The so-called reduced multireference (RMR) coupled cluster method restricted to singly and doubly excited clusters (CCSD) [see X. Li and J. Paldus, J. Chem. Phys. 107, 6257 (1997)] is employed to compute potential energy surfaces for the HF, F-2 and H2O molecules over a wide range of geometries using basis sets of a double zeta (DZ) and DZ plus polarization (DZP) quality. The RMR-CCSD method belongs to a class of externally corrected CCSD approaches, which rely on a suitable non-CC wave function that is flexible enough to describe the dissociation process at hand and is used as a source of 3- and 4-body cluster amplitudes. These amplitudes are in turn used to achieve a more appropriate decoupling of the full CC chain of equations than that leading to the standard CCSD equations. The RMR-CCSD method employs for this purpose a MR-CISD wave function obtained with a relatively small active or model space. To illustrate the capabilities of this approach, the computed potential energy curves for the HF, F-2 and H2O molecules are compared with the exact full CI or highly accurate large scale CI results, as well as with the MR-CISD results that are used as a source of 3- and 4-body amplitudes in the RMR-CCSD method. In all cases, the RMR-CCSD energies are far better than the standard CCSD energies or MR-CISD energies obtained with the same active space. The paper clearly demonstrates that the RMR-CCSD method provides very accurate data, while requiring only a modest increase in the computational effort over that of the standard CCSD method.