Head Tuck -
Parakeet Budgie and Keet Sleeping Habits

When humans, dogs and cats sleep, they get to put their head down to rest their neck muscles. Parakeets don't lie on the ground, so they have to hold their head up all the time. Think of how tired your neck would be if you never got to rest your head on a pillow! Parakeets need to occasionally rest their neck muscles, too. This is why they do the "head tuck" sometimes.

Pinto does the head tuck

This is sometimes, incorrectly, called "tucking their head under their wing". A bird doesn't stuff its head under its wing :) Really it is nuzzling its head into its soft back feathers, like a built-in pillow. This lets them rest their head, and also if it's bright out, it gives them some shelter from the sun. It's like you pulling down the shades to make it darker. All animals find it easier to sleep when its dark, vs when it's light out.

Ivory head tucks

Nazo head tucks

I've even got a video online, of Ivory doing the head tuck.

Ivory Head Tuck Video - 14mb MPG

Parakeet Sleeping and Resting Information