A "DOT shorty" helmet is the smallest helmet you're allowed to wear while still being safe from getting a ticket. Comes from "D.O.T.", or "Department of Transportation", and "shorty" meaning "a very small helmet that doens't come down very far". Also called a "Beanie" or "Skull Cap".
I ordinarily wouldn't wear a helmet, but I don't want to get a ticket, so I wear a DOT shorty.