We study the internal and external quantum efficiencies of vacuum-deposited organic light-emitting devices (OLED's). The internal quantum efficiency of OLED's based on tris-(8-hydroxyquinoline) aluminum is calculated to be 5.7 times the observed external quantum efficiency ?(e), consistent with measurements. We demonstrate a shaped substrate that increases ?(e) by a factor of 1.9+/-0.2 over similar OLED's fabricated upon flat glass substrates and leads to a 100%-emissive aperture, i.e., the emitting area completely occupies the display area even in the presence of metal interconnects. We also discuss a substrate structure that increases ?(e) by an additional factor of 2. The high device efficiencies are promising for developing OLED-based displays with extremely low power consumption and increased operational lifetime.