ABSTRACT. Validation of complex digital circuitry primarily relies upon constrained-random simulation. However, it is intractable to simulate all satisfying assignments (models). Rather, sufficient verification coverage is achieved by selecting test stimuli uniformly at random from the set of valid models. The current state-of-the-art witness generators use hashing to perform this sampling near-uniformly. We present a new, perfectly-uniform witness generation algorithm based on the exact model counter sharpSAT and reservoir sampling. In experiments across hundreds of SAT benchmarks, our algorithm is faster than the state of the art by ten to over a hundred thousand times.