To separate water and lipid resonance signals by phase-sensitive MRI, a two-point Dixon (2PD) reconstruction is presented in which phase-unwrapping is used to obtain an inhomogeneity map based on only in-phase and out-of-phase image data. Two relaxation-weighted images, a "water image" and a "fat image," representing a two-resonance peak model of proton density, are output. The method is designed for T1- or density-weighted spin-echo imaging; a double-echo scheme is more appropriate for T2-weighted spin-echo imaging. The technique is more time-efficient for clinical fat-water imaging than 3PD schemes, while still correcting for field inhomogeneity.