We present device model calculations for the current–voltage (I–V) characteristics of organic diodes and compare them with measurements of structures fabricated using MEH-PPV. The measured I–V characteristics have a Fowler–Nordheim (FN) functional form, but are more than three orders of magnitude smaller than the calculated FN tunneling current. We find that the low mobility of the organic materials leads to a large backflow of injected carriers into the injecting contact. These results account for the experimental observations and also demonstrate how transport layers in multilayer organic light-emitting diodes can be used to improve carrier injection.