Cool Stars 14 - Submitted Abstract # 24 This version created on 05 October 2006 Zeeman-Doppler Imaging of stellar magnetic fields with the Occamian approach Felix Suwald, Institute of Astronomy, ETH Zurich, Switzerland Svetlana Berdyugina, Institute of Astronomy, ETH Zurich, Switzerland We have developed a new code for Zeeman-Doppler imaging (ZDI) of stellar magnetic fields using the Occamian approach for solving inverse problems. We present a series of numerical tests demonstrating the ability of the code to restore various field distributions. The inversions are applied to Stokes IQUV parameters obtained by solving the full set of polarized radiative transfer equations for both atomic and molecular lines. We investigate the effects of data quality and uncertainties of the stellar parameters on the solution and study possible cross-talks between different field components. ----------------------------------