The techniques of partial Fourier (PF) and partially parallel imaging have been combined using a constrained reconstruction technique. The benefits compared with the individual techniques are reduced imaging time and/or an increase in signal-to-noise ratio. Low-resolution phase maps and coil sensitivities may be obtained using autocalibration or from a prescan followed by additional processing. Minor phase artifacts that are introduced by relying on conjugate symmetry can be reduced using a novel regularization scheme to vary the degree to which PF is used in the reconstruction. A nonrectilinear reconstruction algorithm is presented and the potential for motion artifact reduction is investigated using robust reconstruction.