Well-grown 3-D copper clusters were obtained on a Pt(111) surface at intermediate overpotentials from a sulfuric acid solution. The hexagonal and triangular clusters grew layer-by-layer and were aligned to the orientation of the substrate, indicating epitaxial growth without rotation. By using the tip as an anodic electrode, the atomic structure of each layer of the cluster was monitored locally during dissolution. The results show that in the copper clusters the lattice constant relaxes directly to the bulk lattice constant in the second layer (at least after deposition of the third layer). Additional discussion on the dissolution kinetics is also included. The same method has been used to elucidate the structure of the Cu overlayer on Pt(100).