We performed scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED) experiments for Dy adsorbed on Mo(112) in the monolayer regime in order to clarify the concentration dependent reordering of the surface glass that exists for coverages above 0.58 of a monolayer (ML) after annealing to temperatures higher than 400K. The partial reaction model developed earlier is corroborated. The Dy defect structure formed initially in Dy–Mo surface alloy acts as nucleation sites for Dy so that clusters with a wide distribution of lateral distances are formed, as found in particular at a coverage of 0.28ML. The change in bonding character at coverages above 0.58ML leads to reordering of the defects and the concentration dependent modulation of the adsorbed Dy layers. Examples at coverages of 0.7, 0.9 and 1.15ML are shown and compared.