The efficiency of electroluminescent organic light-emitting devices, can be improved by the introduction of a fluorescent dye. Energy transfer from the host to the dye occurs via excitons, but only the singlet spin states induce fluorescent emission; these represent a small fraction (about 25%) of the total excited-state population (the remainder are triplet states). Phosphorescent dyes, however, offer a means of achieving improved light-emission efficiencies, as emission may result from both singlet and triplet states. Here we report high-efficiency (≳90%) energy transfer from both singlet and triplet states, in a host material doped with the phosphorescent dye 2,3,7,8,12,13,17,18-octaethyl-21H,23H-porphine platinum(II) (PtOEP). Our doped electroluminescent devices generate saturated red emission with peak external and internal quantum efficiencies of 4% and 23%, respectively. The luminescent efficiencies attainable with phosphorescent dyes may lead to new applications for organic materials. Moreover, our work establishes the utility of PtOEP as a probe of triplet behaviour and energy transfer in organic solid-state systems.