A small brim sun hat

What do you wear to protect your scalp from the sun? I have a big, floppy straw sun hat that I love, but for plane travel, it's a challenge to pack it without crushing it's shape. (Although I did find an awesome tip that you can stick it inside your suitcase and stuff all your socks into the cap to prevent it from getting damaged.)

As an alternative, I'm considering the small brimmed sun hat above from San Diego Hat Company. It seems so low maintenance and easy—I just need something to wear so that I don't get sunburned!

What do you think? Do you have any tips for shielding your scalp from the sun?

(Image 1, 2)