  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 method, 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.
