Although superior to Kirchhoff images, the common-azimuth images in the subsalt are far from perfect. Sub-optimal images are probably caused by a combination of poor reflectors' illumination and inaccuracies in the migration procedure. The shortcomings in the migration procedure are of two types: common-azimuth approximations and numerical approximations. We plan to address both types. We are developing a narrow-azimuth extension to common-azimuth migration Vaillant and Biondi (1999). And we plan to apply to common-azimuth downward continuation more accurate numerical methods that are based on a combination of the helix Rickett et al. (1998) and Ristow's Fourier finite-difference methods Ristow and Ruhl (1994).