In comparison to flat single crystals, the continuous variation of structure provided by curved crystals offers many benefits for the study of physical and chemical processes at surfaces. However, the curvature of the surface also creates experimental challenges. For infrared spectroscopy in particular, adsorbates on metal samples are typically probed by grazing-incidence Reflection-Absorption Infrared Spectroscopy (RAIRS). In this geometry a convex crystal acts as a strongly diverging mirror. We describe how the experimental difficulties introduced by a cylindrical surface can be resolved for RAIRS. A complementary mirror, placed directly downfield of the curved crystal within the vacuum chamber, minimizes the divergence created by the sample. By simply translating the infrared focus across the sample, we probe adsorbate vibrational spectra as a function of local step-type and step-density with high sensitivity and spatial resolution. Time-consuming sample exchange, and the concomitant sample-to-sample experimental errors, are eliminated. We apply this new technique to carbon monoxide adsorption on a curved Pt(1 1 1) crystal and use it to resolve the influence of step-type and step-density on the CO stretch vibration as a function of coverage.