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 (φ _EL ^{( ext )}) is observed and a maximum of φ _EL ^{( 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 / cm ² . 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 φ _EL ^{( 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.