We regard the amplitude of the magnetotelluric impedance of the transverse electric (TE) mode as output, rather than input, in 2D inverse algorithms. The model obtained in the inversion is in this context only an intermediate product whose TE theoretical response is for all intents and purposes the object of the inversion. The input is the amplitude of the transverse magnetic (TM) mode and the phases of both modes. They are fitted as much as possible by relaxing regularization to its limits, allowing the model to include features not strictly required by the data, but still required by the amplitude of the TE curves. We propose two tests to guaranty the accuracy and reliability of the recovery. The first is a convergence test whereby the output is monitored as a function of the roughness of the model. Second, the TM amplitude data are multiplied by different factors and the output is checked for consistency with the previous test. The resulting TE responses have only electromagnetic induction effects and thus are free from static shifts due to electric charges. We apply the procedure to the synthetic COPROD2S2 data set and compute static factors for TE and TM modes. We propose an image based on depth averages of conductivity along with a nonlinear resolution-variance analysis of the image as the final interpretation of the data. The procedure is also applied to the well-known COPROD2 field data set.