The lower eyes are a tricky area. If you just remove fat, hollowness ensues. If you remove skin in order to tighten the area, the corners of the eye pull down. This in turn causes a rounding of the eye or a distored eye shape.
Yet the lower eyelid has both hollowness and bulges as fat deflates and the center mass of the cheek slides downward.
In our practice we prefer to perform an ultrashort incision cheeklift to tighten the lower eyelid skin.
Laser resurfacing does tighten the skin and we use it frequently, but does not accomplish the structural changes your eye would need to get the best result.
Remember the cheeklift is the trickiest operation in plastic surgery, in my opinion, so be careful to choose a surgeon with great experience in the area.