Actually there was some refraction that wasn't needed. Being lazy I used one of the preset mats to do the liner part of the shade. It was some "plastic" variation that had a nice diffusing quality to it, but it also had refraction. But now it's been tweaked again.

Now I'm suspecting that I probably have some stuff on the shade shaders backwards. So the shader on the liner piece probably needs to be translucent, and the shader on the outer fabric part needs to be transparent. But I'll take a little break for now. (It's looks pretty close, being that the shade model has 3 parts like the real one.)

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Barbequed Pixels?

Your friendly neighborhood Wings3D nut.
Also feel free to browse my freebies at ShareCG.
There might be something worth downloading.