In case anyone's wondering, I'm not husky372.
Actually, the way I read the original question was that there was a tree in an area which could accommodate it falling in any direction. As an exercise (perhaps?) the tree would be felled to the opposite direction from its lean. So what would be a good method to do so?
In that light, husky372 was correct, but didn't address the question, really.
In order to ensure the tree won't barber-chair while making the notch, simply make the notch shallower than "usual". Doing so will require more lift in the back cut but it will be somewhat easier lift (rather like using a longer lever vs. a short one).
There are many ways available to generate the lift. Wedges alone would likely be the most work, but it can be done.
If your feet are going to leave the ground anyway, you should probably drop some of the weight off the backside first and set a rope fairly high (try to guess the point where there is equal moving mass both above and below the attachment point; but at least no higher than the point where the stem can withstand the side load which will be generated). Start the back cut normally, but be sure it's perpendicular to the grain as it heads toward the notch, and insert wedges early and often. It's especially important to have the wedges go into a cut that's at right angles to the grain in this instance since there will be great pressure and you don't want the growth rings to separate because you're not at right angles to them.
Divide the work equally between the rope and wedges, stacking them as necessary, even using the removed notch as filler if required. That way, if the rope setup fails for any reason, at least the tree won't go over backwards, and if the wedge setup fails, (maybe) the rope will hold it.
Making a call as to how thick to leave the hinge is difficult sometimes. If you leave too little, there's a chance of it pulling out and dumping the tree backwards. If you leave too much, it aggravates the situation by requiring more force to bend it. The rule of thumb to leave 10% of the diameter at hinge height is usually a bit too excessive for my taste, but works well for this scenario.
I've also cut pockets and used bottle jacks in lieu of rope. The more a tree leans away from the desired fall, the more work it is to fell it. Sometimes it just isn't feasible.
Okay?
Glen