Working Group 2 of the International Organisation for Standardisation (ISO) recommends a cylindrical PMMA (rod) phantom of 19 mm in diameter for the calibration of extremity dosemeters. Exoelectron emitting BeO thin film detectors on graphite substrates, covered with a polypyrrole foil of 6.7 mg.cm-2, were exposed on this rod phantom to photons and beta radiation for response assessment. Exposures to photons were carried out with heavily filtered X rays of various energies, 137Cs and 60Co, exposures to beta radiation with 90Sr/90Y, 204Tl and 147Pm. For perpendicular radiation incidence the results are related to measurements free-in-air, the angular dependence of the response to photons is compared with calculated data of Hp(0.07,a). For beta radiation the measured Hp(0.07,a) values are, within the margins of measurement uncertainty, comparable with the corresponding values achieved on the commonly used slab phantom. Certain discrepancies at larger angles of radiation incidence are caused by attenuation and scattering effects at the substrate side wall of 0.4 mm height around the TSEE sensitive plane.