We have measured phase delays of fundamental-mode Rayleigh waves for 12 events recorded by the Southern Africa Seismic Experiment at frequencies between 0.005 and 0.035 Hz. A novel multiscale finite-frequency tomographic method based on wavelet decomposition of 3-D sensitivity kernels for the phase of Rayleigh waves is used to map the shear velocities in the upper mantle beneath southern Africa. The kernels are computed by summing coupled normal modes over a very fine grid surrounding the seismic array. To estimate and minimize the biases in the model resulting from structures outside the tomographic grid, a jackknife inversion method is implemented. The contribution of heterogeneities outside the target volume is significant, but produces artefacts in the tomographic model that are easily identified and discarded before interpretation. With structures on length scales as short as 100 km retrieved beneath the array, the deep structure of the Kaapvaal craton is revealed with unprecedented detail. Outside the array, the corresponding resolution is 200 km. High velocity cratonic roots are confined to the Archean craton, and extend to depths of at least 250 km. Confirming earlier surface structural studies, we recognize two distinct units in the Kaapvaal craton. The eastern Witwatersrand block and the western Kimberley block are separated by a major near-vertical translithospheric boundary which coincides with the Colesberg Lineament. Lower than average velocities south and east of the Kaapvaal craton reveal extensive metasomatism and heating of the lithosphere, probably related to the Karoo magmatic event and to the opening of the South Atlantic Ocean.