Which is most efficient way to put an image on a circle? (Solved)

Imagine texturing a disk. It has two circular surfaces to texture. I’m wondering which of two circle-texturing methods would be less taxing on a GPU at render time.
Method 1: The normal method. Fill in the circles with quads and tri’s, UV map them and apply the texture image(s) to the UV mapping.
Method 2: Superimposed squares with transparency maps. Don’t fill in the circles with any faces. Leave that object as just the cylindrical edge of the disk. Instead, superimpose a square plane over each circle of the disk, and parent the squares to that disk cylider. Then UV map the texture image(s) to the square planes. Use a transparency map to make the area of the square planes outside the circle turn invisible.
Method 2 reduces geometry. But I wonder whether this advantage is cancelled out by other factors I don’t know much about.
Comments
Adding transparency mapped surfaces increases the work the render has to do, as the surface has to be evaluated for every path going through it (Iray) and for ray-traced sahdows and other effects (3Delight), so I would expect that method to be less efficient. Whether you would notice the difference would be another matter.
Thanks, Richard.
It sounds like you recommend I stick with regular old method 1. Will do.