I did my own version of Atkins several years ago, I lost 60lbs in 8 weeks. Being grossly overweight is far more unhealthy than losing it fast. I felt like a million bucks compared to when I started. I watched what I ate for several more months but stayed at a plateau so I just ate what ever I wanted, for 2 years!! My weight didn't change more than 3lbs either way.
Then it started to pile back on again. so I did the Atkins again, but not as extreme as the first time and I was only able to drop about 25lbs in 6 weeks. the weight stayed off until I went back to school at which point my activity level dropped 10 fold.
When I first dieted, my initial switch was to remove soda and sugar beverages from my diet. I lost 12lbs in a week without doing anything else. Plus the caffeine intake I had was terrible for me so dropping soda was all around better.
The important thing I did, was take every Saturday and eat a meal of whatever I wanted ( within reason and early in the day). It helps keep you sane when on an extreme diet change. The other thing that made life easier for me was to fast for several days. I was used to eating large portions of food, so I never felt satisfied when dieting and cutting portion sizes. But after fasting a week ( with water and vitamins) even small meals were filling. If you can handle a few days without much or any food, it makes the remainder so much easier to handle.
Obviously most of what I did is probably not considered "healthy" for most people, but I felt better than I had in 8 years. Losing weight at only 1-3lbs a week would be discouraging to me.
I am now still unhappy with my weight so I took a different approach... Today is my first day as a vegetarian (ovo-lacto), total opposite of Atkins.