Eat less, move more. That’s a rough description of nearly every diet or weight loss plan of the last 20 years. But America keeps getting fatter, and every year new diets come out based on the same basic blueprint for dropping pounds.

There’s a reason all these diets tend to fail, says David Ludwig, M.D., Ph.D., a professor of nutrition at Harvard School of Public Health. “When you cut back calories, your body fights back,” he says.

Ludwig is the author of Always Hungry?, a book that picks apart all the conventional (and misguided) wisdom that surrounds dieting.

He says most of these calorie-cutting programs follow a predictable schedule. At first you feel hungry. You also lose some weight—at least during the first days or weeks. But the longer you stick with a restricted eating plan, the more persistent your hunger gets—and the harder your body will work to hold onto whatever calories you feed it.

Ludwig calls this “starvation mode.” Like a squirrel freaking out about the start of winter, your body takes food and tries to pack it away in the form of fat. At the same time, your metabolism drops so you can preserve the fat stores you still have. “All of this means you have to cut more and more calories to keep losing weight,” he says.

Eventually—as weight loss plateaus and hunger peaks—most people give up. And once they re-open the calorie floodgates, their starving bodies stockpile as much energy as they can—knowing that another dietary winter could be right around the corner. The dieter quickly gains back all the weight he lost, if not more.

“This is why the success of long-term obesity treatment is so abysmal,” Ludwig says. He compares it to dealing with a fever by jumping in a bath of icy water. You’re going to cool off in the short term, but in the long term you may just make things worse.

The solution is to feed your body more satisfying, filling foods. This opens up your internal fat lockers and ramps up your metabolism, resulting in lost weight. “It won’t happen overnight, but this kind of weight loss will be more sustainable,” Ludwig says.

So what kinds of satisfying, filling foods does he recommend? Fat. The healthy kind, and lots of it. “Full-fat dairy, nuts, avocados, nut butters, lots of olive oil, some meat and cheese,” Ludwig says.

What he and other experts know—but dieters still don’t get—is that dietary fat does not equate to body fat. In fact, most of the research suggests an inverse relationship. The more healthy fat you swallow, the less fat your body tends to store.

At the same time, Ludwig says you have to take a short break from any and all refined carbohydrates, as well as starchy vegetables. That means no chips, cookies, potatoes, crackers, bread, sugary drinks, or pretty much any snack food that comes in a package. All of these things mess with your blood sugar in ways the spike hunger and promote fat storage, he says. (That’s why you can eat a whole bag of chips and still feel hungry.)

After two weeks on this fat-heavy, low-carb plan, you’ll have successfully knocked your body out of starvation mode. At that point you can start adding back in small amounts of healthy carbs—stuff like whole grain bread or pasta, potatoes, and the occasional dessert. In a pilot study, Ludwig found people dropped up to two pounds a week on this plan, without cutting calories or starving themselves.

It’ll take some getting used to, but pay attention to how full you feel as you eat. You’ll be surprised to find a bowl of full-fat yogurt with berries will last you until lunchtime—something your big helping of cereal with skim milk never could. The same goes for a lunch of salad with lots of olive oil and walnuts, or an apple with peanut butter and avocado on whole grain toast.

Eventually, when you reach a weight you’re comfortable with, you can add back in the occasional Coke or side of potato chips, Ludwig says. Couple all this with regular exercise, and you’ve got a sustainable plan that will keep you trim and healthy for a lifetime.