In-situ STM was used to investigate the adlayer formation and structure of Tl adsorbates at chemically polished Ag(111) electrodes in perchlorate electrolyte, and to study the effect of extended I polarization of incomplete Tl and Pb adlayers at high initial adsorbate coverage. In-the Tl+/Ag(111) system, the full first monolayer adsorbate has a hexagonally close packed structure with interatomic distances that are compressed in comparison with the bulk Tl phase. The subsequently formed second monolayer has also a hexagonally close packed (hcp) structure,but shows more pronounced disordered domains. Incomplete first Tl monolayers of high coverage have the same hcp structure as a complete monolayer, but do not extend to the very boundary of the substrate terrace. Extended polarization of such monolayers leads to a conversion of the original hcp layer into a coverage with [root 3 x root 3]R30 degrees-symmetry which is interpreted as a mixed coverage, where every third Ag atom is replaced by a Tl atom. Similar phenomena are observed during long-time polarization of an incompletely formed, Pb-coverage. The results are discussed with regard to the role of the atomic steps and reveal the importance of surface singularities for the understanding of the adsorption behaviour at real electrodes.