In its 1988 report, the National Research Council Committee on Estimating the Probabilities of Extreme Floods identified principles for improving the estimation of floods with annual exceedance probabilities of the order of 10-3 or smaller. This paper presents a methodology for estimating the probability of extreme floods which makes use of these principles. Its core is the ''peak-to-volume'' method <Bradley and Potter, 1992>, which is based on separately estimating the probability distributions of flood volumes and flood peaks conditioned on volumes. In its original form it relies on extrapolating a conventionally estimated probability distribution, the distribution of flood volumes. To strengthen this step, we propose use of the gradient of extreme values (GRADEX) method <Guillot and Duband, 1967>, in which the upper tail of the flood volume distribution is deduced from that of precipitation. We enhance the GRADEX method by exploiting the work of Smith <1989>, who developed a regional model for estimating the upper tail of a frequency distribution based on extreme order statistics. An example illustrates the proposed method. ¿ American Geophysical Union 1996