"Perfect" Positions

How many chess positions can you come up with that fit the following criteria?

1. The side to move has a mate in 1, whether it is White or Black to move (so there should be a total of TWO mates in one: one possibility for each side).
2. There can only be ONE possible one-move checkmate for each side.
3. Both White's and Black's checkmate must use ALL of that side's remaining pieces (that includes the kings!).

To clarify the rules, here is an example of a "perfect" position (ignore where it says "White to move"; it shouldn't matter whose move it is):

Oh, I forgot something important. There must be at least one of every type of piece (pawn, bishop, knight, etc.) on the board, colors aside, like in the position above.

Nice position -- more perfect than you've realized I think -- there's something called a "perfect mate" in which the square the king sits on and each surrounding square is attacked once, and only once. After f4, the Black King is in a perfect mate! After c1=N# the White King is nearly in a perfect mate, but e2 is attacked twice.  Perfect mates are easy enough to compose but occur in OTB games pretty rarely -- I would think that a perfect position (as you've defined it) plus two perfect mates would be insanely hard to compose -- but this is very close!   

"Insanely hard," you say? Suppose, in that position, the Black pawn is moved from c2 to e2. I'm not sure, but wouldn't that be like "the ultimate position" you just described?

EDIT: Wait, never mind. Then c2 would be attacked twice after e1=N#.

This looks interesting, though:

 Yes, I think you've got it.  Nice. Perfect!

Wow, I never considered something so simple, but that certainly works. Nice!

I'm sorry, I think I'm missing something in the puzzle in the first post. White's move is f4# but what is black's move?

I don't see anything black can do for mate in one...

How's this for symmetry? It's even the same move that mates, Nb4  :)

c1=N #

 Well, TECHNICALLY you're right, but I'm looking for new chess positions, not  refutations of the ones that have already been posted.

Oh, awesome. Thanks, didn't see that!