Three encoding strategies for the measurement of flow velocities in arbitrary directions with phase-contrast magnetic resonance imaging are presented; their noise and dynamic range performance are compared by means of theoretical analysis and computer simulation. A six-point measurement strategy is shown to be quite inefficient in terms of velocity variance per unit time. A simple four-point method exhibits equal dynamic range; its noise depends on flow direction but on average is equal to that of the six-point method. An alternate, balanced four-point method has noise that is direction independent and has, depending on implementation, possibly lower noise levels. Either four-point method is more efficient and is preferred over the six-point approach.