According to the Orkneyinga Saga, he came to prominence when he murdered Earl Paul of Orkney's cup-bearer c. 1134 in a quarrel over a drinking game, and fled to Tiree to take refuge with Holdbodi Hundason.
[1] Some years later, after falling out with his own captains (led by his brother-in-law Thorbjorn Thorsteinsson), Sweyn was driven out of Orkney by Rognvald Kali Kolsson, but King David I persuaded them to make peace.
Sweyn, backed by the new King, Malcolm IV, threw in his lot with Erlend, attacking the shipping of the other two Earls and raiding the east coast of Scotland in his company.
His tale is closely bound up with that of Earl Rögnvald, a more rounded character who is also a troubadour and ultimately a saint, and it may be that the saga writers were seeking to portray them as exemplars of the Viking lifestyle.
[5] Another interpretation of the narrative is that rather than seeing these two men as protagonist and antagonist, that together they live in a golden age where the earl is a cultured ruler and primus inter pares but who owes his position in part to his band of "worthy warriors" and is by no means a despot who rules by divine right.