The light-emitting electrochemical cell promises cost-efficient, large-area emissive applications, as its characteristic in-situ doping enables use of air-stabile electrodes and a solution-processed single-layer active material. However, mutual exclusion of high efficiency and high brightness has proven a seemingly fundamental problem. Here we present a generic approach that overcomes this critical issue, and report on devices equipped with air-stabile electrodes and outcoupling structure that deliver a record-high efficiency of 99.2 cd A-1 at a bright luminance of 1910 cd m-2. This device significantly outperforms the corresponding optimized organic light-emitting diode despite the latter employing calcium as the cathode. The key to this achievement is the design of the host-guest active material, in which tailored traps suppress exciton diffusion and quenching in the central recombination zone, allowing efficient triplet emission. Simultaneously, the traps do not significantly hamper electron and hole transport, as essentially all traps in the transport regions are filled by doping.