Trixie Cat Bed for Shelves with Scratching Board

It fits perfectly into the standard cube shelves you can buy. However, the faux fur goes around the bottom edges, which makes the bed quite slippery. When my cat pulls himself up onto the scratching board with a bit of force, the bed sometimes slides towards him. I cut an anti-slip mat for carpets to size and put it underneath, which helps a bit, but it would be nice if the bed had some anti-slip studs of its own.