Cumulative probability functions (CPFs) for large numbers of radiocarbon age determinations are increasingly being used by scientists as a methodology to discern environmental histories. While the recent compilation of regional databases of the radiocarbon dating control for fluvial sediment sequences has been beneficial for identifying gaps in knowledge and stimulating new research, there are a number of problems that critically undermine the use of these CPFs as sensitive hydroclimatic proxies. (i) The CPF method is underpinned by the assumption that each radiocarbon measurement is a true age estimate for a point in time, whereas each measured age in fact forms a scatter around the true age of the sample; (ii) calibration of radiocarbon ages is responsible for much of the structure in CPFs and compounds the problem of scatter and smears the chronological control; (iii) the databases incorporate multiple types of environmental changes differing chronological relationships between the 14C measurements and the dated events, with pre-dating, dating or post-dating chronological control each displaying variable length temporal lags all mixed together in the same analysis; and (iv) the radiocarbon ages from individual case studies need to be more robustly tested before being incorporated into regional databases. All these factors negate the value of CPFs as sensitive proxies of environmental change, because peaks in probability for individual radiocarbon measurements are likely to be an incorrect estimate for the age of a geomorphological event and this problem is compounded by combining probabilities for multiple unrelated events. In this paper we present a critical analysis of CPFs and their interpretation before suggesting alternative approaches to analysing radiocarbon geochronologies of geomorphic events, which include: (i) Bayesian age modelling of river terrace development; (ii) developing regional databases that test specific geomorphic hypotheses; (iii) Bayesian age modelling of palaeoflood records; and (iv) analysis of sedimentation rates. Copyright © 2011 John Wiley & Sons, Ltd.