Do not prune off the top out of the tree or the ends of the branches! The ideal shape of an apricot tree should be "bowl" or "vase" shaped. In other words, the center of the tree should be open to air and sunlight. Begin by pruning out all dead limbs. Then look for any limbs that are growing into the middle of the tree, crossing other branches, or growing straight up, and remove them. Smaller branches can be removed with loppers. Larger branches can best be taken out with a pruning saw. If you need to prune out a large branch, it is best to make the first cut six to eight inches out from the branch from which you are removing it. (If you try to cut it close on the first cut, the weight of the branch coming down will probably tear the bark beneath the branch, and you don't want that to happen.) After you remove the weighty outer part of the branch, then go in and remove the remaining stump of the branch next to the larger branch from which you are removing it. If you do these two things, your tree will become more bowl-shaped and will produce more fruit.