A green-light-emitting iridium(III) complex was prepared that has a photoluminescence quantum yield in a thin-film configuration of almost unity. When used in a simple solid-state single-layer light-emitting electrochemical cell, it yielded an external quantum efficiency of nearly 15% and a power efficiency of 38 Lm/W. We argue that these high external efficiencies are only possible if near-quantitative internal electron-to-photon conversion occurs. This shows that the limiting factor for the efficiency of these devices is the photoluminescence quantum yield in a solid film configuration. The observed efficiencies show the prospect of these simple electroluminescent devices for lighting and signage applications.