The problem of the exact quantitative determination of the depth p and total excess-mass M of a point- and a line-source is solved with the aid of moments of the mapped gravity anomaly g m , the correction for the regional anomaly being supposed as already applied. The solution does not presuppose that the constant error E in the regional datum is zero and this error is deduced from the gravity map itself. The relative errors which may affect the given estimates of p, M, E are studied and the magnitude of their upper limits is estimated in the case of a point-source only since the same analysis can easily be extended to the case of a line-source. The recommended method of solution reduces the harmful influence of extraneous anomalies from shallow mass points. The details of mathematical proofs are given in an appendix.