GaInN/GaN multiple-quantum-well light-emitting diodes (LEDs) with 0.4 µm-thick AlGaN cladding layers and two quantum wells (QWs), designed for investigating the origin of efficiency droop, are demonstrated to have a lower efficiency droop than typical GaInN/GaN LEDs with 5 QWs. Considering the much less electron leakage over the active region, and the larger carrier density due to the smaller active volume of the LED with AlGaN cladding layers than those of the typical LED, it is suggested that the dominant mechanism responsible for the efficiency droop is electron leakage rather than the Auger recombination which scales with the cubic power of the carrier density.