This paper investigates the applicability of prestack Stolt residual migration when the original image is obtained using an arbitrary velocity model. At its origin, the method is based on an assumption of constant velocity. However, its formulation for depth-migrated images involves a ratio of the reference and target velocities; therefore, for residual migration it is completely irrelevant if the original migration uses constant or variable velocity. Several examples, both on synthetic and real data demonstrate the effectiveness of the method. When applied to a North Sea dataset, the method highlights important features not seen in the original migration.