Fedora Hats at Mens Hat Shop! The fedora is traditionally a soft felt hat, with a large and generally flatter brim than the trilby. Here at mens hat shop we stock the classic fedora styles as well as gangster fedora style and the increasingly popular red bailey fedora. Below you can see our selection of fedoras we stock styles from Stetson Hats, Bailey Of Hollywood Hats, Olney Headwear & City Sport. All our fedora's are made from either fur felt or wool.