Abstract To obtain the shape of a homogeneous body from its gravity anomalies, the inverse of Parker's formula is expressed here by means of a power series expansion in the reciprocal of the density contrast. The calculation of the nth coefficient of the series needs the evaluation of n - 1 Fourier transforms of products and sums of the preceding coefficients and a sufficient storage to contain all of them. Computer time is modest for the first several terms, but grows rapidly as the number of terms increases. Fortunately, most inversions require a small number of terms.The method reproduces Oldenburg's iteration results exactly and faster whenever it converges, and it can also converge in other cases. Nevertheless, its main advantage comes from the fact that once the series coefficients have been computed, the inversion can be performed immediately for a variety of density contrasts, allowing the choice of best values to match constraints such as seismic or borehole data.