Sounds like your hands are wet a lot. I had the same problem when I was a food server and had to bus my own tables. My hands were wet all the time because I'd have to wash them or rinse them off every five to ten minutes. The following takes care of the peel:
Take 1 cup olive oil and mix with one cup dry table salt. Mix well. Soak hands in hot bleach solution (1 part bleach - 5 parts hot water) for ten minutes.
Rinse hands quickly in warm water, shake off but do not dry, and start rubbing the oil/salt mixture between both hands. Hold your hands over a bowl because this gets messy
Five minutes or so should do the trick, but if you feel your skin stinging it means you've gone a little too deep. It will sting before it bleeds, so no need to be totally paranoid.
Now, wash hands with warm water and soap until all oil and salt is gone. Dry hands and apply carmex (yep, lip balm) in generous amouts, rubbing into skin well, and leave on hands for a good ten minutes.
Finally, whipe carmex off with a towel and look at how great your hands look
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