M.W.
Because single rails can slip (because they've got nothing to attach to, other than being slid between the mattresses), I always recommend (as does the Consumer Product Safety Comission) two bed rails that hook/attach to one another. This keeps them in place, and they cannot pull apart creating that "dangerous" gap between the rail and the mattress.
I used the Summer Infant Sure & Secure Double Bedrail rail even though one side of the bed was pushed up against the wall. They fit three bed sizes (I think not King size). The sides fold down for easy sheet changes (which was important while potty training, thus bed wetting accidents). The rails are made of breathable mesh, which was important to me (to know that if she slept with her face on/near the rail she'd still be getting air). I think I got ours at Babies R Us, and here they are on Amazon.com (the blue ones, but they also come in pink):
Summer Infant Sure & Secure Double Bedrail
http://www.amazon.com/Summer-Infant-Secure-Double-Bedrail...
Good luck!
M.