Exposing a Cu(100) electrode surface to an acidic and iodide containing electrolyte (5 mM H2SO4/1 mM KI) leads to the formation of an electro-compressible/electro-decompressible c(p x 2)-I adsorbate layer at potentials close to the onset of the copper dissolution reaction. An increase of mobile CuI monomers on-top of the iodide modified electrode surface causes the local CuI solubility product to be exceeded thereby giving rise to the nucleation and growth of a laterally well ordered 2D-CuI film at potentials below 3D-CuIbulk phase formation. Step edges serve as sources for the consumption of copper material upon compound formation leading to accelerated copper dissolution at the step edges. The 2D-CuI film exhibits symmetry properties and nearest neighbor spacings that are closely related to the (111) lattice of the crystalline CuIbulk phase. Intriguingly, the 2D-CuI film on Cu(100) does not act as an efficient passive layer. Copper dissolution proceeds at slightly higher potentials even in the presence of this binary 2D-compound via an inverse step flow mechanism. Further dissolution causes the nucleation and growth of 3D-CuI clusters on-top of the 2D-CuI film. This several nanometer thick 3D-CuIbulk phase passivates the electrode against further dissolution. Characteristically, the formation/dissolution of the 3D-CuIbulk phase reveals a significantly larger potential hysteresis of about Delta E = 320 mV while the appearance/disappearance of the 2D-CuI film is reversible with a potential hysteresis of only Delta E = 20 mV.