In a previous paper (Szalay, P. G.; Bartlett, R. J. J. Chem. Phys. 1995, 103, 3600) we reviewed all approximately extensive corrected multireference configuration interaction (MR-CI) methods and also proposed a new method called the multireference averaged quadratic coupled-cluster (MR-AQCC) method. In this paper we continue the investigation of these methods and propose new variants by including the effect of (a) virtual orbitals in the EPV (exclusion principle violating) contributions, (b) redundancies due to the MR nature of the reference space. Results of test calculations on water, Be-2, Be/H-2, ozone and NO2/HF systems are presented which show that these new methods are able to describe potential energy surfaces very accurately even if small, but qualitatively correct, reference spaces are used.