[4][5] At the 1900 U.S. Open held at the Chicago Golf Club in Wheaton, Illinois, Simpson carded rounds of 84-84-88-87 for a total of 343 and tied for 14th place.

At the 1901 U.S. Open held at the Myopia Hunt Club in South Hamilton, Massachusetts, Simpson carded rounds of 88-87-87-87 for a total of 349 and again tied for 14th place.

Scottish professional Willie Anderson won his second consecutive, and third overall, U.S. Open title by five strokes over Englishman, Gilbert Nicholls.

[5] Simpson won the 1907 Western Open at the Hinsdale Country Club in Clarendon Hills, Illinois, where he defeated fellow Scotsmen, Willie Anderson and Fred McLeod, by two strokes, in Match Play.

[6] At the 1908 Western Open at the Beverly Country Club Simpson finished third (153) behind Willie Anderson (152) and Stewart Gardner (151), with the lowest round of the tournament (73).