This work identifies an additional source of phase error across ky in multi-shot echo-planar imaging resulting from flow or motion along the phase-encoding direction. A velocity-independent flow compensation technique, gradient moment smoothing, is presented that corrects this error by forcing the phase to have smooth quadratic behavior. The correction is implemented, without compromising scan time, by changing the first moment of a bipolar prephaser pulse on a shot-by-shot basis. In phantom and in vivo experiments, gradient moment smoothing effectively eliminates ghosting and signal loss due to phase-encoding flow. When used in conjunction with a "flyback" echo-planar readout, which compensates for flow in the frequency-encoding direction, gradient moment smoothing renders multi-shot echo-planar imaging relatively insensitive to in-plane flow. This can make multi-shot echo-planar imaging a viable technique for accurately imaging in-plane flow and may desensitize it to the otherwise serious problem of in-plane motion.