Equivalent-offset migration is a methodology for prestack-Kirchhoff time migration that partially reverses the order of velocity analysis, normal moveout correction, stack, and migration. Although claimed to be computationally and analytically superior to earlier time-domain approaches, it is not independent of velocity. Velocity-independent dip-moveout followed by prestack imaging is similar to equivalent-offset migration in that it also postpones normal moveout correction to the post-migration stage, but it is independent of velocity. In this paper, I investigate the theoretical relationship between these two processes, showing that equivalent-offset migration and prestack imaging are asymptotically equivalent. Moreover, equivalent-offset migration has little, if any, computational or analytic advantage. The fact that the combination of dip-moveout followed by prestack imaging is independent of velocity is a major advantage and suggests that this latter method is better suited to problems of velocity estimation.