late to chime in here... I've got the Power Support Air Jacket - very thin - from the photo earlier in this thread of the Osir case, the Air Jacket looks to be about same thickness but it covers the bezel much more than the Osir one does.
it doesn't cover the bezel completely however - but certainly more than that other case in the photo. but not a big deal IMO.
there are no logos on the Power Support Air Jacket, and no big hole for the Apple logo like some of the others I've seen. switches all easily accessible.
the Air Jacket comes with both clear and matte screen protectors - IMO theirs are the easiest to put on first try without getting dust or bubbles underneath, plus they're easily removeable and can be just as easily reapplied. they're easy to apply because they're stiffer than others and don't require liquid application.
I used to use a silicone case but didn't like those because they didn't slide in/out of my pocket easily and were kind of bulky in comparison. the Air Jacket is perfect in this regard.
the one downside I'll mention is the matte black Air Jacket has a tendency for the color to slightly wear off at the edges - but just at the very edges, not on the back - mine is 9months old now and if you look closely at the very edges you can see this in some places. If you're not looking for this you can't really tell, it's minor. but the iPhone black plastic underneath looks brand new. there's a clear version as well if you prefer, obviously that one wouldn't have the color wear off.