The dispersion of longitudinal stress waves as they propagate in pressure bars distorts the shape of the puise, and so can be a limitation to the accuracy of high strain rate tests such as the compressive split Hopkinson pressure bar (SHPB). The method of dispersion correction described in this paper is based on a bar phase characteristic which is derived entirely from measured stress pulses generated by the elastic impact of small spheres. This method does not depend on any theoretical model of wave propagation, and automatically includes all distortions that could arise in mechanical or electronic aspects of the test. It is quick and convenient enough to be used on a routine basis to improve the accuracy of SHPB tests.