The local structure around adsorbed carbon atoms on Ni (100) has been determined by C 1s scanned-energy mode photoelectron diffraction both at low coverage (0.15 ML) and at 0.5 ML in the 'clock'-reconstructed (2x2)p4g phase. At low coverage the C atoms occupy simple undistorted hollow sites; the radial strain of the Ni atoms surrounding the adsorbed carbon, proposed on the basis of STM images, is not found. The comparative study of the (2x2)p4g phase confirms the structural parameters of earlier studies, but allows direct comparison between the two phases free from systematic errors. The C-Ni near-neighbor distances to both top and second layer Ni atoms are unchanged by reconstruction, but the Ni-Ni nearest-neighbor distance in the top layer increases significantly. This implies that the adsorbate-induced compressive stress is associated with Ni-Ni, rather than Ni-C, repulsion as has previously been proposed. Special care has been taken to check for coupling of structural parameters in the analysis which might influence the precision of these comparisons, and a new methodology for identifying and assessing such parameter coupling is described.