Is it possible to tighten the brim of a hat?

I recently made a hat for myself and made the brim too loose. Is there any way to tighten it without unraveling it and starting fresh? The brim is 2x2 ribbing for 2 inches and then goes into a stranded pattern.
Any suggestions would be great - I don’t care it the brim looks perfect!

One easy thing to try is running a double thickness of elastic thread in a matching color through the ribbing all around the brim. You can do this in 2 or 3 places depending on how deep the ribbing is.
It works fairly well although the elastic eventually gives out and has to be replaced. A more permanent solution, but more time consuming is to cut the hat at the brim and reknit the ribbing from where it joins the hat to the end. Sort of like this treatment for a sweater.

I know a few people who’ve tightened sweater necks with a row of single crochet between the body and ribbing. Maybe that would work on a hat, too.