It's a really hard diet to stick to. I've found that the only way to avoid Sugar is to not eat it at all - if I have some, then I think it's ok and have some every day for awhile. I sometimes have a little wine on the weekends, but not every week.
I eat apples and berries, but stay away from bananas that have more sugar.
I drink flax oil with my veggie juice, so the Sugar in the carrots doesn't get absorbed as much - and my Dr. said to have nuts then too.