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In the 13th century collection of sagas, Heimskringla, Snorri Sturluson tells that Sweyn Forkbeard was captured in an attack on the Jomsvikings, and turned over to Burislav, king of Wendland. As part of their negotiations, it was agreed that Sweyn would marry Gunhild, the daughter of Burislav, while the latter would marry Sweyn's sister Tyri. By Gunhild, Sweyn is said to have had Harald II of Denmark and Cnut the Great. While this account agrees with certain aspects of the historical record, there are also differences.
There is scant material in medieval chronicles to provide details regarding the marriages of Sweyn of Denmark:
Several alternative interpretations of these data have been proposed. Gunhild might be identical to the historical wife of Sweyn. Further, the dual marriage reported by Adam of Bremen matches the Heimskringla account of Sigrid the Haughty. This may represent confusion between two wives, or it could be that Sigrid is a confused duplicate memory of the same historical wife. This would mean that the woman called Gunhild in the sagas was Eric's widow, as several historians have concluded. Finally, it is possible that Gunhild is simply a legendary invention, not directly based on Sweyn's known Polish wife.