In the year 1016, the succession was bitterly contested between Edmund Ironside and Canute the Dane. Edmund the Aetheling was elected King by the citizens of London, and Canute was elected King by the Witan in Southampton. Although Edmund stoutly aided London in its defense against the Danes, he frequently left the city in order to draw the Danes away from their siege. This resulted in at least five major battles in the south, the last of which, the Battle of Assandun, ended in disaster for the Saxons because of the treachery of Eadric Streona, who took to flight with his forces and turned the tide against Edmund.
The Saxons withdrew but the Danes followed them up the Severn river into Gloucestershire, finally stopping at an island called Olney (or Alney). There, in deference to the chieftains of the land who had had enough (led by Eadric Streona, who somehow retained the goodwill of Edmund Ironside), the two Kings decided to solve the issue by single combat. This is according to the chroniclers, as unlikely as it sounds.
The Saxon King was said to have been the stronger fighter and soon hammered the Dane, breaking his shield and beating him down when Canute called a stop to the fight. ”Bravest of youths,” he cried out, “why should either of us risk his life for the sake of a crown?” Edmund paused, considering. “Let us be brothers by adoption,” the Dane continued, “and divide the kingdom, governing so that I may rule your affairs, and you mine.” (this came from Florence of Worcester).
The single combat story is probably apocryphal, but the ensuing treaty is not. According to their agreement, Canute was to rule Northumbria and Danish Mercia, while Edmund was ruler of Wessex, Essex, East Anglia, and English Mercia. It’s unclear who was supposed to rule London (I found it stated both ways), but in the end, the Londoners were obliged to come up with their own tribute payment to Canute and permit him to anchor his ships in the Thames for winter, so I guess the result speaks for itself.
Most importantly, it was stated that this treaty excluded brothers and children of the two Kings; if either was to die, all the possessions would revert to the other. And so when Edmund Ironside died suddenly in the winter of 1016, Canute took the crown and made sure to bring the witnesses forward to confirm the terms of the treaty. An exhausted England accepted his claim without demurring.