The internal and external obliques, which I like to call "nature's girdle," are located at the sides of the rectus abdominis. They are the muscles you use when you bend sideways at the spine or twist at the waist. They also contract to compress the abdomen, so you should work them just as hard as you work the rectus abdominis. Adding a twist to crunches works, as well as dumbbell side bends, but be careful not to use any jerky motions, especially if you've had back problems.
The trick here is not only to avoid all obvious sources of carbohydrate (sweets, bread, spaghetti, rice, potatoes), but also to be careful with your protein intake. If you eat large amounts of meat, eggs and the like, the excess protein will be converted into glucose in your body. Large amounts of protein can also raise your insulin levels somewhat. This compromises optimal ketosis.
If you watch TV often, you've probably seen a commercial pop up for Jenny Craig. When you do the diet, you receive a unique weight loss plan for your specific lifestyle and have a personal consultant to check in with at least once a week. And, the meals are delicious: There are more than 100 menu items to choose from for your meals, which are five a day plus one snack of your own.