See, even if I wind the hair really tight and keep it on top of each other, I can get about half of my hair onto the headband before it starts overlapping.
So, for those interested, I would suggest pretty damp hair AND big sections. I do have really thick hair but it all fit when I did big sections (and my hair is fairly short right now, just at bra strap length). You should get big, loose but stable curls from my experience.