To enhance susceptibility-related contrast of magnetic resonance images, the phase of susceptibility weighted data needs to be corrected for background inhomogeneities and phase wraps caused by them. Current methods either use homodyne filtering or a combination of phase unwrapping and high pass filtering. The drawback of homodyne filtering is incomplete elimination of phase wraps in areas with steep phase topography produced by background inhomogeneities of the static magnetic field. The disadvantage of phase unwrapping is that it requires subsequent high pass filtering, which introduces artifacts in areas with very steep transitions, such as areas near interfaces between parenchyma and bone or air. A method is proposed that reduces the artifacts associated with high pass filtering without sacrificing the advantages of phase unwrapping. This technique is demonstrated with phantom data at 1.5 T and with human data at 1.5, 3 and 7 T.