You have to burn off 3500 calories more than you eat in order to lose a pound of fat.
To that point: I recommend spending one week per month going wilderness backpacking, preferably at altitude. You'll burn thousands and thousands of calories per day lugging your gear up and down hills, and won't be able to over-indulge in food because you must ration your food due to weight considerations.
The main drawback is when you get back to civilization. For a few days your metabolism will be raging and you'll be able to indulge your cravings without much problem. But then your metabolism will cool off and you'll need to be careful to adjust your appetite accordingly, or you'll cancel out the benefits.
More generally, the way to deal with the need to burn a lot of excess calories in order to lose weight is high-impact exercise. Losing weight via caloric restriction alone is a no fun and very slow. Low-impact cardio exercise is great and all, but it only burns calories while you're actively exercising. So unless you can spend hours every day doing it, you won't be burning all that many more calories. If you do high-impact exercise (weigh-lifting, skiing, rock climbing, whatever), you end up elevating your baseline metabolism, and so are burning extra calories even while asleep. The downside is that you won't be able to sleep for more than 5-6 hours at a stretch without waking up from hunger, and may form bad habits like eating a big snack before bed (which will come back to bite you in the ass if you ever slack off on the high-impact exercise). Plus, these types of exercise tend to be a lot more fun than plain old jogging for hours.
Nevertheless, I still maintain that the fastest, cheapest way to lose weight is to be severely mauled by a wild animal/piece of industrial machinery. It's near-instantaneous, free, and can cut total body weight by large percentages. This thread should be asking "what is the cheapest, fastest
safe way to lose excess fat?" If safety and the loss of non-excess-fat weight are not important, then no diet or exercise regimen can possibly compete with radical amputation.