The problem is that of radiocarbon dating, and 65 dates from Danebury were involved. The analysis is based on a data-generating model, which takes careful account of the various kinds of uncertainty involved in relating observed radiocarbon dates for artifacts to successive chronological beginning and ending dates of significant archaeological phases. In addition to its intrinsic interest as a possible model for many kinds of archaeological data of this type, the model poses some challenging inference problems. Maximum likelihood techniques do not seem adequate to the task, and a Bayesian approach has been adopted.