Perfect sphere mapping?

Google hasn’t helped me much with this. Are there any tricks on mapping a sphere perfectly so there would be no distortion at the poles? So far the closest I’ve gotten is unwrapping a cube that has a level 6 subsurf but that doesn’t work with 2:1 ratio textures.

Delete pole vertices, extrude edge loops twice, position on z to recreate sphere form. Do not close/ scale to 0 top loops, mark meridian and pole rings as seams. Unwrap as sphere will give nice result. If you really need to close that little hole, idk…

.blend

Add a Grid, move the vertices up a little, UV map the image.

In front view, SHIFT+W 180 degrees.

Then in side view, SHIFT+W 360 degrees.

Remove doubles.