Neutral and anionic Cu-n clusters (Cu-2, Cu-3, Cu-6 and Cu-7(-)) are studied within density functional theory via (a) the local-density approximation (LDA) and (b) the generalized-gradient approximation (GGA) of Perdew and Wang (GGA-PW) for exchange and correlation. GGA reduces by similar to 20% the binding energies, while the bond lengths are increased by similar to 3-4%. The different levels of GGA approximation, involving optimization of the electronic density and/or of the geometry, are shown in detail. In the case of Cu-6 the GGA configurational ground state is a planar structure of D-3h symmetry. This result differs from the one obtained by LDA, where the three different isomers (one two-dimensional and two three-dimensional) were found to lie within 0.04 eV.