Limited previous experience with the mean value total dressing (MVTD) method had shown that MVTD energies for closed shell systems are generally better than CCSD(T) ones compared to FCI. The method, previously published as total dressing 2′(td-2′), is based on the single reference intermediate Hamiltonian theory. It is not a CC method but deals in a great part with the same physical effects that CC methods that incorporate amplitudes of triples such as CCSDT or its CCSDT-1n approaches. A number of test calculations comparing to diverse CC methods, as well as FCI and experiment when available, have been performed. The tests concern equilibrium energies in NH3 and CH2, equilibrium energies and distances in some diatomics (BF, NO+, CN+, C2, BeO), different bond breaking situations (H2O, BH, HF, SiH2) and spectroscopic properties of different bonding conditions (Li2, LiNa, LiBe+, NeH+, and O3). The results are in general closer to the full CCSDT ones in the equilibrium regions and close to CCSDT-1 along most dissociation curves. A few exceptions to this rule are analyzed with the help of an approach to MVTD that does not take into account the effects of linked quadriexcitations. Such analysis suggests the interest of improving the treatment of effects of linked triples in the MVTD model. The separate contributions of linked and unlinked triples and quadruples are also analyzed for some of the above diatomics representing different behaviors of bond breaking. The interest of such analysis is illustrated in the NeH+ molecule. The MVTD results show, in general, a high quality, provided that the nature of the correlation problem does not become largely multiconfigurational, as occurs in multiple bond dissociation or in the asymmetric stretching of ozone.