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Land is under pressure from a number of demands, including the need for increased supplies of bioenergy. While bioenergy is an important ingredient in many pathways compatible with reaching the 2 °C target, areas where cultivation of the biomass feedstock would be most productive appear to co-host other important ecosystems services. We categorize global geo-data on land availability into productivity deciles, and provide a geographically explicit assessment of potentials that are concurrent with EU sustainability criteria. The deciles unambiguously classify the global productivity range of potential land currently not in agricultural production for biomass cultivation. Results show that 53 exajoule (EJ) sustainable biomass potential are available from 167 million hectares (Mha) with a productivity above 10 tons of dry matter per hectare and year (tD Mha⁻¹ a⁻¹), while additional 33 EJ are available on 264 Mha with yields between 4 and 10 tD M ha⁻¹ a⁻¹: some regions lose less of their highly productive potentials to sustainability concerns than others and regional contributions to bioenergy potentials shift when less productive land is considered. Challenges to limit developments to the exploitation of sustainable potentials arise in Latin America, Africa and Developing Asia, while new opportunities emerge for Transition Economies and OECD countries to cultivate marginal land.