I know of 3 different approaches, there may be more.
1. Blepharoplasty - removing excess skin and fat from the eyelid so it is not as heavy for the muscles to lift.
2. Levator resection - they shorten and tighten the levator muscle that lifts the eyelid. I think this is what might cause the failure to close completely. There is also something called an internal levator aponeurosis but I don't know how that compares.
3. Frontalis sling - they attach a sling from the inside of the eyelid up to the forehead. This surgery would be reversible if there's a problem. I have considered asking about this, but I'm afraid my forehead would tire and limit the success of this approach.
Here's an article if you're interested
http://www.aao.org/publications/eyen...derForPrint=1&