Size adjustable headwear piece

A headwear piece comprising:

• a crown comprising a plurality of gores, including first and second gores that are joined at a connecting line at a first circumferential location on the crown, to cooperatively produce an inverted cup-shaped receptacle with a diameter into which a user's head can be directed with the headwear piece in an operative position,
• the crown having a bottom portion that extends at least partially around a wearer's head to embrace a wearer's head with the headwear piece in the operative position;
• and
• a sweatband on the crown that engages a wearer's head with the headwear piece in the operative position,
• the first and second gores stretchable circumferentially away from the connecting line in response to direction of a user's head of at least a predetermined effective diameter into the receptacle so as to thereby increase the diameter of the crown,
• the sweatband having a portion that is locally non-stretchable at the first circumferential location so that the sweatband and first and second gores are circumferentially stretchable together away from the first circumferential location in response to the direction of a user's head, with at least the predetermined effective diameter, into the receptacle.