Since a UV sphere has poles, the best way to make a "perfect" sphere is subdividing a cube and casting it to a sphere, so there is no pinching. You can make a hemisphere by deleting the bottom half.
However, the vertices don't go around it in flat rings, so I can't use this method to make, say, a top third of a sphere.
Is there a better way to make a third of a sphere without a pole at the top?