We use Density-Functional Theory to investigate the structure and stability of a methylthiolate self-assembled monolayer (SAM) on Ag (111). Focusing on the role of substrate vacancies, we indeed find various structures with a reduced Ag-atom density in the outermost substrate layer that are significantly more stable than an unreconstructed SAM/substrate interface. The most stable structure exhibits a very small rumpling of the methylthiolate layer and a mean height of the anchoring S atoms above the surface that are both in excellent agreement with experiment. Previously reported discrepancies thus result from an insufficient configurational screening. (C) 2011 Elsevier B. V. All rights reserved.