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Before storing, I always gently dry my razor with a towel without touching the edge and then finger dab mineral oil all on the blade. I highly recommend this practice.

Look at this Barber strop:


http://www.youtube.com/watch?v=7tXN4N1x0m0&feature=youtu.be

I personally find the hand stropping puts a really nice final polish on the edge that is even finer than that you can get off a strop, unless you have very rough palms ;)

It can also be handy...