Much concern has been expressed about the sustainability of fuelwood harvesting in Africa. Most models predict that demand will outstrip supply within a few decades, resulting in severe deforestation. However, despite substantial impacts of harvesting on woody vegetation structure, the ‘fuelwood crisis’ predicted since the 1970s has not materialized. We propose that this is at least partially because regeneration through coppicing has been poorly accounted for in most models. We developed a local fuelwood model that is demographically and spatially explicit, and that incorporates coppice dynamics. The model simulates the dynamics of multiple stem size classes (seedling, sapling, pole and adult), the harvesting decisions of villagers based on fuelwood availability and village demand across the landscape. Importantly, we specify size-dependent coppice production of cut stems, and the probability of progression of coppice shoots into larger size classes, after accounting for self-thinning of shoots. In general, our model projections for a rural South African savanna system suggest that current levels of harvesting (barring changes in human population size) are relatively sustainable. Declines in total woody biomass were predicted to be modest (˜20%), and the loss of intact stems of sapling size was predicted to be more than offset by increases in coppiced stems. Synthesis and applications. The results from our local fuelwood model clearly demonstrate that the impact of deforestation and wood removal on tree populations and wood resources is strongly influenced by the resprouting ability of trees. This highlights the importance of considering coppice dynamics when assessing the sustainability of wood harvesting. Our model is not system specific, and can be transferred to other systems, with the relevant parameters and geographic information system layers specified. Because of the transferability of this model, it can help address key international concerns about deforestation and sustainable fuelwood management.