We investigate theoretically the role of carrier trapping on the efficiency of single-layer organic light-emitting diodes (OLEDs) by incorporating traps into the OLED device model of Davids et al. [J. Appl. Phys. 82, 6319 (1997)]. Carrier trapping directly affects the density and mobility balance between electrons and holes through its effects on injection and mobility. In addition, trap-mediated changes in density alter recombination rates and spatial profiles of recombination that become important when excited state quenching at metallic contacts is considered. We illustrate these various influences of traps on device efficiency through computations on a series of model devices. Good agreement is obtained with previous experiments by Menon et al. [Chem. Mater. 14, 3668 (2002)], where energetic disorder from transport traps was shown to reduce device efficiency. Our model, however, predicts circumstances where traps will improve device efficiency as well and can assist with selection of contacts to realistic organic materials.