Roll it up & stick it in your pocket..
I thought you were joking about this.
Well I was looking to upgrade my polyester panama and I found this:
www.panamahats.co.uk/folder-panama-brisa-3-5/
Who would have thought?
www.panamahats.co.uk/panama-hat-tube-for-folder/
They even make tubes to roll the folded panamas. Just incredible. Now I can dunk my Randolphs.