I've noticed that most people use double diminutives, like "tiny little." People seldom seem to use "little" without another adjective to emphasize it. "Great big" is even more common, but doesn't seem to be quite as obviously redundant.
I think redundancy can be a colorful and interesting part of our language. Rules, in grammar and in life, have a valuable function. But grammatical fundamentalism can really put a damper on the English language. A little redundancy is good for the soul.
-Joe, who gets his money from an ATM machine-