Illustration by Joel Kimmel
Use a single- or double-bit ax with a long handle and a slim head. Determine the direction in which you want the tree to fall. Make a horizontal cut on that side, then angle your ax down into that cut to chip out a notch. Make sure your first strikes are far enough apart to give your ax room to remove wood as the notch becomes deeper. Depending on the tree and its lean, continue this cut-and-chip action to the center of the tree. A slight twist of the ax head at the end of each stroke will help pop chips free and keep the notch open.
When the notch reaches the midpoint of the tree's diameter, move to the opposite side of the tree. An inch or so above the notch, chop down at a gentle angle so your ax reaches the middle of the tree just above the original cut. A straight tree should fall obediently to the notch side. If you must fell the tree "against the lean," you might need a wedge or two to encourage it in the right direction.