For as long as I can remember I have had the problem of my butt tucking under once i reach parallel in my squat -- either my lower back rounds and I cannot stay vertical, or I stay vertical and fall over backwards. It improves significantly under heavy weights, but the tuck is still there to some extent. As far as I know my hips and thoracic spine have no serious mobility issues. Here is a video of an air squat with the tuck under:
I have read in some places that some people have levers such that they won't be able to squat below parallel correctly, but I would like to think that I can improve with some flexibility work. Any ideas?