Can a breast reduction make my chest significantly smaller? And, can I have one even if my breast are already somewhat small?

So I have a 32C chest, which I guess is considered average. However, I am also short with a small frame so they feel and look way too big for my body. I have always liked the aesthetic of flatter/smaller chests and personally I would like to go down to an A cup. Would a surgeon be willing to do this? I have a lot of crippling self-esteem issues surrounding my chest and have done for years, to the point where I've actually started wearing binders used by FTM transgendered people.