This surgery would probably fall under the "breast lift" or mastopexy procedure. I only say this because it sounds like the larger breast is lower than the other.
It is great that you don't want implants, they were a disaster for me, had to have them removed after 10 years. Many, many procedures to resolve problems with implants.
I don't know how old you are, but as one ages, there is usually a weight gain. So as you get older you breasts will probably enlarge some.
Fat transfers have not worked successfully, it isn't that Doctor's don't do them and get paid for them... it is that they don't work long term.
Remember, the Dr gets paid, no matter what.
I would suggest serious research on plastic surgeons in your city or nearby. I would not go to a university teaching hospital unless you don't care if a student intern operates on you. I would not run the risk myself.
You want to know what the specialty is of this Doctor. One Doctor in Hollywood ONLY does breasts, her Advertisement Reads... we do better breasts than God... apparently she does, she is very successful.
What you want to know is who certifies this Doctor (you want preferably the two biggest Plastic Surgeon Certifications to be on his record). Where did he graduate in his class, avoid guys from the bottom should go without saying.
Check with the State Medical Board of Licensing, what problems has he had... has he practiced in other states... check them too.
If you like the sound of him/her, run a net check with a good service and see if he has ever been sued and for what and what the disposition of the suit was.
BEWARE of a Doctor that doesn't carry Mal-Practice Insurance... if his rates are too high, maybe it is because he is a bad surgeon.
Ask questions, if questions offend him.... run.
Consider a woman surgeon, ask the same questions, check the same checks.
Be very frank with your Doctor, I was, tell them you are a symetry, everything matches and is even type of person and those are the results you are looking for.
Take pictures of breasts you find attractive. This means either find magazines (ugh) or else look at plastic surgeon sites on the net and copy and save pictures of breasts you find attractive. Many surgeons have before and after pictures on their sites... just remember all Dr show their good work only.
Keep a copy of what you give the Doctor, notice if he is making notes about what you say you want. He should be working off these notes when he does your surgery. Not off the top of his head.