Granulite grade Precambrian gneisses have usually undergone at least one period of strong U depletion. While rock U-Pb isotope studies can determine the time(s) of the severe depletion, and this work attempts to place such studies on a more rigorous footing. Two-stage U-Pb systems can be described in terms of one major, episodic differentiation into rocks with varying U/Pb ratios, while three-stage systems can be described by two such distinct episodes. Most of the Precambrian granulites that have been isotopically analyzed have histories too complex to be described as two-stage systems. However, it is demonstrated here that U-Pb data on whole rock suites can yield the complete U-Pb chemical history of a three-stage system (in terms of U/Pb ratios). For a suite of granulites, present-day 207Pb/204Pb and 206Pb/204Pb ratios and element concentration data allow these ratios to be calculated at a number of specific past times and plotted as an array. The degree of scatter in each of these 'past arrays' is graphed as a function of time. The point of least scatter denotes the age of the end of stage 2 in the history of the system. The array slope and the dating of the end of stage 2 also permit the beginning of stage 2 to be calculated. All other parameters in the system (U and Pb concentrations, Pb isotopic ratios) can now be determined for each individual rock throughout its history. The new interpretive method also distinguishes sensitively among various kindds of uranium fractionation which may have operated during the differentiation episodes. It is applied here to uranium-depleted granulites in the deeper part of the Vredefort crustal profile. The times of the two fractionating episodes are calculated at ~3860 and ~2760 m.y., respectively. The Vredefort 3070 m.y. event, when geochemical systems in the upper half of the crystalline basement became permanently closed, evidently had little significance for the lower half of the crystalline basement. Some fundamental features of Archean basement evolution, whose detailed significance is still poorly understood, were elucidated for the first time by this U-Pb isotope study on whole rock samples. Rocks which suffered little uranium depletion at the end of stage 1 suffered least at the end of stage 2. Rocks which were most affected at the end of stage 1 suffered the strongest depletion at the end of stage 2. Evidently, repeated high-grade metamorphism purges certain granulites of their U content but leaves others relatively unscathed.