Its not Atkins, but it is low carb, other than the weekly refeed and possibly free meal. Definitely much more restrictive than Atkins, but for a variety of reasons, isn't really difficult, IMHO.

Although, my body really starts to balk after about 4 days. I know its wanting MORE calories! Fortunately, it gets them!

The diet is called "Rapid Fat Loss" and it's by Lyle McDonald at http://www.bodyrecomposition.com