The Anti-Tragus is the raised fold of cartilage that sits on the outer side of the ear, above the ear lobe and just opposite the tragus. Many people's anti-tragus' are too small to be pierced, however micro jewellery is often successfully used. Ball Closure Rings can be used, but they will flop about a lot and aggravate the piercing. Using a curved barbell will probably improve the chances of a quick healing.
Healing Time: 8 - 16 weeks
Ear cartilage piercings generally take longer to heal than lobe piercings.
This is often due to a combination of things, such as the location of the piercing in the cartilage, the type of jewellery used and the tension that jewellery creates to the structure of the cartilage.
Using biocompatible plastics (like PTFE), cleaning cartilage regularly, and increasing your intake of minerals will certainly benefit your piercing; however a piercing will almost always be doomed to failure if improper jewellery and poor planning are used and left unmonitored.