Beat butter in large bowl with electric mixer on medium to high speed for 30 seconds. Add 1 1/2 cups sugar, cream of tartar, baking soda and salt. Beat until well mixed, scraping sides of bowl occasionally. Beat in eggs and vanilla. Beat in as much of the flour as you can with the mixer. Using a wooden spoon, stir in any remaining flour. Cover.
2. Refrigerate 2 to 3 hours or until dough is easy to handle.
3. Preheat oven to 375°F. Shape dough into 1-inch balls. Roll balls in 1/4 to 1/3 cup sugar. Place balls about 2 inches apart on ungreased baking sheets.
4. Bake 7 to 8 minutes or until edges are lightly browned. Cool on baking sheets 1 minute. Remove to wire racks; cool completely.