Hi, have a look at air dried or freeze dried like “Ziwi Peak” small pieces are like jerky type meat or K-9 Natural, you add water to the K-9 Natural both are limited ingredient with no starchy carbs.. http://www.ziwipeak.com/
My boy did well on a Fish & Rice kibble, it had no other ingredients except beet pulp & the usual vitamins/minerals, there’s “California Natural” Lamb & Rice or Chicken & Rice both just have 3 ingredients… http://www.californianaturalpet.com/products
but a kibble does need a carb to bind the kibble like Pitluv said….
