We present a detailed investigation of the adsorption of Cl on the Si͑113͒ surface based on x-ray standingwave experiments and density-functional theory calculations with additional characterization by low-energy electron diffraction and scanning tunneling microscopy. For the whole accessible range of Cl coverages, ͑2 ϫ n͒-like surface reconstructions are identified. Despite this apparent complexity, it is shown that these surface structures consist of only a few atomic adsorption geometries with the most prominent one being the Cl adsorption on top of a Si surface adatom. The required redistribution of Si concurs with a pronounced straightening and alignment of step edges along the ͓110͔ direction. Furthermore, it is argued that this adatom site plays a key role in step-edge geometries on vicinal Si͑111͒ and Si͑001͒ surfaces.