We do not use classifications AAAA or A +++ which are not official, and make subjective a classification already difficult to realize objectively. 
We use the official classification of the Ministére de la Perliculture:
Top Gem : perfect pearl, with an excellent luster
Grade A : surface without imperfections on 90%. Very beautiful luster.
Grade B : Smooth surface on 70%. Good luster at minimum.
Grade C : Smooth surface on 40%. Medium luster at minimum.
Grade D : Weak luster, Small imperfections on more than 60%

There are other secondary criteria that define the surface quality of the pearl, the basic color, the secondary tints etc…
Besides its diameter and its weight, its shape is classified as follows:

• Round and half round.
• Half baroque in the shape of drop, buttons and oval pearls. 
• Circled, baroque

Conversion between Tahitian classification and Institute Gemnological of America classification :
We require your attention concerning the differences of taxonomy with the Tahitian system. Indeed A grade within the Tahitian classification correponds to top gem pearls, whereas withing the AAA classification, the A grade is a quality so poor that we don’t actually them. AAAA, or more A with ++++ don’t exist in official grades.