Abstract: We present a new gravity inversion method, which produces an apparent density contrast mapping on the horizontal plane by combining the minimization of the first-order entropy with the maximization of the zerothorder entropy of the estimated density contrasts. The maximization of the zeroth-order entropy is similar to the global smoothness constraint whereas the minimization of the first-order entropy favors solutions presenting sharp borders, so a judicious combination of both constrains may lead to solutions characterized by regions where the estimated density contrasts are virtually constant (in the case of homogeneous bodies), separated by sharp discontinuities. The method is applied to synthetic data simulating the intrusive bodies in sediments. By comparing our results with those obtained with the smoothness inversion we show that both methods produce good and equivalent locations of the source positions, but the entropic regularization delineates the contour of the bodies with greater resolution, even in the case of 100 m wide bodies separated by a distance as small as 50 m. Both, the proposed and the global smoothness inversions, have been applied to real data produced by the Lands’ End batholithic intrusion from England. The entropic regularization inversion delineates a batholith with horizontal and nearly flat top being consistent with the known geological information.