Combine shortening and chocolate in top of a double boiler; bring water to a boil. Reduce heat to low; cook until chocolate melts, stirring occasionally. Remove from heat; add 1 1/2 cups sugar and eggs. Beat well with an electric mixer.
Sift together flour and baking powder in a small mixing bowl. Add half of flour mixture to chocolate mixture, stirring until well blended. Stir in vanilla. Add remaining flour mixture, stirring well.
Coat hands well with powdered sugar, and roll dough into 1-inch balls. Place 2 inches apart on lightly greased cookie sheets. Lightly sift powdered sugar over cookies.
Bake at 325° for 15 minutes. Cool slightly on cookie sheets. Remove to wire racks to cool completely.