Current methods of potential field inversion require measurements to be reduced onto a level plane, resulting in a loss of resolution. This is especially true for draped surveys in areas of extreme topography. We examine a method that bypasses this limiting step by making use of an approximately equivalent geometry from which data are directly inverted. Corrections are applied to an initial solution to account for errors generated by the transformation of geometries. A numerical model and an example data set are used to explore this method's benefits and drawbacks in relation to the conventional approach of data reduction onto a level plane prior to inversion. We show that this direct inversion method is particularly better than the conventional approach at resolving fine-scale features, such as the narrow zone of crustal emplacement at the Mid-Atlantic Ridge and adjacent areas of tectonic disruption and magnetic source alteration. ¿ American Geophysical Union 1995