The structural and electronic properties of small (n_eti) Cu clusters are determined from first-principles calculations based on the local-spin-density approximation, using an all-electron, Gaussian-orbital formalism. The computational method includes use of a systematically refined numerical integration mesh, providing extremely accurate total energies and atomic forces, and a variational technique for treating accidental degeneracies at the Fermi level. Equilibrium geometries have been determined for the neutral clusters for n_eti5, as well as for the Cu2 and Cu3 anions. The calculated properties of the dimer and trimer structures are examined in detail and compared to existing experimental measurements. The influence of the Cu 3d states on cluster properties is analyzed. It is shown that there is significant hybridization between the 3d and 4s in the cluster bonding states. One effect of this hybridization is a strong bond-length preference in the clusters.