When he caught his first possum you needed to kill it, and beat the dead possum growling while you do it, give him a big growling too and then the possum and then him etc etc while hitting the possum. I did that with a possum, rabbit and goat when I was training my pig-dog. I even went so far as hitting him with it. Not so hard it hurt him but hard enough so he knew that catching one of those was not pleasing. He also related the animal to the punishment as well. I got the idea from a book on teaching retrievers. You are supposed to pat and praise the duck then dog etc. This is how the connect the praise with the animal.
He was an intelligent dog but I only had to do it once per species and he never chased, bailed or caught one ever again.
Bookmarks