Preheat oven to 350 degrees F. Lightly grease a cookie sheet.
Cream butter and sugar together until light and fluffy. Add vanilla. Beat in eggs, one at a time, beating well after each addition.
Sift together flour, baking soda and cream of tartar, then beat into creamed mixture.
Divide the dough into 3 or 4 portions and roll them out, one at a time, on a lightly floured board to a thickness of 1/4-inch. Cut with a cookie cutter and transfer cutouts to a greased cookie sheet. Bake at 350 degrees F. until lightly browned -- no longer than 10 minutes.