The electrical conductivity distribution within wide palaeochannels is usually well-mapped from airborne electromagnetic data using stitched 1D algorithms. Such stitched 1D solutions are, however, inappropriate for narrow valleys. An alternative option is to consider 2D or 3D models to allow for finite lateral extent of conductors. In airborne electromagnetic data within the Musgrave block near the well-studied Valen conductor, strong induced polarization (IP) and superparamagnetic (SPM) effects make physical property and structure estimation even more uncertain for deep channel clays, particularly those whose channel widths are comparable to their depth of burial. We developed a recursive data fitting algorithm based on dispersive thin sheet responses. The separate IP and SPM components of the fit provide near-surface chargeability and SPM distributions, and the associated electromagnetic (EM) fit provides stripped data with monotonic decays compatible with a simple nondispersive conductivity model. The validity of this stripped data prediction was tested through a comparison of 1D conductivity-depth imaging and 3D inversion applied to the original data and the stripped data. Due to the forked geometry of the deep conductivity structure in the region we investigated, we successfully used 3D rather than 2D inversion to predict the conductivity distribution related to the EM data. We recovered from the stripped data a continuous conductivity structure consistent with a branching, clay-filled palaeovalley under cover.