Safeguarding the world's remaining forests is a high-priority goal. We assess the biophysical option space for feeding the world in 2050 in a hypothetical zero-deforestation world. We systematically combine realistic assumptions on future yields, agricultural areas, livestock feed and human diets. For each scenario, we determine whether the supply of crop products meets the demand and whether the grazing intensity stays within plausible limits. We find that many options exist to meet the global food supply in 2050 without deforestation, even at low crop-yield levels. Within the option space, individual scenarios differ greatly in terms of biomass harvest, cropland demand and grazing intensity, depending primarily on the quantitative and qualitative aspects of human diets. Grazing constraints strongly limit the option space. Without the option to encroach into natural or semi-natural land, trade volumes will rise in scenarios with globally converging diets, thereby decreasing the food self-sufficiency of many developing regions.