Stability is an important feature in a cat tree. Of course, you don’t want the cat tree to topple over when your cat jumps on and off from the higher levels, or gets into a rambunctious mode. Look for cat trees with larger bases that are wide enough to support a tall structure, and are made of heavy material like wood. Also, for extra protection, some brands of cat trees come with optional hardware to secure the unit to the wall. However, if the cat tree is sturdy enough on its own, it may not need to be tethered to the wall.