I'd be happy to look further tomorrow. I did find Niels Carstensen, b. 1858 on Ellis Island records. He arrived 8 April 1884 from Prussia on the ship Frisia. There is a Doris Carstensen on the ship, also. On the Hamburg Passenger list, his residence ( and Doris') is given as Lugumkloster, Schleswig. The first "u" has an umlat over it. They left Hamburg on 26 March 1884 on the Frisia. I don't know the area that your family is from but I think that it would have still been a part of Denmark when Niels was born. Did he shorten his name to Nels after he arrived? Do you know if he lived in Iowa before moving to SD?