Increasing agricultural productivity to 'close yield gaps' creates both perils and possibilities for biodiversity conservation. Yield increases often have negative impacts on species within farmland, but at the same time could potentially make it more feasible to minimize further cropland expansion into natural habitats. We combine global data on yield gaps, projected future production of maize, rice and wheat, the distributions of birds and their estimated sensitivity to changes in crop yields to map where it might be most beneficial for bird conservation to close yield gaps as part of a land-sparing strategy, and where doing so might be most damaging. Closing yield gaps to attainable levels to meet projected demand in 2050 could potentially help spare an area equivalent to that of the Indian subcontinent. Increasing yields this much on existing farmland would inevitably reduce its biodiversity, and therefore we advocate efforts both to constrain further increases in global food demand, and to identify the least harmful ways of increasing yields. The land-sparing potential of closing yield gaps will not be realized without specific mechanisms to link yield increases to habitat protection (and restoration), and therefore we suggest that conservationists, farmers, crop scientists and policy-makers collaborate to explore promising mechanisms.