Diffraction events contain more direct information on the medium velocity than reflection events. We have developed a method for migration velocity improvement and diffraction localization based on a moveout analysis of over- or undermigrated diffraction events in the depth domain. The method uses an initial velocity model as input. It provides an update to the velocity model and diffraction locations in the depth domain as a result. The algorithm is based on the focusing of remigration trajectories from incorrectly migrated diffraction curves. These trajectories are constructed by applying a ray-tracing-like approach to the image-wave equation for velocity continuation. The starting points of the trajectories are obtained from fitting an ellipse or hyperbola to the picked uncollapsed diffraction events in the depth-migrated domain. Focusing of the remigration trajectories points out the approximate location of the associated diffractor, as well as local velocity attributes. Apart from the migration needed at each iteration, the method has a very low computational cost, but relies on the identification and picking of uncollapsed diffractions. We tested the feasibility of the method using synthetic data examples from three simple constant-gradient models and the Sigsbee2B data. Although we were able to build a complete velocity model in this example, we think of our technique as one for local velocity updating of a slightly incorrect model. Our tests showed that, within regions where the assumptions are satisfied, the method can be a powerful tool.