New theoretical framework for the method of moments of coupled cluster equations (MMCC) [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 18 (2000)] that, in a natural way, assures the connected form of the resulting MMCC corrections is discussed. In order to maintain the validity of the proposed expansion in the presence of strong quasidegeneracy effects, the regularization of the correlated part (gamma) of the overlap between the exact and approximate coupled cluster wave functions is required. It is shown that related approximations accounting for the effect of triples require a rudimentary form of the gamma-regularization (based on the regularization of cluster amplitudes) in order to provide results of completely renormalized CCSD(T) or better quality in situations when a single bond is broken (the HF molecule). For strongly correlated systems (C(2)) more efficient regularization schemes are required especially for stretched internuclear distances. Discussed type of the regularization procedure can also prevent the unphysical propagation of strong correlation effects through the products of cluster operators toward highly excited sectors of the Hilbert space.