Here is some proof as to how easy it is to towel Calypso. Most birds are not so accommodating.
Actually, in this video, he wasn't too accommodating as he decided to fly away instead of being toweled!
But this is what usually happens:
Sorry for the poor picture quality and the back-lit environment. I needed both hands to towel him so I had to place the camera ahead of time.
He just sits there while I towel him, and I don't have to worry about controlling his head to avoid a bite or anything. This is not typical parrot behavior!