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Here is how to get the flattest lapel in town; it is better than using an iron. Take your shirt out of the dryer and hang up on a hanger damp or if it's already dry apply a mist of water to the edge you are looking to press.
Lay piece of cardboard under the edge of fabric you're looking to press. Then fold the piece of cardboard over the edge as if you were grabbing the edge with the cardboard. Secure the cardboard with two clothespins.