We present an azimuthally anisotropic 3-D shear-wave speed model of the Australian upper mantle obtained from the dispersion of fundamental and higher modes of Rayleigh waves. We compare two tomographic techniques to map path-average earth models into a 3-D model for heterogeneity and azimuthal anisotropy. Method I uses a rectangular surface cell parametrization and depth basis functions that represent independently constrained estimates of radial earth structure. It performs an iterative inversion with norm damping and gradient regularization. Method II uses a direct inversion of individual depth layers constrained by Bayesian assumptions about the model covariance. We recall that Bayesian inversions and discrete regularization approaches are theoretically equivalent, and with a synthetic example we show that they can give similar results. The model we present here uses the discrete regularized inversion of independent path constraints of Method I, on an equal-area grid. With the exception of westernmost Australia, we can retrieve structure on length scales of about 250 km laterally and 50 km in the radial direction, to within 0.8 per cent for the velocity, 20 per cent for the anisotropic magnitude and 20° for its direction. On length scales of 1000 km and longer, down to about 200 km, there is a good correlation between velocity heterogeneity and geologic age. At shorter length scales and at depths below 200 km, however, this relationship breaks down. The observed magnitude and direction of maximum anisotropy do not, in general, appear to be correlated to surface geology. The pattern of anisotropy appears to be rather complex in the upper 150 km, whereas a smoother pattern of fast axes is obtained at larger depth. If some of the deeper directions of anisotropy are aligned with the approximately N–S direction of absolute plate motion, this correspondence is not everywhere obvious, despite the fast (7 cm yr−1) northward motion of the Australian plate. More research is needed to interpret our observations in terms of continental deformation. Predictions of SKS splitting times and directions, an integrated measure of anisotropy, are poorly matched by observations of shear-wave birefringence.