The Kyrenia Ship, found off the north coast of Cyprus, is a key vessel in the history of scientific underwater excavations and in the history of Greek shipbuilding. The first volume of the site's final publication appeared in 2023 and provides detailed archaeological information tightly constraining the dating of the ship. A very specific date range is proposed: ca. 294-290 BCE, but is based on a less than certain reading of one coin recovered from the ship. While there is clear benefit to finding high-precision dates for the Kyrenia Ship and its rich assemblage using independent scientific dating (combined with Bayesian chronological modeling), efforts to do so proved more challenging and complex than initially anticipated. Strikingly, extensive radiocarbon dating on both wooden materials from the ship and on short-lived contents from the final use of the ship fail to offer dates using the IntCal20 calibration curve-the current Northern Hemisphere radiocarbon calibration curve at the time of writing-that correspond with the archaeological constraints. The issue rests with a segment of IntCal20 ca. 350-250 BCE reliant on legacy pre-AMS radiocarbon data. We therefore measured new known-age tree-ring samples 350-250 BCE, and, integrating another series of new known-age tree-ring data, we obtained a redefined and more accurate calibration record for the period 433-250 BCE. These new data permit a satisfactory dating solution for the ship and may even indicate a date that is a (very) few years more recent than current estimations. These new data in addition confirm and only very slightly modify the dating recently published for the Mazotos ship, another Greek merchant ship from the southern coast of Cyprus. Our work further investigated whether ship wood samples impregnated with a common preservative, polyethylene glycol (PEG), can be cleaned successfully, including a known-age test.