We have presented a review of common-azimuth prestack depth migration theory and proposed an extension to improve the imaging where there are strong lateral variations of the velocity model. Since the extended code is still ``work in progress,'' we are not, as yet, able to present concrete results. We intend to test the program in the case of a simple V(z) medium and with more complex synthetics, before applying both common-azimuth and narrow-azimuth on a real dataset adequately preprocessed with AMO.