Based on the escape cone concepts, high-brightness light-emitting diodes (LEDs) have been analyzed. In AlGaAs or InGaAlP LEDs, photon absorption in the ohmic region under the electrode is known to be significant. Thus, ins general, a thick window layer (WL) and a transparent substrate (TS) would minimize photon shielding by the electrodes and considerably improve photon output coupling efficiency. However, the schemes do not seem to be necessary in InGaN system. Photon absorption in ohmic contact to a wide bandgap semiconductor such as GaN may be negligible and, as a result, the significant photon shielding by the electrodes will not degrade the photon output coupling efficiency so much. The photon output coupling efficiency estimated in InGaN LEDs is about 2.5 - 2.8 times that of the conventional high-brightness LED structures based on both WL and TS schemes. As a result, the extenal quantum efficiency in InGaN LEDs is as high as 9% despite the presumably very low internal quantum efficiency.