plus I spray it with liquid vits everyday when it is served to the king. He eats it the same later in the week as he does when it's freshly chopped. I work all day and my son is at school, so when he comes home, he sprays what's left with water to remoisten what has been dried out by the basking bulbs and adds some fresh, if needed.
I don't know what you mean by 'real fine,' but mine is usually around 1/4" - 1/2" pieces and so far, so good. Air is what causes wilting and drying, so be sure and keep it in an air tight container in the fridge.
I also read a post a few days ago that someone uses ice (I'm too lazy to go find the post, I just cleared my cache.. lol) under the greens to help keep them fresh through the day. I haven't tried this yet, because someone brought up the question of the beardie's tongue getting stuck to the ice, and I haven't read the answer, but it sounds like a good idea.
Hope this helps, and now I'm off to find the ice post!
Denise
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Denise (Mom) and/or Jared (son)
Take care! 
1.0 Ball Python - Roy (name change)
1.0 Bearded Dragon - Merlin
1.0 Pixie Frog - Pixel
2.0 Chinese Fire belly Newts - Fred n' Ed, and Ed n' Fred
1.0 Black Cat - Shorty
1.0 Anery Kenyan Sand Boa - coming soon (completing brumation with present owner before joining our home)
0.0.4 Tanks waiting on us to decide what is going in them! LOL