  We present three modifications to our recently introduced fast randomized
iteration method for full configuration interaction (FCI-FRI) and investigate
their effects on the method's performance for Ne, H$_2$O, and N$_2$. The
initiator approximation, originally developed for full configuration
interaction quantum Monte Carlo, significantly reduces statistical error in
FCI-FRI when few samples are used in compression operations, enabling its
application to larger chemical systems. The semi-stochastic extension, which
involves exactly preserving a fixed subset of elements in each compression,
improves statistical efficiency in some cases but reduces it in others. We also
developed a new approach to sampling excitations that yields consistent
improvements in statistical efficiency and reductions in computational cost. We
discuss possible strategies based on our findings for improving the performance
of stochastic quantum chemistry methods more generally.
