Heat oven to 375. Mix sugars, butter and eggs. Stir in remaining ingredients. Drop by rounded teaspoonfuls about 2 inches apart on ungreased cookie sheet.
Bake until almost no indention remains when touched (about 8-10 mins.); cool. Frost w/ lemon frosting (below). Makes 3 doz.
Lemon Frosting: Mix sugar, butter and lemon peel. Beat in lemon juice and water, adding more water if necessary.
FOR CARROT COOKIES, substitute carrots for zucchini.