The interactions between N-terminally acetylated α-synuclein and Cu(II) at several binding sites have been studied with DFT calculations, specifically with the M06 hybrid functional and the ωB97X-D DFT-D functional. In previous experimental studies, Cu(II) was shown to bind several α-synuclein residues, including Met1-Asp2 and His50, forming square planar coordination complexes. Also, it was determined that a low-affinity binding site exists in the C-terminal domain, centered on Asp121. However, in the N-terminally acetylated protein, present in vivo, the Met1 site is blocked. In this work, we simplify the representation of the protein by modeling each experimentally found binding site as a complex between an N-terminally acetylated α-synuclein dipeptide (or several independent residues) and a Cu(II) cation, and compare the results with a number of additional, structurally analogous sites not experimentally found. This way of representing the binding sites, although extremely simple, allows us to reproduce experimental results and to provide a theoretical rationale to explain the preference of Cu(II) for certain sites, as well as explicit geometrical structures for the complexes formed. These results are important to understand the interactions between α-synuclein and Cu(II), one of the factors inducing structural changes in the protein and leading to aggregated forms of it which may play a role in neurodegeneration.