A new depth migration method derived in the space-frequency domain is based on a generalized phase-shift method for the downward continuation of surface data. For a laterally variable velocity structure, the Fourier spatial components are no longer eigenvectors of the wave equation, and therefore a rigorous application of the phase-shift method would seem to require finding the eigenvectors by a matrix diagonalization at every depth step. However, a recently derived expansion technique enables phase-shift accuracy to be obtained without resorting to a costly matrix diagonalization. The new technique is applied to the migration of zero-offset time sections. As with the laterally uniform velocity case, the evanescent components of the solution need to be isolated and eliminated, in this case by the application of a spatially variant high-cut filter. Tests performed on the new method show that it is more accurate and efficient than standard integration techniques such as the Runge-Kutta method or the Taylor method.