In Stochastic-GAS, occupation number constraints (local or cumulative) are embedded within the precomputed heat bath (PCHB) excitation generation. Our algorithm does not incur runtime overheads to adhere to the GAS constraints, instead they are automatically accounted for by precalculated heat bath probability distributions. Moreover, the Stochastic-GAS dynamics automatically benefits from other recent development in FCIQMC, the adaptive shift with an offset, that greatly improves the convergence with respect to walker numbers.