This randomized phase IIb trial studies how well alternative dosing of exemestane before surgery works in treating in postmenopausal patients with stage 0-II estrogen positive breast cancer. Chemoprevention is the use of drugs to keep breast cancer from forming or coming back. The use of exemestane may treat early stage (stage 0-II) breast cancer. Comparing the exemestane standard dose regimen versus two alternative, less frequent dose regimens may decrease undesirable symptoms and be more effective in treating breast cancer.