It is suggested that Bayesian statistical methods for radiocarbon data interpretation, already widely used in archaeology, also have potential to improve the dating of tephra layers and hence enhance their use for tephrochronology. By re-analysing data from a recently published paper in which the authors sought to identify the calendar date of the eruption of fourteenth-century AD Kaharoa Tephra, a key marker in New Zealand prehistory, it is shown that Bayesian methods can be used to draw together a coherent collection of radiocarbon data, undertake formal outlier detection, and include prior information. Regardless of the calibration curve adopted, the distribution of likely dates for the Kaharoa eruption is multimodal. By including prior information from wiggle-matched dendrochronology, the uncertainty on the estimate of the calendar date is reduced from a range of about 100 years to about 25 years (i.e., 648-623 cal. BP, with modes at 638 and 632 cal. BP). Using sensitivity analysis, however, it is shown that such estimates are affected by the quality and nature of the prior information available. As a result, we urge tephrochronologists to seek fastidiously both high-quality radiocarbon data and reliable stratigraphic sequences that might inform future geochronological model building.