Eyelid surgery is recommended for those with excess fat deposits or bags above or below the eye. These puffy fat deposits cause the skin to stretch and sag, and can make you appear worn and tired. The genes you inherit from your parents may determine the extent of your eyelid problems. If droopy eyelids impair your vision, this procedure may be covered by insurance. This procedure can be done alone, but often performed in combination with brow lift, facelift or skin resurfacing to achieve the best results.