binding for wool covers

[chi_mama]

this may be obvious but this will be my first sewing project.

I am making a wool cover like this http://www.boiseclothdiapers.com/sew_wool_wrap.htm

Do I have to use wool for the binding? If not what else can I use?
I was thinking FOE but I can't find any locally. Will fleece work? I have a bunch of old 100% poly footsie sleepers that I was thinking of using for the binding if that will work.

TIA

[Michigan Mama]

I thought about using FOE but hesitate to try it because I think it might need to be washed more often than the wool does. I bought some fleece binding, but haven't tried it yet, but it might have the same issue with washing. Fleece, for us, tends to get stinky sometimes (depends on quality).

I made my one-layer covers without a binding. Instead, in the area where the elastic needs to go, I made a tab for the lenth of that area, sewed it into a casing, then threaded the elastic through and sewed it in place. I wish I had pictures. I serged the whole thing first, so once I had the elastic in place, it was ready for velcro...

Most of my wool covers I make with 2 layers, so I simply do them inside out, sew the elastic in, then turn & topstich.