I threaded thin cotton yarn though every other stitch of the brim and blocked it around a large dinner plate, cinching it closed. That hat became a tam and the bind-off neatened up.
I had more of the yarn (Cascade Pastaza) and wanted a matching cowl. I'm trying to knit accessories that, you know, match (instead of being the crazy miss-matched knitting lady). Here's what I did for the cowl:
Cast on 80 st. Knit one round. Purl one round. K2TOG, YO around. Purl one round. Knit one round. Start Leaf chart from Foliage pattern. Work for 12 inches and finished with the same k2tog/yo border.
I blocked it around a shoebox. It came out a little loose, so I added a lone shell button. All the yarn-overs around the edge are like a row of buttonholes. The cowl looks nice folded over a bit and buttoned.
And a set!
If I were to do this again, I would choose a different yarn. It gets a little itchy after a while.