Accurate measurements have been made of the impact and rebound behaviour of 5-mm aluminium oxide spheres impacting a thick soda-lime glass anvil, for impact angles from normal to very near glancing incidence. Speed, angle and rotation before and after impact have been measured with a strobe and single-frame digital camera. Reproducibility and precision are considerably better than in any previously published work, and have been achieved by careful attention to all aspects of the experiment, including the mechanical and optical systems, illumination, electronic control, computer-based image measurement, and the geometry and condition of the impacting surfaces. All aspects of the rebound dynamics of the elastic spheres, including the motion of the centre of mass and of the contact patch, the spin and the partition of energy, are fully described by the measured variation of the normal and tangential restitution coefficients over the range of impact angles. These measurements show very close agreement with the numerical work of Maw et al. which takes into account the effects of sticking, microslip and tangential compliance. For impacts with a greater obliqueness than about 30 degrees from the normal, the results also agree closely with the classical theory of rigid body sliding.