Low coverages of sulfur chemisorbed on the rhenium(0001) and platinum(111) surfaces were studied in UHV by scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED). On both of these surfaces of triangular symmetry the lowest coverage (almost-equal-to 0.25 monolayers) ordered structure is p(2 x 2). Exposure of this ordered sulfur overlayer on either surface to low pressures (10(-9) Torr) of CO induces compression of the sulfur layer to a structure associated with a higher local coverage and CO chemisorbs in the holes created in the sulfur layer. The reordering was observed by both a change in the LEED pattern and by real space STM imaging of the surface. On the Re surface the new overlayer has (3 square-root 3 x 3 square-root)R30-degrees symmetry, while on the Pt surface it has (square-root 3 x square-root 3)R30-degrees symmetry. There was no increase in the amount of sulfur on the surface during this reordering. On both surfaces the overlayers could be returned to the original p(2 x 2) by annealing for several seconds at 600-degrees-C, during which CO desorbs and sulfur atoms reoccupy the vacant metal sites. This phenomenon of the compression of atoms in a strongly chemisorbed layer upon coadsorption of another molecule provides a mechanism for carrying out catalytic reactions on metal surfaces that are covered with strongly chemisorbed layers that do not participate in the reaction.