Here's the thing, today's processed food is literally engineered to make you hungry, so you eat (and buy) more of it. So while you can still have processed food and lose weight, you are not setting yourself up for long-term success. Food manufacturers spend billions of dollars trying to figure out how to change your brain chemistry to make you crave more food. And they've been pretty darn successful. You may be able to over ride that for a while, but eventually that processed food, no matter how little, will trigger your brain to want more and more, making it much, much harder to not over eat.