I inherited bags under my eyes which made the appearance of dark circles as well. Sometime in my late 40's I also had a drooping forhead which made my eyes look even smaller. I think there is a misconception that a face lift fixes your whole face. Truth is, the face requires many separate types of surgery to be wholly rejuvenated.
I had the most wonderful renowned plastic surgeon in the Chicago area. His specialty is making the eyes look natural and boy he is truly the best. He changed my life. I also had laser treatments at the same time and I think this helped to lighten and tighten the skin. My doctor told me that once he removed the fat under my lower lid and removed some skin from the upper, I wouldn't have to have it done again. He was right as it's been 10 years now and they still look the same.
My advice is don't put money (within reason) into the equation when looking for any kind of plastic surgery. You should not go to doctors advertising on billboards or advertize with discount coupons in the valupak. Do your homework, go to several and ask to see results from patients in your same age bracket with similar facial features and problem areas.