A new method is presented for using known ordering or other relationships between 14C samples to reduce 14C dating uncertainty. The order of sample formation is often known from, for example, stratigraphic superposition, dendrochronology, or crosscutting field relations. Constraints such as a minimum time between dates and limits from historical information are also readily included. Dendrochronologically calibrated calendric date histograms initially represent each date. The method uses Bayes theorem and the relational constraints to upweight date ranges in each date distribution consistent with the other date distributions and the constraints, and downweight unlikely portions. The reweighted date distributions retain all dating possibilities present in the initial calibrated date distributions, but each date in the result now reflects the extra information such as ordering supplied through the constraints. In addition, one may add information incrementally, and thus analyze systematically its effect on all the date distributions. Thus, the method can be used to assess the consistency of the quantitative data at hand. The Bayesian approach also uses the empirical calibrated date distributions directly, so information is not lost prematurely by summarized dates to a mean and variance or "confidence intervals." The approach is illustrated with data from two densely sampled paleoseismic sites on the San Andreas Fault in southern California. An average reduction in 14 C date distribution variance of 59% is achieved using ordering information alone, and 85% is achieved by also applying sedimentation rate constraints and historical information.