The interaction of Cu with the Al-terminated alpha-Al2O3(0001) surface has been investigated within a range of coverage using a periodic supercell approach. The calculations have been undertaken within the density functional theory using a generalized gradient approach. Our results show that at a coverage of 1/3, Cu atoms reduce the outermost Al ions, leading to a large surface relaxation mainly involving a displacement of the outermost aluminum layer. The preferred surface sites are those in which Cu(I) atoms are close to oxygen atoms. Increasing the coverage to 2/3 leads to a coexistence of Cu(I) and Cu(0), in agreement with experimental data. For higher coverage, the surface is still found to be reduced, but the charge transfer formally results from the oxidation of the 4s Cu metallic band, and therefore Cu(I) and Cu(0) species may not be distinguished. In this regime, the formation of 3D clusters would take place, supporting a Stranski-Krastanov growth mechanism.