The saga relates how Sveinn's father, Óláfr Hrólfsson, was one of several chieftains who supported Páll Hákonsson, Earl of Orkney, in a victorious sea battle against a fleet led by Ölvir Rósta in support of Rögnvaldr Kolsson, who had been appointed the earl of half of Orkney by the King of Norway. Óláfr was later burned to death inside his own house by Ölvir, the grandson of Frakökk, an ambitious woman, portrayed as a villain in the saga. Frakökk attempted to win the Earldom of Orkney for her descendants—particularly Ölvir. The saga relates how in Orkney, Sveinn murdered one of the earl's followers, and immediately fled to the Bishop of Orkney. The bishop protected Sveinn by sending him away to the "Suðreyjar", into the care of Holdboði Hundason, a chieftain on the Inner Hebridean island of Tiree. Later, in early spring, the saga relates how Sveinn travelled to Atholl, where he stayed for a long period of time. From Atholl, Sveinn made his way back towards Orkney by land, and on the journey northwards, he passed through Thurso, in Caithness. The saga notes that Sveinn was accompanied by Ljótólfr, and that Sveinn had spent much of the previous spring with Ljótólfr. The chieftain who lived at Thurso was an earl named "Óttarr", who is described as "a man worthy of honour". Earl Óttarr was a brother of Frakökk, and the saga relates how Ljótólfr negotiated a truce between Sveinn and Earl Óttarr, after Sveinn's father was killed by Ölvir. The saga states that Sveinn made numerous Viking expeditions throughout the Hebrides, and into the Irish Sea zone. On one such occasion, Sveinn set up a base on the Isle of Man, where he married a wealthy widow. Some time later, Sveinn and his men were attacked by a force led by Holdboði, and in consequence Sveinn left the island and sailed north into the Hebrides to Lewis.