By simply eliminating or reducing consumption of refined flours, starches, sugars and grains, one will reduce calories automatically. By increasing intake of protein and fat, the body will feel full much faster and stay that way for much longer. So, you end up eating far less than when eating high carb foods. A LC meal is very satisfying. So much so that I don't even think about food if I happen to be busy. HC meals tend to be full of empty calories that, while satisfying for a few minutes, leads to hunger within a short period. Rice is a good example.

Further, it takes far more processing by the colon to digest protein than carbs or fat. Therefore, by eating lean proteins you are, in fact, enhancing your fat burning process even further. It simply takes more calories to digest protein than it does fat or carbs.

For this fact alone you can eat more calories in protein than you can carbs. The protein isn't stored as fat (except under extreme conditions).

That doesn't mean you would eat more calories than a 'normal' diet (which I use loosely). And yes, you are still eating lower volumes of food and lower calories.
I personally don't count calories. I eat enough until I'm just barely full. Which takes a lot less than it did with a HC diet.

As far as carbs and fruit 'being the enemy', they aren't an enemy. They are just way overused in commercial foods. You pick up any food on any store shelf and you count the carbs on the package. I don't mean look at the nutrition label either. I mean, actually read the ingredients and decipher what is a carb and what isn't. You'll find the descrepancy between the nutrition label and the real ingredients to be 'the enemy'.

Since you can't trust labeling, you have to take control of the carbs yourself. THIS is why Atkins (and other low carb plans exist). To allow us to control our own carb intake based on intelligent food choices. Not by starving and being miserable all the time trying to 'work' the 'normal' HC diet based on false labels and bad advice.

Take care.