I've been waking up more and more frequently with puffy undereyes. Chalk it up to getting older and not getting enough sleep/drinking enough water, etc but it's happening. I read about this little trick a few years ago and find it's the most effective thing I've tried to reduce puffiness.
It's as simple as you could imagine. When you wake up, simply roll/slide/shift over so that your head is hanging over the edge of your bed. You'll know if you've shifted too far over because your neck will hurt and you'll feel the strain - you don't want this. The position, at least for me, is comfortable enough that I've fallen back asleep like this. All this position does is get your head below your heart, allowing blood to flow a bit faster, loosening up the puffiness under your eyes (and effectively perking up your brain and waking you up gently).
Try it!
C.