A note on elimination diets (and yes, they should only be performed under a doctor's care, although I'm not; I'm just bad). My advice is to do as I say, not as I do. You should eat foods that you don't normally eat. The premise is you can become allergic to things you eat on a regular basis. The side effect of this is you probably won't like what you are eating for the first couple of weeks. If you are just eliminating a single group of foods, or trying out a nutrition plan (like paleo, or going dairy free), you should stick to the diet for a minimum of two weeks. If you are attempting a very strict elimination diet (such as the traditional "lamb & pears" or "turkey & pears" that I have modified for my purposes) because they can quickly cause malnutrition, generally only one week is done before beginning to add additional foods. For both diets, a carefully kept journal detailing both the meals and symptoms is necessary.
After the first week, a new food item is added. Eat a portion of the new food for two of the three daily meals, for two days. Then discontinue the new food item, carefully noting any symptoms, for three days. The new food can then either be added to the 'safe' or 'problem' list, and the process is repeated.
For my diet, I was careful to remove both lactose and high-sulfite foods, since I already know I'm intolerant. This includes the cruciferous vegetables. I also have to avoid foods with a high arginine (it's an amino acid) to lysine ratio. I took out the "big eight" allergens (milk, eggs, peanuts, tree nuts, fish, shellfish, soy, and wheat), the latex cross-sensitive plants (banana, kiwi, papaya, grape, avocado, watermelon, tomato, potato, celery, and chestnut; to a lesser degree spinach, broccoli, apples, squash family, pumpkin, legumes, beans, mint, cinnamon, mango), citrus fruits, and the nightshade veggies (potatoes, tomatoes, eggplant, sweet peppers, hot peppers, ground cherries, tomatillos, naranjillas, pepinos, and pimentos). I am supposed to cook all my veggies on account of the gastritis.
Pears -- peeled, preferably cooked
Green tea, plain
Salt, Coarse Non-Iodized
Safflower oil, organic refined (I actually use this item quite a bit, but I use every oil quite a bit and so far as I could tell, this is one of the most innocuous oils. Apparently, I'm not alone in my canola/rapeseed oil allergy.)
Lettuce, organic (e.g. romaine, green leaf, red leaf, bibb, and butter) -- blanched, preferably cooked
Endive/chicory -- blanched, preferably cooked
Escarole -- blanched, preferably cooked
Swiss chard -- blanched, preferably cooked
3) soy milk (West Soy unsweetened is just organic soy & water)
4) brown rice
5) squash / zucchini