The potential-energy curves for the X (1)Sigma (+)(g), a (1)Pi (g), a(') (1)Sigma (-)(u), w (1)Delta (u), c(3) (1)Pi (u), and b (1)Pi (u) states of N-2 have been investigated in full configuration interaction (FCI) and coupled-cluster response calculations. The equilibrium bond lengths, adiabatic excitation energies, and harmonic frequencies have been obtained with the coupled-cluster singles model (CCS), an approximate coupled-cluster singles and doubles model (CC2), the coupled-cluster singles and doubles model (CCSD), and an approximate coupled-cluster singles, doubles, and triples model (CC3), and subsequently compared to FCI results. The weak and strong features of the coupled-cluster models are discussed and illustrated. Overall, improvements towards FCI are obtained in the hierarchy CCS-CC2-CCSD-CC3. CC3 is always consistently better than CCSD, and for all the considered spectroscopic constants CC3 provides excellent results. Examples where the CC3 model fails are also given. The noniterative triples model, CCSDR(3), is compared to the iterative triples models CC3 and FCI. CCSDR(3) recovers the major part of the CC3 correlation contribution and is thus a cheap alternative to the CC3 model.