@Jura11: Roughness of any amount only blurs the reflections for me and makes it worse. My problem is that I'd like the very bright reflections to reflect and the darker stuff to not reflect as much. It would be like a high contrast reflection.

@Wolf359: That looks good! I think I'll try adding some contrast to the iris texture maps, that may help a bit with getting them darker. The reflections still a prob for me.

W10, Ryzen 5 1600x, 16Gb,RTX2060Super+GTX980, PP11, 11.3.740