Thank you, Les.

I didn't notice there was another page here (at least for me there is) before my last reply.
But I wasn't thinking at the time - all I have to do is make some of the outer cornea material become the sclera material. I think I actually had it that way at one point but screwed up somehow and didn't notice.
So I tried that and it looks better, but now I have to remap and re-texture the sclera. I have to add a few more edges to make the iris more easily morphable, too, so that means I have to redo that as well.

Yeah, it's got too much shine to it, that's for sure.. I got sick of messing with the sclera settings, and just left it the way it was to concentrate on the cornea and iris. I think I need a better background HDRI too. I have a whole folder full of them that I bought, and I keep using the same one. ;-)