Indeed, the whole point of the Sherpa's is that you can smoosh them down. You would think this would annoy the pet, but it didn't seem to bother my cats at all. In fact, when I first put a cat in one and slung the strap over my shoulder, I noticed that the bag sort of curved around my hip. It looks like the cat is totally squashed. It didn't bother them at all, and actually seems to kind of soothe them. Maybe because they can smell that I'm so close by.