We find that extremely shallow quantum wells (QW's) are capable of modulating high-intensity light due to the enhanced sweep out of photogenerated carriers. These QW's are especially well suited for use in self-electrooptic effect devices (SEED's) due to the existence of a strong room-temperature exciton that ionizes rapidly with field. For a 3-mu-m-diameter spot, we obtain bistable reflectivity changes (for a symmetric-SEED arrangement using a 7 V power supply) of 18% at 1 mW (24 kW/cm2), 10% at 2 mW, and 4% at 3 mW compared to 6.8% at 0.4 mW for our previous best sample.