We have carried out an extensive DFT-based search for the structure of the (√43 × √43)R ± 7.5° reconstruction of S on Cu(111), which exhibits a honeycombtype structure in scanning tunneling microscopy (STM). We apply two criteria in this search: The structure must have a reasonably low chemical potential, and it must provide a good match with STM data, both our own and the data published by Wahlström et al. Phys. Rev. B 1999, 60, 10699. The best model has 12 S adatoms and 9 Cu adatoms per unit cell. Local defects within the Cu9S12 framework, consisting of one missing or one extra Cu adatom per unit cell, would be difficult to detect with STM and would not be energetically costly. There is no obvious correlation between this model and the structure of bulk CuS. If the √43 reconstruction is viewed in terms of local building blocks, then CuS3 and CuS2 clusters, linked by shared S atoms, provides the best description.