Safe and Effective Chemical Peel for Under Eye Area?

I just had my first glycolic acid peel (20%) for the under eye and felt a slight burn. But after that, nothing realy happened. The doctor said she will be using more concentration every time, but I wonder if it works at all? I have a fair skin and "some" pigmentation and fine mechanical wrinkles under eyes when I smile. Nothing severe, but I feel less elasticity of skin under the eyes. How effective would be 8 treatments of glycolic acid peels, starting at 20% conentration, and increasing it every time?