We demonstrate high-brightness and high-efficiency blue-green to yellow-green electrophosphorescent organic light-emitting diodes employing a series of organic Ir complexes [Ir-(C∧N)2(N∧N)]. Three different complexes have been synthesized showing high photoluminescence solid blend efficiencies up to 44%. A low current density increase of the electroluminescence (EL) external quantum efficiency (φEL(ext)) is observed and a maximum of φEL(ext)=10.6%±0.8% photon/e and power efficiency η=27±2 lm/W are achieved at a current density of j=0.01 mA/cm2. We examine various electronic processes that underlie a nonmonotonous current density dependence of the EL quantum efficiency of electrophosphorescent light-emitting diodes. The shape of φEL(ext) versus j is shown to reflect a trade off between electron-hole encounter and charge carrier transit times, electric field effect on electron-hole pair dissociation time, and current driven triplet molecular exciton lifetime.