As requested, here is a picture of Gus the blue & gold macaw on the new perch suggested by SailBoat. The perch is about 3" in diameter where he's sitting. He's small for his breed, not quite 900 grams, and has a misshapen spine which seems to make it difficult for him to perch comfortably and securely. Thanks 'Boat, it's just what the doctor ordered.
Interesting discussion about the feet. Kiwi has a wide variety of perches (and things he perches on that aren't really perches per-se). For some reason he seems to prefer the smaller diameter ones for playing/hanging out, though he sleeps on the widest one.