You may NOT have deep set eyes, despite your impression. Some darker pigmentation of lower eyelid skin does not necessarily indicate your eyes are deep set, or that you have enophthalmos. The measurement to determine relationship of your ocular globe (eyeball) to the orbit (bony space within which the globe rests) is exophthalmometry, which is easily measured by a plastic surgeon with a Hertel exophthalmometer (a ruler, basically). To resolve the impression of deep set eyes requires in person examination. To lighten the lower lid pigment, a variety of approaches are possible, but they all follow a diagnosis. Is the darkness shadow, is it pigment, or is it both? Shadow can be managed by filling the hollow of the lower lid with pedicled (vascular, living) fat which is reliable, with grafted fat, less reliable, with filler (reliable but may be temporary and may be unnatural appearing or lumpy, and may add gray discoloration), or an implant (my favorite is the Flowers tear trough from Implantech, Inc.). If pedicled fat is used during blepharoplasty and pigment is contributing, stretching and lifting lower lid skin may also lighten the lower lid by decreasing density of pigment in the multiple very fine skin folds of thin lower eyelid. You can try bleaching (hydroquinone, azelaic acid, kojic acid, tretinoin, others) lower eyelid skin if that skin is darker than surrounding skin. Opening the upper lids and re-shaping the palpebral aperture with canthopexy also may lighten, awaken, and change the slant of your eyelids a bit so they appear less deep set. YOU ARE SPECIAL and BEAUTIFUL, do not embark upon any surgical treatment without carefully considering upside vs. downside. Seek help from a board certified plastic surgeon or an excellent oculoplastic surgeon.