A survey of early medieval computistical works into the early Carolingian period reveals a number of interesting and unexpected themes on the subject of the leap year. Representative examples are presented in this paper. It was common knowledge that Julius Caesar, in order to keep the calendar aligned with the seasons, had introduced the practice of inserting an additional day in February every four years, so that the date we would call 24 February occurred twice in that fourth ‘bissextile’ year. There was uncertainty as to why this additional day was called bissextus. More curiously, there were two schools of thought on the duration of the bissextus: was it a 24-hour day or a 12-hour day? The more scientifically inclined understood that the leap-year day was necessary because the solar year is a quarter of a day, a quadrans, longer than the 365 days of a normal calendar year. From that perspective, it followed that each year contributed a 6-hour quadrans toward the bissextus. There was, however, a long tradition, which was imported into Britain and Ireland, that the annual contribution to the bissextus was a 3-hour quadrans. Some of the justifications, implications and consequences of this erroneous belief are examined, and it is noted that these are mostly found in texts with insular connections.