Prestack frequency-wavenumber (f-k) migration is a particularly efficient method of doing both full prestack time migration and migration velocity analysis. Conventional implementations of the method, however, can encounter several drawbacks: (1) poor resolution and spatial aliasing noise caused by insufficient sampling in the offset dimension, (2) poor definition of steep events caused by insufficient sampling in the velocity dimension, and (3) inadequate handling of ray bending for steep events. All three of these problems can be mitigated with modifications to the prestack f-k algorithm. The application of linear moveout (LMO) in the offset dimension prior to migration reduces event moveout and hence increases the bandwidth of non-spatially aliased signals. To reduce problems of interpolation for steep events, the number of constant-velocity migrations can be economically increased by performing residual poststack migrations. Finally, migration with a dip-dependent imaging velocity addresses the issue of ray bending and thereby improves the positioning of steep events. None of these enhancements substantially increases the computational effort of f-k migration.Prestack f-k migration possesses a limitation for which no solution is readily available. Where lateral velocity variation is modest, steep events (such as fault-plane reflections in sediments) may not be imaged as well as by other migration approaches. This shortcoming results from the restriction that, in the prestack f-k approach, a single velocity field must serve to perform two different functions: imaging and stacking. Nevertheless, in areas of strong velocity variation and gentle to moderate dip, the detailed velocity control afforded by the prestack f-k method is an excellent source of geologic information.