A very good point! When I got my first grey, I had five cats. After the initial introduction, three fell into the third catagory, and we never had any problems, even with a later dog who took some training. I've lost those three cats, and the two I have left fall into the "rabbit" category. The dogs don't chase them, but they are much more aware of Fred and Ethel, and the cats mostly stay in their "cat rooms". It very much depends on the cat, as well as the dog!