We describe a technique to increase the velocity-to-noise ratio (VNR) of phase-contrast magnetic-resonance velocity images based on making three measurements/flow encoding axis rather than the usual two. A phase-aliased high first moment data set and a nonaliased low first moment data set are acquired, and the high-moment data are phase unwrapped using the low-moment data. The VNR of the resulting measurement is given by that of the high-moment measurement and increases linearly with the first moment. A factor of 4 gain in VNR was observed with only a 50% increase in scan time. Thus, this method is a much more efficient way to increase VNR than simple averaging.