The technique of normal-incidence X-ray standing wavefield (NIXSW) absorption has been applied to an investigation of several structural phases of S on Ni(111), specifically the (2 × 2), (√3 × √3)R30° and (5√3 × 2)rect. phases, with a view in particular to clarifying recent controversy over the structure of the last of these. Absolute adsorbate site determination has been effected through real-space triangulation using both (111) and (1̄11) Bragg reflections. For the (2 × 2) phase the results are consistent with a simple overlayer structure with S atoms occupying the “fcc” hollow sites (directly above third-layer Ni atoms), in agreement with earlier determinations by LEED, ion scattering and SEXAFS. The same local site is found to be occupied in the (√3 × √3)R30° phase, although the NISXW data indicate poorer local order. For the (5√3 × 2)rect. phase, a simple undistorted missing-row model is found to be inconsistent with the data, as is any ideal “coincidence lattice” structure, including a simple undistorted pseudo-(100) surface reconstruction. A modification of this latter model, in which some S atoms penetrate the pseudo-(100) layer to bond to the underlying (111) substrate does, however, contain the main ingredients needed to fit the data. By using not only (111) and (1̄11) NIXSW but also (11̄1) and (111̄) absorption profiles, recorded from a near single-domain structure formed on a miscut crystal surface, specific information on some of the structural parameters of this modified reconstruction model is obtained and compared with complementary data from other published studies.