Stereotomography is a tomographic method that uses slowness-vector components to improve traveltime inversion. We extend it to general anisotropic media and implement it for media with elliptic and anelliptic anisotropy. Such media depend on only three elastic parameters, which makes stereotomography less sensitive to ambiguity resulting from limited coverage of surface seismic experiments than it would be in transversely isotropic or orthorhombic media. The corresponding approximations of the slowness surface restrict the validity of the present approach to qP events and mild anisotropy. Our numerical analysis demonstrates that stereotomography can be used to estimate macrovelocity models in the presence of anisotropy. For elliptic anisotropy, the parameter that is most difficult to estimate is the orientation of the symmetry axis. For anelliptic anisotropy, estimation of stereotomography parameters is possible in principle; however, it will be mostly ill conditioned in practice, even for low noise levels. Better results are achieved, if transmission events from multiple-offset vertical seismic profiling experiments are included in the inversion.