In a previous paper we proposed a Projected Configuration Interaction method that uses sets of axially deformed single particle states to build up the many body basis. We show that the choice of the basis set is essential for the efficiency of the me
thod, and we propose a newly improved algorithm of selecting the projected basis states. We also extend our method to model spaces that can accomodate both parities, and can include odd-multipole terms in the effective interaction, such as the octupole contributions. %A universal algorithm of the choice of the PCI basis was presented in details. Examples of $^{52}$Fe, $^{56}$Ni, $^{68}$Se, $^{70}$Se and $^{76}$Se are calcualted showing good agreement with the full Configuration Interaction results.
