Cream butter in a medium mixing bowl; add 1/2 cup sugar, water, and vanilla, beating well.
Combine flour and pecans in a small mixing bowl; stir well. Gradually add to creamed mixture, stirring well.
Pinch off small portions of dough, and shape like dates. Place 1 inch apart on ungreased cookie sheets, and bake at 325° for 25 minutes or until lightly browned. Remove from cookie sheets while still warm, and roll each cookie in remaining sugar. Place on wire racks to cool completely.