The potential-dependent phase behavior of specifically adsorbed iodide on Cu(1 1 1) in 10 mM HClO4 containing either 0.1 or 0.05 mM KI has been studied using cyclic voltammetry in combination with in situ scanning tunneling microscopy. The adsorption of iodide on Cu(1 1 1) at negative electrode potentials close to the onset of the hydrogen evolution reaction leads to the formation of a (root3 xroot3)R30degrees-I structure. However, at more positive electrode potentials a transition to a uniaxially incommensurate (UIC) iodide adlayer takes place caused by a unidirectional compression of the (root3 xroot3)R30degrees-I phase. This compressed adlayer shows an additional one-dimensional long-range height modulation superimposed on the atomic corrugation. The process of compression can be described rather by the insertion of super-heavy domain-walls (shdw) into the (root3 xroot3)R30degrees-I phase than by a uniform and continuous compression of the adsorbate adlayer. Within the UIC phase regular (root3 xroot3)R30degrees-I regions are separated by broad and 'fuzzy' shdw instead of sharp dislocation lines as expected for ideal shdw. This observation points to a partial relaxation of these walls. Within these domain-walls the smallest nearest neighbor distance (NND) of 3.7 Angstrom is significantly smaller than the van-der-Waals diameter of the uncharged iodine particle (3.9 Angstrom) while the NND within adjacent commensurate (root3 xroot3)R30degrees-regions exceeds the 'Pauling' diameter of the single charged iodide (I-) by 1.85%. Both the NND at domain-walls and the wave-length of the striped superstructure change with the applied potential. (C) 2003 Elsevier Science B.V. All rights reserved.