Abstract: A bill 3 or stiffening member for a bill for headwear 1, such as a baseball cap, having first and second opposed surfaces and including a retaining means 9 arranged to automatically retain the bill in either of a first curved state in which the first side of the bill is convex and the second side concave and a second, oppositely, curved state in which the first side is concave and the second side is convex when the bill it urged towards the first or second states respectively. The retaining means may be a curved, resilient, elongate member such as a rod 9. The retaining means may be secured to a flexible sheet of material 6. The sheet of material may also be resilient.