If you want to remove them permanently, I watched the programme 'ten years younger' the other week. Apparently bags under the eyes are 'little pockets of fat', and they made an incision in the pink bit of the eye (the bit you can see when you pull your cheek down) and just lifted the little pieces of fat out! It was amazing and she only had one stitch in each eye! Not too sure of how much this would cost, but for permanent results it may be worth looking in to.