I can't believe noone has asked that the Elemental Staffs be added to the list.
The NQ Elemental Staff's all have a hidden effect of -2 perp cost for their corresponding Avatar.
aka
If you have the Light Staff equiped while Carbuncle is out you recieve a -2 perp cost for Carbuncle.
This applies to all of the combinations.
Also! The HQ Elemental Staff's apply a -3 perp cost!!!!!!! Same as the NQ version... just match the elements.
Again. I can't believe noone mentioned it yet! After all this is what makes free Carby possible from lvl 51+ when paired with Carbuncle Mitts
Enjoy!