AWS D1.1 and welding classes

Hello from Italy.
I have been working around a big steel structure to erect in middle east. I am arranging the general specification regarding the weldings in
accordance to the American standard AWS.
Some of these structures are more stressed than others and a "better" welding is required. I mean better in sense of percentage and type of inspection (visual, dye penetrant, magnetic particle, ultrasonic, etc.) and acceptability criteria.
I'd like to know if AWS D1.1 includes the classification of weldings and, if it does, if class A is stricter (better) than class B, C, D or the quality classification sequence is the opposite (D then C, then B, A last).
If a class A weld better done than a class C one?
Thanks a lot frank
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