The external quantum efficiency of light-emitting diodes (LEDs) is usually limited by total internal reflection at the semiconductor-air interface. This problem can be overcome by a combination of light scattering at a textured top surface and reflection on a backside mirror. With this design, we achieve 22% external quantum efficiency. One of the main loss mechanisms in such nonresonant cavity (NRC) light-emitting diodes is coupling into an internal waveguide. Texturing the surface of this waveguide allows the partial extraction of the confined light. In this way, we demonstrate an increase in the external quantum efficiency of NRC-LEDs to 31%. (C) 1999 American Institute of Physics. [S0003-6951(99)03916-9].