For me, I haven't been able to give up sugar, but have drastically reduced my consumption. Every day I have a teaspoon or two in my coffee and every night I have either chocolate or ice cream, plus I eat fruit. I maybe eat 1 large chocolate bar or a pint of ice cream a week, plus what, 10-14 teaspoons in my coffee.
I have not had binges since starting, but then again have never full eliminated the sugar. However I eat far less than before. It used to be more like 1-2 tablespoons in my coffee, and then probably 3-4 portions of other sweets a day. And I have emptied a bag of mini candies on many, many occasions.
I'm not a big believer in full on eliminating foods, though that is what I had to do with wheat.