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When something is very close fitting. Also can mean when someone is a cheapskate.

Also can be a play on words. Dick is a man's name and he wears a hat that is too tight....but it can also refer to the male genitalia and the foreskin around the head.
"Man, that dress she had on was tight as dick's hat band!"

"I will never date Johnny again. He is too cheap! Tight as dick's hat band."
by Kani's world April 02, 2017
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