Is it possible to get a breast reduction from a D down to an small A/B size? (photo)

The cup size measure has inherent variability.  Tissue density will always play a big role in the number of grams removed.  Going too small can sacrifice the shape of the breasts.  The nipple has to have a blood supply to survive from the underlying tissue.

Congratulations on your decision to proceed with breast reduction surgery; it is one of the most patient pleasing operations we perform.
Yes, it is possible to reduce the breasts size very significantly. The concern with the amount of tissue removed is related to blood flow to the remaining tissue; if too much tissue is removed in one operation the blood flow to the remaining tissue (including nipple/areola) may be compromised. Part of the tissue that is left in place is called the “pedicle"; this segment of tissue is responsible for delivering the blood supply to the nipple/areola tissue. If the pedicle is made too small (in the effort to reduce the breasts as much as possible) then patient will likely have problems with tissue survival. 
My best suggestion: seek consultation with board-certified plastic surgeons who can demonstrate significant experience achieving the types of outcomes you will be pleased with. This careful selection of plastic surgeon will be the most important decision you make.
Before undergoing the breast reduction procedure it will be very important to communicate your size goals with your surgeon. Most patients wish to achieve a enough of a reduction to help with their symptoms while remaining proportionate with the remainder of their torso. I suggest that you do not communicate your goals in terms of achieving a specific cup size. For example, a “A/B cup size” may mean different things to different people and therefore may be a source of miscommunication. In my practice, I ask patients to communicate their goals with the help of goal photographs.
I hope this helps. Best wishes.