The 45 °monochromatic one-way wave equation, along with the thin-lens term, is used, and a depth-migration algorithm is developed in the frequency–space (ω, x) domain. Using this approach, an unmigrated stack section is directly transformed into a depth-migrated section taking into account both vertical and lateral velocity variations. In practice, the algorithm can accommodate steep events with dips of the order of 60–65°. The use of the frequency–space domain offers several advantages over the conventional time–space and frequency–wave-number domains. Time derivatives are evaluated exactly by a simple multiplication, while the use of the space (x, z) domain facilitates the handling of lateral velocity inhomogeneities. The performance of the depth-migration algorithm is tested with synthetic data from complicated models and real data from the Foothills area of western Canada.