Preheat oven to 400° F. In a small saucepan, combine butter, oil, salt, cayenne and water; bring to a boil. Add flour all at once; stir until mixture forms a smooth ball. Cook over low heat until mixture is drier but still smooth; place in mixing bowl. Beat in eggs, one at a time, incorporating completely. Stir in cheeses. Drop small spoonfuls of batter onto greased baking pans. Bake for 20 minutes, or until golden brown and firm. Serve immediately.
*For lighter puffs, use 2 whole eggs and 4 egg whites in place of 4 whole eggs.