The difficult task of estimating recurrence intervals for large floods has long plagued hydrologists because statistical measures fail when return intervals of floods exceed the length of historical data sets. Sediments deposited in the backwaters of large floods may accumulate thick sequences in tributary mouths. Stratigraphic and sedimentologic studies of these sequences combined with radiocarbon dating have established a 10,000-year paleoflood record for the lower Pecos and Devils rivers in southwestern Texas. This technique is rapid and relatively inexpensive and can be used where historical records are short or entirely absent.