Let us know how it works out! Maybe a 4' round fence? If you cover it over with net, it only has to be about 4' tall to keep the little animals from getting caught in the net. I have to warn you that a bird CAN get caught in the net. A robin got caught in the net over our chicken run, and when I found her she was dead. It was heartbreaking.I may try that with one of them. Most of them are sprawling and cover a good 4 ft squared area.

I actually cut one down because it was never going to get big enough to survive the deer, and I was tired of looking at fence instead of a beautiful tree. 
