I have always assumed that the word in question should be written "Dúnedain", but in reading The Hunt for the Ring in Unfinished Tales, I came across a puzzling passage:
Night was waning on the twenty-second day of September when drawing together again they came to Sarn Ford and the southernmost borders of the Shire. They found them guarded for the Rangers barred their way. But this was a task beyond the power of the Dúnedain; and maybe it would still have proved so even if their captain, Aragorn, had been with them. But he was away to the north, upon the East Road near Bree; and the hearts even of the Dûnedain misgave them. Some fled northward, hoping to bear news to Aragorn, but they were pursued and slain or driven away into the wild. Some still dared to bar the ford, and held it while day lasted, but at night the Lord of Morgul swept them away, and the Black Riders passed into the Shire....
Which of these renderings is correct? Is it "Dúnedain" or "Dûnedain"? Is there a difference, however subtle?
Bonus points for explaining why Tolkien used two versions of the word in a single paragraph.