Canthopexy is the name of an eyelid surgery used to strengthen the lateral canthal tendon and surrounding supporting structure known as the lateral retinaculum. The orbicularis muscle is also reinforced in the process.
The goal is to strengthen the tissues of the canthus to help maintain the normal position and relationship between the eyelid and eyeball. Canthopexy is typically used as part of lower eyelid blepharoplasty, especially when done from a transcutaneous approach.
Canthopexy is non-destructive in that the canthal tendon is not disinserted as is done with canthoplasty. It is thus a relatively weak but also safer and less complex procedure.