Processing algorithms for transversely isotropic (TI) media are widely used in depth imaging and typically bring substantial improvements in reflector focusing and positioning. Here, we develop acoustic image-domain tomography (IDT) for reconstructing VTI (TI with a vertical symmetry axis) models from P-wave reflection data. The modeling operator yields an integral wave-equation solution, which is based on a separable dispersion relation and contains only P-waves. The zero-dip NMO velocity (Vnmo) and anellipticity parameter η are updated by focusing energy in space-lag images obtained by least-squares reverse-time migration (LSRTM). Application of LSRTM helps mitigate aperture- and illumination-induced artifacts in space-lag gathers and improve the robustness of η-estimation. The impact of the trade-off between Vnmo and η is reduced by a three-stage inversion algorithm that gradually relaxes the constraints on the spatial variation of η. Assuming that the depth profile of the Thomsen parameter d is known at two or more borehole locations, we employ image-guided interpolation to constrain the depth scale of the parameter fields and the migrated image. Image-guided smoothing is also applied to the IDT gradients to facilitate convergence towards geologically plausible models. The algorithm is tested on synthetic reflection and borehole data from the structurally complicated elastic VTI Marmousi-II model. Although the initial velocity field is purely isotropic and substantially distorted, all three relevant parameters (Vnmo, η, and δ) are estimated with sufficient accuracy. The algorithm is also applied to a line from a 3D ocean-bottom-node data set acquired in the Gulf of Mexico.