As I see it, the main point of an Atkins-type approach is that you convert from a carbohydrate (sugar) burning regime to a fat burning one (your fat). Diets that have not been based on this often fail in the long run, do not stop cravings, and do not succeed in controlling blood glucose levels or bad cholesterol. Obesity and diabetes cases have rocketed while such diets have been popular, and while the number of products promoted, for example, as "low fat", only 10% fat", "90% fat free" - at the expense of increased sugar - have rocketed. These such diets include ones where the number of calories are restricted, and/or the amount of fat. With an Atkins-type low-carbohydrate/high protein regime calories are irrelevant and fat is not so bad as you are burning it for energy.
Following the advice freely given on the Atkins website or in the books, one can not only reduce weight in a healthy way, but also help control blood glucose levels and bad cholesterol levels, and eat generally in a nutrient-rich life-enhancing way. For instance, carbohydrates in the form of many types of vegetables are allowed; these are slower release carbs (lower glycaemic), and the vegetables contain many valuable nutrients. Avocados are allowed, even in the first phase of Atkins, and are a truly wonderful food, especially the Haas variety, with a dark green to purplish-black pebbly skin.
Fruit, especially berry fruits (very healthy, good source of anti-oxidants), are allowed after the first few weeks of Atkins, and can be served with a dollop of double cream. Fantastic! Nuts and seeds are great for snacks, in cooking, or as a desert, and contain very valuable nutrients, but go easy on the quantity - one handful, not one bag!
I have found that the diet, or "approach", can be further enhanced and varied by the use of low carb, high protein, high nutrient shakes or bars, perhaps to replace breakfast and/or lunch. I have found these very sustaining, reducing the desire to snack between meals. I have a Ultra Energy Shake for breakfast, and low carb/high protein bar mid morning, or even to replace lunch, particularly if I am busy or travelling. The nutrients in these products help make up for not eating fruit or drinking fruit juice, and the enzymes aid digestion and normal function, if you know what I mean. They are all available, surprise surprise, in this shop, along with a number of other brands of suitable bars and shakes.