An iterative partial-Fourier technique which is capable of improved local phase recovery and, hence, improved magnitude images when only limited, asymmetric, uniformly sampled Fourier data are available is presented. The phase information available from the central, symmetric data is improved by letting the phase in a limited region containing the high spatial frequency components and the magnitude of the whole image be determined by an iterative POCS (projection onto convex set) technique. The complex image obtained is found to be similar to that derived from a formal least-squares solution for an overdetermined problem, but in practice, is similar to the zero-filled solution in the limited region only. The method is fast and particularly applicable to gradient-echo as well as spin-echo techniques. It promises to give optimal resolution and signal-to-noise (S/N) when no other information is available. The method is evaluated for models, spin-echo data, 2D gradient-echo data, and short-TE, asymmetrically sampled, 3D, gradient-echo, flow imaging techniques. The S/N behavior is studied as a function of phase, amplitude, and number of extra points, m, retained past the center sampled point. The resulting graphs can be used to decide how large m should be chosen for a particular imaging sequence and phase error.