In FCI-FRI the fully-weighted PCHB particle selection was combined with fully-weighted Power-Pitzer hole-selection. Based on the previous discussion, our improvements to the sampling of double excitations in PCHB are twofold: (a) we suggest optimal combinations of fast-, fully-weighted, and uniform sampling depending on general features of the systems investigated, and (b) we improve the sampling speed from constrained distributions. We will present these improvements separately in the next two subsections.