This underpad is da bomb. Yes, it was so exactly what I wanted, I got really excited - maybe more so that about the carpet (weird, eh?). I installed it on the stairs under a low-pile runner. 

The high density of it should help the carpet not wear out as much and has added just enough squish while still keeping the steep stairs safe for walking.

The rubber backing does not budge when on a tile/wood surface (and, of course, we stapled it to the stairs as well, but not before testing it on the floor!).

Easy to cut to shape, and the natural materials in this padding made it a pleasure to work with, unlike some others I've encountered. Would definitely recommend.