3 sluicing puzzles: Number two

This one isn't at all involved, it's just a simple query: Does anybody's theory explain why you can't sluice an embedded yes/no question?

E.g., what's wrong with (1)?

1. *Bill guessed that Mary had left, but when I asked, Sue didn't know whether.

or, to make the antecedent and the sluice even more parallel:

2. *Bill asked if Mary had left, but I didn't know whether.

Maybe you can sluice them but the C° has to be null, as in

3. Bill asked if Mary had left, but I didn't know.

Any opinions?

Update: Norvin Richards writes:

"Anne Lobeck had a theory that was intended to handle this, which she talks about in her book Ellipsis (and some other folks have used it or developed similar theories--Saito and Murasugi have a relevant paper in a J/K from 1990).

The theory is that you can only elide the complement of a head that agrees with its specifier--so the fact you're discussing here is grouped together with contrasts like "I wanted to read a book, so I stole John's __" vs. *"I wanted to read a book, so I stole a __".

I don't think they have a story about why agreeing with your specifier has anything to do with being able to elide your complement. And the facts for NP-ellipsis are not so clear--it sure looks like you can have D's like "that" or "five" with elided complements (unless there's something more complicated going on in "...so I bought five"). Ignoring this, I have an article where I try to get the facts to follow from tenets of Kayneanism ("Why there is an EPP")."

Thanks, Norvin!