Lead halide perovskites are promising semiconductors for light-emitting applications because they exhibit bright, bandgap-tunable luminescence with high colour purity(1,2). Photoluminescence quantum yields close to unity have been achieved for perovskite nanocrystals across a broad range of emission colours, and light-emitting diodes with external quantum efficiencies exceeding 20 per cent-approaching those of commercial organic light-emitting diodes-have been demonstrated in both the infrared and the green emission channels(1,3,4). However, owing to the formation of lower-bandgap iodide-rich domains, efficient and colour-stable red electroluminescence from mixed-halide perovskites has not yet been realized(5,6). Here we report the treatment of mixed-halide perovskite nanocrystals with multidentate ligands to suppress halide segregation under electroluminescent operation. We demonstrate colour-stable, red emission centred at 620 nanometres, with an electroluminescence external quantum efficiency of 20.3 per cent. We show that a key function of the ligand treatment is to 'clean' the nanocrystal surface through the removal of lead atoms. Density functional theory calculations reveal that the binding between the ligands and the nanocrystal surface suppresses the formation of iodine Frenkel defects, which in turn inhibits halide segregation. Our work exemplifies how the functionality of metal halide perovskites is extremely sensitive to the nature of the (nano)crystalline surface and presents a route through which to control the formation and migration of surface defects. This is critical to achieve bandgap stability for light emission and could also have a broader impact on other optoelectronic applications-such as photovoltaics-for which bandgap stability is required.