The simplest stochastic implementation of GAS constraints consists in performing excitations using the conventional FCIQMC excitation generators and to discard GAS forbidden excitations a posteriori. The discarding GAS implementation can be easily combined with any already available FCIQMC excitation generator, including PCHB, and represents the natural choice for benchmarking more sophisticated GAS excitation generators, such as the GAS-PCHB algorithm, that a priori suggests only GAS allowed determinants. We have also implemented a discarding-GAS algorithm and found that when GAS constraints simply aim at removing deadwood configurations, the discarding-GAS performs surprisingly well, and it is rather challenging to develop GAS excitation generators that aim at excluding configurations a priori, without incurring overheads that make the discarding implementation faster in practice. We succeded in this task via the GAS-PCHB algorithm.