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1. Catching birds - you can't unless you keep her on leash when you have her outside.

2. You have to keep dog and rabbits separated at all times with no way for the dog to get to near them. She is made up of high prey drive breeds and will attempt to kill the rabbits and she will also terrify them.

You can't remove instinct, you have a hunting dog. Keep it on a leash is the only way to stop the hunting. I have a JRT and he hunts all the time. He's in a fenced yard so he rarely catches anything.If he catches anything it's a mouse or rat and I let him.That's one less in my house.