When adsorbed on the strongly anisotropic Pt(110) surface Br forms a sequence of (n × 1) structures. In the present study we investigate the (4 × 1) structure by scanning tunneling microscopy, quantitative low-energy electron diffraction and density-functional calculations. We show that the optimal structural model contains essentially the same adsorption sites as the (3 × 1) structure, but with a different preference. The positions of the substrate atom are consistent with a frozen surface phonon of fourfold periodicity, suggesting that the phase diagram can be understood on the basis of a tunable charge density wave (Swamy et al 2001 Phys. Rev. B 86 1299). The structure could also be explained by assuming short-range interactions only, but evidence is presented that adsorbate-adsorbate interactions mediated by quasi-one-dimensional surface resonances play a major role in both cases.