If you saw the other thread then you will see links to what is available in the way of low profile cards.
They are exactly the same power etc as the normal cards but are just smaller but as I'm sure you have noticed the choices are very limited.
I can only assume manufacturers don't make many low profile cards because there are relatively few PCs sold that need a low profile card.
Half height is as far as I am aware just another way of refering to low profile.
If I a wrong in this assumption then I'm sure someone will correct me.