You need bigger birds. A friend of mine brings his hawk over to hunt and when he lets it go, any squirrel in sight is a goner. If it runs into a nest, the hawk will stand on one leg and shred the nest out of the tree til he gets his man.
It's very impressive to watch. (especially since the bird comes back to him, I couldn't believe it til I saw it, I figured it was a one-time deal)