The salient features of the recently introduced general-model-space (GMS) state-universal (SU) coupled-cluster (CC) method are illustrated on the case of the LiH molecule. Describing the breaking of the Li-H bond by relying on an open-shell-type GMS reveals the importance of the connectivity conditions (C conditions), which represent a crucial new ingredient of the GMS SU CC theory. Only when we properly account for these C conditions can we uniquely represent the full configuration interaction (FCI) wave functions in terms of the multireference SU exponential cluster ansatz and recover the FCI energies via the GMS SU CC method, assuming that all the relevant clusters at a given level of the theory are considered. Drawing on various GMSs, we compute the potential energy curves for three (1)Sigma(+), two (3)Sigma(+), three (1)Pi, and three (3)Pi states, using the GMS SU CC method truncated at the singly- and doubly-excited level (GMS SU CCSD), as well as the externally corrected (N,M)-CCSD method that exploits the NR-CISD wave functions as the external source of higher-than-pair clusters in the MR SU CCSD method. In all cases we obtain excellent results: For Sigma(+) states, the maximum difference between the FCI and various SU CCSD energies is about 0.5 millihartree. These errors are further reduced when we employ the (N,M)-CCSD methods. For the Pi states, the deviations of the SU CCSD energies relative to FCI amount to at most a few hundreds of a millihartree. We also report on the size-extensivity tests and the exactness of the formalism for two-electron systems. (C) 2003 American Institute of Physics.