Using half the flour (3/4 cup) coat the pieces of rabbit, shaking off any excess.
Heat the oil and butter in a large heavy-bottomed saucepan, and brown the floured rabbit on all sides.
Add the celery, carrots, onions, salt, pepper, bay leaves, 6 cups water and red wine, and stew for about 2 hours.
Add the potatoes 45 minutes into the stewing process. Once the rabbit and all the vegetables are cooked, use some water to form a paste with the remaining 3/4 cup flour. Stir the flour mixture into the pot as a thickener.
Add the already sauteed mushrooms to the stew and allow to simmer for about 10 minutes. Adjust seasonings, if necessary, and serve.