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I've got a small pocket in my coat. Don't want that information left on the bike. Good hidy hole if that's what you want to do is under the faux point cover. Empty hole for that secret stuff.
I laminate mine (clear packaging tape) and then zip-tie them under the passenger seat. I also have my iPhone with me so I can pull up my insurance card that way.
Personally I don't understood the the need for showing registration to an officer. In Michigan the plate has a yearly tag which is supplied with the registration and therefore, if you have the proper tag affixed to the plate, the registration is valid. This combined with a valid DL should be all that is needed. Just my 2 cents.