True-amplitude Kirchhoff depth migration is a classic tool in seismic imaging. In addition to a focused structural image, it also provides information on the strength of the reflectors in the model, leading to estimates of the shear properties of the subsurface. This information is a key feature not only for reservoir characterization, but it is also important for detecting seismic anisotropy. If anisotropy is present, it needs to be accounted for during the migration. True-amplitude Kirchhoff depth migration is carried out in terms of a weighted diffraction stack. Expressions for suitable weight functions exist in anisotropic media. However, the conventional means of computing the weights is based on dynamic ray tracing, which has high requirements on the smoothness of the underlying model. We developed a method for the computation of the weight functions that does not require dynamic ray tracing because all necessary quantities are determined from traveltimes alone. In addition, the method led to considerable savings in computational costs. This so-called traveltime-based strategy was already introduced for isotropic media. We extended the strategy to incorporate anisotropy. For verification purposes and comparison to analytic references, we evaluated 2.5D migration examples for and reflections. Our results confirmed the high image quality and the accuracy of the reconstructed reflectivities.