Recently, a new energy correction to standard approaches of the coupled-cluster (CC) method has been proposed, namely the so-called (complete) renormalized CC method [K. Kowalski and P. Piecuch, J. Chem. Phys. 113, 5644 (2000) and references therein], as well as the energy-corrected CCSD approach [X. Li and J. Paldus, J. Chem. Phys. 117, 1941 (2002) and references therein], which are based on the method of moments of the CC method of Kowalski and Piecuch [Computational Chemistry: Reviews of Current Trends (World Scientific, Singapore, 2000), Vol. 5, p. 1]. These methods provide an efficient and noniterative, and thus less demanding, approach than do the iterative approaches and avoid, e.g., the fallacies of the standard CCSD(T) method. We show how this type of energy corrections may be related to Lowdin's projection and bracketing techniques and also to a standard extrapolation scheme which is applied here to the results of the new energy corrections. (C) 2003 American Institute of Physics.