Efficiency droop is a serious concern in InGaN/GaN light emitting diodes (LEDs) in which the radiative efficiency decreases as the current through the device increases. Droop is widely believed to be associated with a non-radiative recombination mechanism that increases with carrier concentration faster than the approximately quadratic dependence of radiative recombination. In modeling nitride LEDs, defect-induced recombination is often assumed to depend linearly on the carrier concentration. However, this is not generally true. Many defects in semiconductors have multiple charge states and therefore multiple defect levels. Any given defect can only be in one of its charge states at a given time, and changes in charge state are associated with the capture or emission of carriers. As the carrier concentration increases, the predominant charge state of the defect can shift, opening up new defect levels for recombination. We will show that such multilevel defects can induce recombination that has a highly non-linear dependence on carrier concentration. Furthermore, using a microscopic InGaN/GaN LED model, we will show that a multilevel defect with plausible properties (concentration, defect levels, and capture cross-sections) can reproduce the essential features of the experimentally observed droop phenomenon for InGaN/GaN LEDs in the absence of Auger recombination. This work was supported by Sandia’s Solid-State Lighting Science Energy Frontier Research Center, sponsored by the Department of Energy Office of Basic Energy Science. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under Contract DE-AC04-94AL85000.