First of all, in response to bluuugirl's reply, Dr Atkins does NOT say that all will lose weight from low-carb dieting.

New Diet Revolution, pg 21:

"I'm not about to fall into the error of the low-fat dieting devotees who claim that their diet works for everyone. I would feel rather foolish if I did. No diet works for everyone. Human biological individuality is very marked."

He does go on to say that it does work for most people, of course.

But I didn't see you mention exercise. If you're on the induction diet and you're not regularly exercising, you may feel tired through the day and actually reduce your activity level. This can have a profound effect on serum chloresterol, regardless of your diet.

A second caveat I would forward is to be leery of going to low-carb, low-fat WOE. I know of one person who went on such a diet and his cholesterol skyrocketed. Our conversation went something like this:

"I tried low-carb eating, and my cholesterol went from 220 to 260 [US numbers, normal is 130-200]"
[Me] "Were you consuming fat?"
"No, it was a protein diet."
[Me] "Well, if you don't consume enough dietary cholesterol, your body will produce its own, and if you consume zero cholesterol, your body will overcompensate. Consuming too little cholesterol can be just as dangerous as consuming too much."

He had been unaware of this.

Another thing to look at is supplements that lower serum cholesterol naturally. Also from Atkins' book (pg 210):

"For the lowering or prevention of cholesterol elevations, I use lecithin granules, chromium, pantethine, niacin and other B complex factors, garlic, vitamin C, GLA (borage, primrose, or black-currant oils), EPA (fish oil), beta-sitosterol, glucomannan, guar gum, pectin, psyllium husks, dimethyl glycine, CoQ10, phosphanatidyl choline, or I use the Vita-Nutrient 'Cholesterol' formula plus the Essential Oils Formula".

All that having been said, you may be of the genetic type that responds better to a fat-restricted diet. But I wouldn't go down that road except as a last resort, because you have to count calories and really restrict your food intake to make it work.

Good Luck!