So, eat some apricots or prunes or plums. I never gave up fruit; so I didn't reach ketosis. That means I lost weight slower.
I also didn't give up wine either. But eliminating starchy carbs like bread and potatoes and corn helped me lose 15 pounds in three months.
That's what I've done. And sugar. Mainly sugar. That Splenda stuff works great.
I still eat very limited amounts of bread and pasta. And almost never touch sugar.
Luckily I also love seafood - tuna, salmon, etc... and it's great for ya :)
I am not perfectly abstinent on all of these items. If a food has a small amount of them in it, I might still have some. But I generally keep away from them, and I HAVE lost weight (about 20 pounds since March) without really "dieting" at all and almost painlessly. I must have my blood fats checked to see where I am on those.
My only quarrel with Atkins is that I believe he restricts what I regard as "good" carbs. (most naturally ocurring fruit/vet. carbs.) too much. But I used to be totally skeptical of the general low-carb. approach, and I am now quite a supporter of it.