They pack flat or fold down to go in a bag which is supplied with the hat

Barmah Hats the original Australian Bush Hats-

has established an enviable reputation as a designer of unique, quality headwear. The original flexible and foldable Barmah Hat is one such product. Using distinctive Australian materials and paying attention to detail and style, Barmah Hats give the wearer a stylish, comfortable and practical hat.