The texture, size, and thickness of these are perfect.  Our stairs are 9" deep each and these come out to just the right spot so that they're covered but not at the edge for folks to trip over.  So far, without carpet tape, they've been staying put.  We looked at at least 2 dozen kinds before ordering these and these are by far the best we found.   The quality is high -- not thin or cheap feeling at all, like many others are.  Sturdy yet stylish.  They're mostly flat after 
1 day - I'm confident they'll be fully flat this week.  If not, we'll iron with a damp cloth over.  Buying more for other stairs in our house!