We will show evidence in Sec. 4 from the results of LASSI[r,q] calculations that it is profitable to use different number of eigenstates for different fragments in different rootspaces, because whole categories of model states can be shown to be "deadwood" by examining the LASSI eigenvectors. In particular, we will show that to obtain qualitative agreement with CASCI, it is often not necessary to include "local excitations" (i.e., n K > 0), except where a particular fragment has a different number of electrons than in the reference LAS wave function.