What is this (folk) song (from Dances with Wolves)?

Near the beginning of Dances With Wolves, we hear Kevin Costner’s character singing a few lines of an unidentified folk song. The lyrics we get–“Why should I marry an ugly little girl when I got a pretty wife at home?”, IIRC–reminded me a lot of the British song “Gentleman Soldier,” but I can’t find anything online about an American version of that and it’s a totally different tune. Does anybody know what it’s called, and/or if it and “Gentleman Soldier” really do share some common origin?

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Moved to CS. Also, edited the title to be more specific.

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It’s “Soldier, Soldier Will You Marry Me?”. Natalie Merchant did a version. Nick Cave, too.

Lyrics of the Natalie Merchant Version (scroll down a bit). Some other versions, like Nick Cave’s, have lyrics slightly different from the ones Costner was singing.