What to light the background with?

If I have a 3-light setup (main and fill with octaboxes, and the third to light the background), do I need another octabox or a softbox or umbrella or snoot on the third (background) light? If not these, then what would you recommend?

Is it unreasonable to just shoot without any sort of modifier on the third flash head?

I have used a snoot, softbox and a grid in the hairlight, depending on what I need the look to be. Different modifiers for different looks. As far as the actual background, they make a scoop type of reflector for the Alien Bees that I use for that purpose.