Preheat oven to 275 degrees. In a large mixing bowl with an electric mixer on medium speed cream together butter and sugar until smooth. Beat in vanilla. Gradually add flour and mix just until blended. Stir in pecans.
With floured hands roll dough into 1 inch sized balls, continue to dust your hands with more flour as you make more balls. Place balls 1 inch apart onto ungreased baking sheets.
Bake for 30 to 35 minutes. When cool enough to handle, but still warm roll cookies in additional powdered sugar. Place cookies onto cooling racks to cool completely.