Will a benelli lift reduce areola puffiness? How will this affect my areola shape and size? (photos)

I had a breast augmentation done 12 years ago (265cc), mostly for size but also the shape. I have puffy areolas, which gives the cone shape to my breasts. I'm getting another breast augmentation (adding 100-150cc), and my surgeon suggested a benelli lift to remove the puffy areolas. Will it help, and will it be permanent? Will it make the areolas bigger or smaller? I'd like them to be smaller if anything.