I have several for various reasons. While I like the video, I prefer to put mine on a flat surface and push the crown down so that it is flat (almost) with the brim, and then slide it into my pack or put it on top of my duffle bag. Once I get to where I am walking, I pop the crown out. Otherwise, I wear it most of the time.
ps. if you haven't registered your Tilley, it's worth doing that. The guarantee of lifetime replacement requires the hat to be registered within a certain time of purchase.
pps.
@Icacos, I sympathise. This happened to my original Tilley after being washed last year on the CP. I was fortunate enough to have some white sports strapping tape which I used to contain the plastic cord and make a few other repairs at the same time. I keep wearing it when I can, even though my wife insists on me wearing the nice new one she bought for me when I am in her company!!
ppps, If I am using an umbrella, I will clip the cords under my sternum strap and let the hat hang down in front of me. It's out of the road, and I don't have to worry about