I cut leaning trees a lot in my woods, as they are white oaks that are growing towards the light (old pasture over the line fence). I use the technique with an undercut, then a plunge cut for the backcut, leaving about a one-inch hinge and 2-3 inches on the up side of the undercut. This 2-3 inches is the last bit to cut off, which will cause the tree to fall very fast.
Seems about 1 out of every three or four trees I cut are leaners. I work them up into great firewood when they are leaning that much. Then I don't have to deal with the stresses in the lumber. When I first started cutting these leaners, the old farmer next door suggested I use a log chain wrapped around the trunk above the cut, to keep the upper side from splitting off and barber-chairing", which has been known to catch a lot of tree fallers under the chin, sending them to hither and yon. I didn't like this technique, as once the chain blew apart with the force of the log splitting. I trust the plunge cut approach the best. Be careful that the tree isn't rotten when this is done. If rotten, then draw up a new plan.