESOMs), show that there is potential for meeting national and global climate mitigation targets more economically and with less technological uncertainty, while buying time during the transition. Some LED scenario narratives envisage deeply transformative societal changes, while others are more focused on demand reduction with technology improvement measures such as energy efficiency. In a review of 11 LED modelling studies, demand reductions by 2050, compared to 2020, range from moderately (8%) to much higher (56%) than non-LED scenarios. SDG targets for OECD countries that are most likely to be negatively affected by a LED approach are poverty (1.2), overcoming inequality (10.1), and participatory decision making (16.7). Those SDGs more likely to see win-wins include access to energy (7.1), renewable energy (7.2), energy efficiency (7.3), and use of resources (12.2). When modelling LED scenarios in ESOMs, there should be more representation of the rebound effect and feedback between demand and economy, heterogeneity in societal responses to LED-type policies, and the idea of sufficiency to better reflect the novelty of pathways to achieving LED scenario narratives.