Pork Pie Hat
A pork pie hat is similar to a flat topped fedora and typically made of felt or sometimes straw. Unlike the fedora, however, a pork pie hat has much sharper lines and less of a curved profile. The crown of a pork pie hat can come in a variety of heights (either shallow or tall) and there is no standard definition for what crown size is acceptable; rather crown size is chosen by the individual based on personal preference and where the hat is to be worn.
The popularity of pork pie hats has fallen and risen many times since their introduction in the mid 19th century. Currently they are quite popular among jazz and blues musicians; however they do not have a wide following outside these circles.