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Despite the growing research effort in formal verification, constraint-based random simulation remains an integral part of design validation, especially for large design components where formal techniques do not scale. However, stimulating important aspects of a design to uncover bugs often requires the construction of complex constraints to guide stimulus generation. We propose Toggle, a stimulus generation engine, which features (1) an entropy-based coverage analysis to efficiently find portions of the design inadequately sensitized by simulation and (2) a novel strategy to automatically stimulate these portions through a specialized SAT algorithm that uses small randomized XOR constraints. As our experimental results demonstrate, Toggle requires minimal input from the verification engineer, and significantly improves the coverage qualities of the generated stimuli when compared to plain random simulation.