I know about SortedSet, but in my case I need something that implements List, and not Set. So is there an implementation out there, in the API or elsewhere?
It shouldn't be hard to implement myself, but I figured why not ask people here first?
There's no Java collection in the standard library to do this. LinkedHashSet<E> preserves ordering similarly to a List, though, so if you wrap your set in a List when you want to use it as a List you'll get the semantics you want.
Alternatively, the Commons Collections (or commons-collections4, for the generic version) has a List which does what you want already: SetUniqueList / SetUniqueList<E>.