Two somewhat different versions of the travels of Karlsefni appear in the sagas; they are found in the Hauksbók and the Flateyjarbók. They tell that Straumsey (Current-isle) lies at the mouth of Straumfjörð; this is an island with an extreme density of birds.
Flateyjarbók in the context of Saga of the Greenlanders
Grœnlendinga saga (Old Norse pronunciation:[ˈgrøːnˌlendingɑˈsɑɣɑ]; Modern Icelandic: Grænlendinga saga, Icelandic pronunciation:[ˈkrainˌlɛntinkaˈsaːɣa], literally Saga of the Greenlanders), is one of the sagas of Icelanders. Like the Saga of Erik the Red, it is one of the two main sources on the Norse colonization of North America. The saga recounts events that purportedly happened around 1000 and is preserved only in the late 14th century Flateyjarbók manuscript.
The Saga of the Greenlanders starts with Erik the Red, who leaves Norway and colonizes Greenland. It then relates six expeditions to North America, led respectively by Bjarni Herjolfsson, Leif Erikson, Thorvald Eriksson, Thorstein Eriksson and his wife Gudrid Thorbjarnardóttir, Thorfinn Karlsefni, and Freydís Eiríksdóttir. Bjarni and his crew discover three lands by chance during their voyage to Greenland, but they never set foot on the lands themselves. Leif learns about Bjarni's encounters and, after buying Bjarni's ship, sails to the lands to explore them. During his adventures, Leif names the three lands Helluland, Markland, and Vinland. Later, Thorvald, Leif's brother, sets sail to Vinland and lives there until he gets killed by the natives in a combat. Thorstein and Gudrid attempt to travel to Vinland but eventually fail, and thereafter Thorstein dies of an illness. Karlsefni, who then marries Gudrid, journeys to Vinland and stays there until the following spring. The final expedition is made by Freydís, who sails to Vinland with the brothers Helgi and Finnbogi but eventually slaughters their crew and returns to Greenland.
The þættir (Old Norse singular þáttr, literally meaning a "strand" of rope or yarn) are short stories written mostly in Iceland during the 13th and 14th centuries.
The majority of þættir occur in two compendious manuscripts, Morkinskinna and Flateyjarbók, and within them most are found as digressions within kings' sagas. Sverrir Tómasson regards those in Morkinskinna, at least, as exempla or illustrations inseparable from the narratives that contain them, filling out the picture of the kings' qualities, good and bad, as well as adding comic relief.