Oops, I didn't mean to click "finish".....
So continuing on,
That would be about all the major pruning I would do for now. A few little things here and there would be fine; I just like to stay close to the "no more than one-quarter of total foliage pruned at one time" theory. Maybe that's not so important in warm climates, I don't know. Obviously, Greene does it, and no matter what, it certainly won't kill the tree.