Quantum dot light-emitting diodes are promising light sources for applications in displays. However, to date, there have been no reports of devices that simultaneously offer both high brightness and high external quantum efficiency. Here, we report red, green and blue quantum dot light-emitting diodes based on CdSe/ZnSe core/shell structures that have these attributes. We demonstrate devices with maximum external quantum efficiencies of 21.6%, 22.9% and 8.05% for red, green and blue colours with corresponding brightness of 13,300 cd m–2, 52,500 cd m–2 and 10,100 cd m–2. The devices also offer peak luminance of 356,000 cd m–2, 614,000 cd m–2 and 62,600 cd m–2, respectively. We postulate that this high performance is due to the use of Se throughout the core/shell regions and the existence of alloyed bridging layers at the core/shell interfaces. This study suggests that in the future visible quantum dot light-emitting diodes will also be suitable for lighting applications.