Rule Number 1: Fat does NOT make you fat!
Rule Number 2: Eat enough protein
Rule Number 3: Cut back on the carbs
Rule Number 4: Increase your fat intake.
Rule Number 5: Remove all refined carbs
Rule Number 6: Remove all transfat
Why don't you check out some reading by Lyle McDonald to understand better.
Fat does not make you fat. When I cut, my fat intake goes up a lot higher than if I am maintenance and bulking! I've gone as high as 50% of my calories from fat, not to say that is ideal but it works. Why do you think Atkins works?