Independence of Smith-dominated alternatives

Independence of Smith-dominated alternatives (ISDA), also sometimes called Smith-IIA (Smith-Independence of Irrelevant Alternatives), says that if one option (X) wins an election, and a new alternative (Y) is added, X will still win the election if Y is not in the Smith set. ISDA implies Smith and thus Condorcet, since logically speaking, if an ISDA-passing method's winner were not in the Smith set, eliminating everyone outside of the Smith set would have to change the winner. Some Condorcet methods (e.g. Schulze) satisfy ISDA.