My 2 yorkies are on the Hill's prescription canine i/d diet. One has pancreatitis. the other one is a bit chubby. I agree with your vet- they appear to be on the forefront of good nutrition. I also mix Wellness food from Mother Hubbard Company. That food is full of human grade chicken, sweet potatoes and other great veggies. Our chubby one is prone to allergies also and we haven't seen anything out of the ordinary with her. If that food is helping your baby, I would not fool around looking for alternatives. If they are eating and not itching hallelujah!
