Neutral and anionic Cu-n clusters (Cu-2, Cu-3, Cu-6 and Cu-7(-)) are studied within density functional theory via the local density approximation (LDA) and the generalized-gradient approximation (GGA) of Perdew and Wang for exchange and correlation. Three different levels of improvement upon the LDA are considered. In the first level, the GGA correction to the exchange-correlation energy is evaluated using the electronic density and the atomic coordinates obtained in the LDA calculation. In the second level, the electronic density is obtained self-consistently within the GGA while keeping the LDA structural configurations. In the third level, both electronic density and ionic positions are obtained fully self-consistently within the GGA. We found that the first level of approximation is already sufficient to correct the overbinding found in the LDA. With respect to the LDA, the self-consistent GGA enhances the electron charge accumulation around the nuclei by depleting the interatomic bonding regions, (C) 1998 American Institute of Physics. [S0021-9606(98)30240-8].