A slowness-weighted diffraction stack algorithm is used to migrate crustal seismic reflection data. Slowness information is extracted from the data using a slant stack (beam-forming) process. The main purpose of beam forming is to improve the signal-to-noise ratio over a given range of slowness values. Localized slant stacks are used to design a coherency-weighted slowness filter in the time distance domain. Through migration the subsurface structure and observed seismic data are tied via slowness-selective diffraction curves. A combination of nonlinear slowness filtering with migration gives excellent noise rejection and leads to an improved image in the depth domain. The method, which is particularly effective for migrating moderate to steep dipping events with low singal-to-noise ratio, is applied to various poststack and prestack synthetic data examples and to a deep crustal data set collected on Vancouver Island as part of the Canadian Lithoprobe project. ¿ American Geophysical Union 1987