Abstract: Headwear reduces radiation exposure with a brim on a top crown that generally surrounds the head. The brim is above a bottom of the crown to avoid interfering with the ears, face, and/or adjustment strap of the cap, which may be of critical importance for those needing protection from sunlight. Brims are positionable a half-inch or more above the bottom of the crown and may completely or partially extend about the crown. Brims may extend at an angle of 20-degrees or more to provide clearance for the ears, face, and any adjustment structure. Brims may be integral with or nondestructively removable from the crown and may include bands or cut-outs for existing brims, bills, or adjustment structures for fitting of hats to which removable brims are added. Headwear may be rigid or a flexible canvas.