Anything durable is fine, just not to thick. In reality, if you are just binding where the split leaves the edge and a bit above and below it, it doesn't seem to matter if you use thicker material. I've only noticed tillering issues when the bind was long and thick. In the past I would also make a mirror bind on the opposite limb to balance the tiller as I was taught by the local aboriginal archers, but now I feel like it is more aesthetic than anything. Looks nice and is surprisingly durable. If it is a real concern, horizontal threads can be laid down over the run off soaked in whatever glue you want. When it dries, sand it smooth then bind over the top of it. Sinew can be used this way too.