Dear Marian, First of all, I'm glad you are describing your concerns so precisely. Often times people call them under eye bags, not knowing the hollows exaggerate the swollen look of the lower eyelid. By filling the hollows, these bags can be less noticeable. Our filler of choice for the tear trough is the Restylane-L. This small particle-size filler allows for fine adjustments to fill in subtle areas and achieve smooth outcome. Another advantage of hyaluronic acids in general is that they can be easily removed/softened with a hyaluronidase. To avoid swelling in this delicate area, we normally build it up gradually. Even if you might need 3 ML (that's 3 syringes) to achieve the best result, we rarely recommend more than one syringe (divided to both sides) at each visit. Regards, Dr. Niu