I'm glad you asked this, because I wanted to ask the same question, but was afraid of the responses

Years ago, I did the Low Fat No Fat diet, and lost a lot of weight. Never counted anything but fat grams. Now that I'm calorie counting, I was getting out some of my old cookbooks. Most of them were from my low fat days.
I was reading the front of the cookbooks, and it was telling you why "Low Fat" eating would help you to lose the weight. I remember my aunt going to a nutritionist years ago, and the only rule for her diet was that she could not have more than 20 grams of fat per day. She lost the most weight she has ever lost with any diet. She did not count calories, and she would eat healthy foods, but also have things like fat free candy (jelly beans).
How did this work?
Yes, I know we need the healthy fats, and I'm not saying I want to do this diet again, but I just want to know, how did we lose the weight just keeping our fat intake under 20, but our calories may have been a lot higher than we are keeping them at now?
Just wondering why it worked back then, and not now?
What if we ate really healthy foods that were naturally lower in fat, but did not count calories, would we still lose the weight? For example, I love my Ezekiel bread (all natural sprouted bread), but it has 170 calories for a hamburger bun, but only has 2 grams of fat. I would love to do a healthy version of a low fat diet, but scared of not being able to lose.
Any insight?
Thanks
Cathy