In a large mixing bowl, dissolve yeast in warm water. Add sugar/water mixture, shortening, salt, eggs and whole wheat flour. Beat until smooth. Stir in enough all-purpose flour to form a soft dough.
Turn onto a floured surface; knead until smooth and elastic, about 6-8 minutes. Place in a greased bowl, turning once to grease top. Cover and let rise in a warm place until doubled (about 1 hour).
Punch dough down. Turn onto a lightly floured surface; divide into four pieces. Shape into 2-inch balls. Dip balls into melted butter and place in 8" x 8" baking pan allowing balls to just touch. Cover and let rise until doubled (about 25 minutes).
Bake at 375 degrees for 11-15 minutes or until browned. Remove from pans to wire racks. Serve warm.