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If you just cut calories, your body compensates by lowering its energy use.  Instead, increase the rate at which your body burns fat by replacing starchy carbs with good fat, fiber and protein. 

Carbs keep insulin levels high, and the more insulin, the more fat your body will make.  So, yes, cut those calories -1,000 calories roughly equals a bagel with cream cheese and a 16-ounce soda.  Then speed your fat burn by eating 8 to 10 ounces of protein (chicken, beef, or fish) and 4 to 5 cups of high-fiber vegetables or fruit a day.  Spice up your breakfast of eggs and fruit with vegetables.  Exercise, and after a couple of months, you will see your weight loss average out to 2 pounds per week.