This paper proposes a new method for bracketing a set S defined by nonlinear inequalities between an inner set S- and an outer set S+. Contrary to eixting approaches for which S- and S+ are unions of boxes, these two sets are defined as unions of polytopes. This characterization makes it possible to describe S and compute its volume in a more accurate way than with classical methods. The resulting approach is used to quantify the influence of a given interval datum in parameter estimation, whan the feasible set for the parameters is defined as the set of all parameters vectors consistent with all intervall data. In order to detect potential outliers, we characterize the influence of any given datum on this set by its safety defined as the ratio between the volumes of the feasible sets computed with and without this datum. This problem amounts to computing volumes of sets as acurately as possible.