We report a detailed high-resolution, x-ray-scattering study of the commensurate-incommensurate transition of Kr on ZYX exfoliated graphite powder. As the Kr coverage is increased, the transition proceeds as follows: A sharp diffraction line from the commensurate phase drops in intensity and is replaced by a diffuse incommensurate line. The scattering from this disordered phase sharpens continuously as it moves to higher wave vector. We have followed this evolution up to 4 compression, where the line shape is adequately described by a power-law correlation function characteristic of two-dimensional solids. In one sample, there was a significant two-phase coexistence region which we ascribe to a distribution of critical points. We place an upper limit of 1 on the possible first-order jump. No evidence for a uniaxially compressed phase is seen. The weakly incommensurate diffraction line is accompanied by a satellite which may arise from either a domain-wall superlattice or a weak strain modulation of the overlayer. A detailed description of domain lattice models is presented. The loss of long-range order at the transition is discussed in the light of current theories. © 1984 The American Physical Society.