A new, efficient approximation for coupled cluster singles and doubles (CCSD) is proposed in which a CCSD calculation is performed in a valence active space followed by a second-order perturbative correction to account for the inactive singles and doubles cluster amplitudes. This method, denoted VCCSD(SD), satisfactorily reproduces CCSD results in a variety of test cases, including spectroscopic constants of diatomic molecules, reaction energies, the Cope rearrangement, and other relative energies. Use of VCCSD alone is significantly less satisfactory. Formally, the (OV4)-V-2 scaling of CCSD is reduced to o(2)v(2)V(2), where o is the number of active occupied orbitals, v is the number of active virtual orbitals, and V is the total number of virtual orbitals. We also investigate the role of orbital optimizations and the appropriate choice of an active space in such methods.