Inverse doping pro le problems are linked to inverse conductivity problems under the assumptions of zero space charge and low injection. Unipolar inverse conductivity problems are analyzed theoretically via three uniqueness proofs, the rst of which has been published as a paper in Inverse Problems [34]. Also, optimized numerical methods are developed for solving the unipolar direct conductivity problem with a piecewise constant conductivity coe cient. Finally, the unipolar inverse conductivity problem is solved for inclusions de ned by as many as 9 parameters, or by as many as 120 parameters when an initial guess for each parameter is known with less than 10% error. Our free boundary identi cation algorithm produces a sequence of improved approximations in a way that provides both regularization and accelerated convergence towards the solution.