Imaging in deep-water environments poses a specific set of challenges, both in data preconditioning and velocity model building. These challenges include scattered, complex 3D multiples, aliased noise, and low-velocity shallow anomalies associated with channel fills and gas hydrates. We describe an approach to tackling such problems for data from deep water off the east coast of India, concentrating our attention on iterative velocity model building, and more specifically the resolution of near-surface and other velocity anomalies. In the region under investigation, the velocity field is complicated by narrow buried canyons ( wide) filled with low-velocity sediments, which give rise to severe pull-down effects; possible free-gas accumulation below an extensive gas-hydrate cap, causing dimming of the image below (perhaps as a result of absorption); and thin-channel bodies with low-velocity fill. Hybrid gridded tomography using a conjugate gradient solver (with vertical cell size) was applied to resolve small-scale velocity anomalies (with thicknesses of about ). Manual picking of narrow-channel features was used to define bodies too small for the tomography to resolve. Prestack depth migration, using a velocity model built with a combination of these techniques, could resolve pull-down and other image distortion effects in the final image. The resulting velocity field shows high-resolution detail useful in identifying anomalous geobodies of potential exploration interest.