1. In a bowl, beat butter and confectioners' sugar until smooth and creamy. Add vanilla.
2. On low speed, beat in flour and pecans. Wrap dough in plastic wrap and refrigerate 1 to 2 hours, until firm.
3. Heat oven to 325 degrees . Pinch off pieces of dough in rounded teaspoonfuls. Roll into logs, taper ends and bend into crescents. Place on ungreased baking sheets.
4. Bake at 325 degrees for 19 to 20 minutes, until lightly browned.
5. Remove cookies to a wire rack. Sprinkle with a heavy layer of confectioners' sugar. Cool completely. Sprinkle again with confectioners' sugar.