The Even Better Serum is not designed to specifically be used around the eye area. Many people still do, but the Even Better Eye is Ophthalmologist tested and approved to be safe for the eyes. The same thing with the moisturizer. Unless it is an actual eye cream, most moisturizers are not recommended to be used around the eye area as they can "seep" into the eyes and cause irritation. Clinique designs and tests each product to insure it is safe.
If your primary concern is dark circles around your eyes, I would recommend using this product. I have used it since Clinique introduced it (actually before it was released on the market as I worked for them at the time). I have seen fabulous results and only use the product now on occasion to maintain my results. Now I just use the Repairwear Laser Focus eye cream.