Yes, there are places to tuck them into the top of the bag at the ends. If I am not going to be opening my bag for a while I tuck them in, otherwise I leave them out.
I have an aldo version of this ( some day hoping for the real deal) anyway I dont care for the look with them out. I tuck mine in and just leave the tassel out.
I find there isnt much need for doing the zipper up, but if you need too its not that big of a deal.
Oh good!! Thanks all, it would really bug me if I couldn't tuck those things in. I'm still undecided whether my first bbag will be a First or a City, so all I can know about them will help when I have to decide!