Way back in the days of yore when I was taking Gung Fu lessons, the teacher taught a method of breathing where you breath in slowly and fill first the upper lungs fully and then let that air down into the lower lungs to breath in even more and fill your lungs further. Then, when you exhale you exhale first from the upper lungs and then empty out the lower lungs. You develop a kind of rythym and he asserted that doing so not only lead to relaxation, but also to full oxygenation of the entire lungs. Not sure if that is helpful or not, but it surely did seem to make a difference to a young and impressionable guy once upon a time.