Preheat oven to 350° F.
Beat butter until light and creamy.
Thoroughly mix flour with 3/4 cup sugar; add to butter and blend until consistency of coarse crumbs.
Add pecans and vanilla to form a smooth dough.
Roll into 1-inch balls; place on ungreased cookie sheet and bake 10 to 12 minutes, or until cookies are very lightly browned.
Roll in remaining powdered sugar while warm.
Cool on wire rack.