K.U.
My daughter has really fine hair too - I can vouch for the tiny hair elastics that look like the rubber bands people use on braces, like some others have suggested. I got a pack of like 500 of them from Walmart for just a few bucks 2 years ago and I still have a bunch of them left - if you lose some, no big deal, but they hold her hair great. I have to brush her hair through with detangler all the time, since the "tangle fairies" like to visit on a nightly basis. Clips are worthless for her hair.