Green tea will give you the antioxidants and nutrients you need while still adhering to the diet. Bonus points if you add milk or cream, because, you know, those kinds of calories are good here. Drinking enough water can help you burn fat and increase your energy levels. This page explains exactly how much water you should drink in a day. No matter which diet you follow, you should be able to add a few servings of low-carb fruits and vegetables to your meals every day.