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 zeroth-order entropy of the estimated density contrasts. The interpretation model consists of a horizontal slab divided into a grid of vertical, juxtaposed prisms in both horizontal directions. The top and the bottom of the gravity sources are assumed to be flat and horizontal, and the parameters to be estimated are the prism 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 constraints 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 has been applied to synthetic data from simulated intrusive bodies in sediments, presenting flat and horizontal tops. By comparing our results with those obtained with the smoothness inversion, we show that both methods produce good and equivalent locations of the sources’ central positions, but the entropic regularization delineates the boundaries 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, England, and by the Matsitama intrusive complex, northeastern Botswana. In the first case, the entropic regularization inversion delineates a batholith with horizontal and nearly flat top being consistent with the known geological information. In the second case, both inversions produced virtually the same estimate. According to tests with synthetic data, similarity between the smoothness and the entropic regularizations indicate that the tops of the sources are neither flat nor horizontal.