Today＇s practice of interpreting Hg capillary pressure curves -a widespread method in porosimetry - is generally unsatisfactory. This has already been demonstrated by Fatt. First, the saturation branch of such a curve is interpreted using the concept of a pore space model in which essential features of a network structure are disregarded. Second, the data provided by the desaturation branch are not used. Distributions of radii of capillaries within porous materials derived by this technique are usually incorrect in that the frequencies of occurrence of the greater radii turn out too small, those of the smaller radii too large. We present a more reliable approach which constrains radii frequency ranges for the Hg saturated pore space and for both the part of the pore space that desaturates and the part that traps mercury when Hg pressure is released. The pore space may be of an arbitrary geometrical structure, the radii distribution may be continuous. Also, the Hg desaturation may enable one to distinguish experimentally between structural and contact angle hysteresis.