Cream butter or margarine and sugar together until fluffy. Add eggs and vanilla and beat for 2-3 minutes.
Whisk or sift together flour, baking powder and salt. Slowly add to creamed until combined.
Place dough in refrigerator and let chill for at least 2 hours.
Roll about 1 t. of dough into a ball. Combine 1/3 c. sugar with cinnamon. Roll dough in cinnamon sugar until covered.
Place dough on cookie sheets, flatten slightly with the bottom of a glass, and bake at 350 degrees for 10-12 minutes, until edges are very lightly browned.
