* In Hawaiian it's "`i`iwi", and the `okina is a letter, so it's a six-letter bird, but its English name counts as 4 letters.
** not sure if I've ever seen one in the wild.
Added from the comments: Rook, Dodo, Kaka, Weka, Cock
Bonus list: Four letter birds I found on Wikipedia that I'm not sure I was aware of before:
Point of ambiguity: Does "Bird" belong on the list?