Turmeric Slim The Paleo Diet, on the other hand, does not encourage one to completely eliminate wheat, rice, and corn from their diet, but to moderately reduce them. In fact, experts state that there are actually particular times when eating those foods is encouraged. The Caveman Diet also is very specific that you don't eat any and all kinds of meat, but rather the healthier lean meats, as well as fish. By eating lean meats and fish, you'll gain the necessary proteins, healthy fats, and Omega 3s that are necessary for a healthy lifestyle.