I happened to be near Walmart a few days ago so I stopped in to check out the sun hats. There it was as Deathwind mentioned. A very Tilley-esque hat. Near the top of the crown is a mesh band all the way around, but only .75" (19mm) wide. I would prefer more mesh area but will see how well it works.

There is a small pocket in the inside of the top of the crown with a hook & loop closure.

It was marked $10. Unlike Deathwind I paid $10.

Seems like a good hat for the money.

My wife recently noticed a large sun hat in Costco. Sun Protection Zone . Looks well constructed but there is only one size and no adjustment. She will be trying it out this summer.