You might find this study interesting.

Reference:
Kasper, H., Thiel, H., Ehl, M., "Response of Body Weight to a Low Carbohydrate, High Fat Diet in Normal and Obese Subjects," The American Journal of Clinical Nutrition, 26, 1973, pages 197-204.

Summary:
The object of this study was to analyze the relationship between carbohydrate and fat as it pertains to regulation of body weight. Five volunteers were fed a formula diet comprised of 168 grams of carbohydrate, 64 grams of protein and 39 grams of fat for 45 days. Every five days, the amount of fat in the diet was increased via ingestion of either corn oil or olive oil. Researchers noted that the body could use up to 600 grams of fat daily, and this utilization was not compromised in any form, meaning individuals experienced increases in thermogenisis. At daily intakes of 300 to 400 grams of fat, subjects reported feeling warm all over and had an increased tendency to sweat. The individuals consuming the olive oil experienced an average weight gain of 20 pounds. Individuals consuming corn oil, although ingesting approximately 6,000 calories per day, experienced a decrease in weight. Researchers postulated that this discrepancy was due to the corn oil containing more of a particular essential fatty acid (linoleic acid). Based on the results obtained from this pilot study, the researchers placed 25 obese subjects on one of five diets varying in caloric value and ranging from low-fat/high-carbohydrate to high-fat/low-carbohydrate. All diets were supplemented with either corn oil or olive oil. Individuals consuming a low-fat, 855-calorie diet lost an average of 1.1 pounds daily while individuals consuming a low-fat, 1,006-calorie diet lost an average of 0.57 pounds daily. By comparison, the low-carbohydrate, high-fat diet group eating 1,707 calories lost 0.66 pounds daily while those eating 2,150 calories lost 0.70 pounds daily, regardless of whether they ate corn oil or olive oil. Eating less did not significantly alter weight loss in the low-carbohydrate groups. Researchers believed that this was a result of an increased energy output in the higher calorie group released by the body in the form of heat. Researchers also concluded that the weight loss was not water loss due to the length of the study and the total amount of weight loss achieved.

You might wish to note that those who were eating low carb consumed 700-1100 more calories than the low fat group and still lost more weight.

This one too: Please note that those that ate the most calories also lost the most weight by a good amount.

Summary:
This study tested whether a low-carbohydrate diet that did not restrict calories would be more successful in promoting weight loss than a low-fat, low-calorie diet. Researchers also tested to see if such a diet would have negative effects on blood lipid profiles, thus increasing cardiovascular risk. To test their hypothesis, they recruited 39 obese adolescents for the study; 20 were placed in a low-carbohydrate diet group while 19 were placed in a low-fat diet group. Subjects in the low-carbohydrate group were allowed to consume as much protein and fat as they wanted, so long as carbohydrate intake remained below 20 grams for the first two weeks and below 40 grams for the next nine weeks. Members of the low-fat group were instructed to consume fewer than 40 grams of fat per day. The low carbohydrate group participants consumed an average of 1,830 calories per day while those in the low-fat group consumed 1,100 calories per day. Both groups showed improvement in HDL ("good") cholesterol, triglycerides and total cholesterol. The improvement in triglycerides was much more pronounced in the low-carbohydrate group. Eating 700 more calories per day than the low-fat group, the low-carbohydrate group lost twice as much weight (an average loss of 48 pounds for the low-carbohydrate group versus an average of 20 pounds for the low-fat group). Neither diet had any effect on liver or kidney function. The researchers concluded that the low-carbohydrate diet significantly improved weight loss despite a higher caloric intake. Also, contrary to their hypothesis, despite increased fat intake, the cardiovascular risk profile did not worsen, but in fact improved in certain aspects including HDL cholesterol and triglycerides.

I'm not arguing that you don't have to restrict calories to lose weight, but if I had a choice between restricting them to 1,800 calories a day and losing weight or restricting them to 1,100 calories to lose weight (and lowering my metabolism in the process), it's not a difficult choice to make now is it?