Abstract: In this paper, a new inversion technique, called the minimum first-order entropy (MinEnt-1) method, is proposed for the reconstruction of two-dimensional geoelectric conductivity distributions from magnetotelluric (MT) data. The method combines an iterative search with a regularization technique based on the minimization of the entropy measure of the vector of first-differences of the unknown conductivities. Numerical simulations, using synthetic data corrupted with gaussian noise, show that the MinEnt-1 algorithm converges to excellent conductivity reconstructions, yielding in many cases results that are superior to those obtained by the maximum entropy formalism. Unlike other classical regularization schemes, which maximize smoothness for a given data, the proposed method constrains the class of possible solutions into a restricted set of low entropy models, constituted by locally smooth regions separated by sharp discontinuities. This may be an effective approach for the incorporation of prior information about the local smoothness of the real physical model.