Cream butter, sugar and vanilla with a spoon and gradually blend in flour. Mix in pecans.
Shape into 3/4 inch ball, rolling in palm of hands. Place about 1/2 inch apart on ungreased cookie sheet.
Bake in 325 degrees F oven for about 30 minutes. Cookies should be creamy colored. Let cook until slightly warm, then take out of oven and roll in extra sugar that has been placed in mixing bowl. Then roll a second time, cool completely and store in tight container.