Tallulah has a bunch of allergies. We're not sure completely what right now, since they just went crazy when I adopted her. It might have been a stress reaction, but my vet advised me to cut out virtually everything. She's not allowed any grains or any animal protein other than fish. She eats Natural Balance L.I.D. Sweet Potato and Salmon.
There are matching dog biscuits that she gets, too. So she can have peanut butter. The vet said dairy was okay, though I have't tried it yet; I'm waiting until things are really under control before we start reintroducing. We tried a peanut butter treat that she didn't like, and now I have some freeze-dried salmon that she loves. We need a good treat for training.
She's not super gassy, but it comes and goes. Anything other than the basic kibble can give her innards a little riot. But I think that we could build up a better tolerance for her, too.
I think there are other brands that have a similar set of limited ingredients.