The last section of this paper presents a rigorous version of Tiebout's theory of local public goods. It is shown that equilibria exist and are Pareto optimal. This rigorous theory follows closely the more rigorous part of Tiebout's work. This rigorous theory makes a number of very special assumptions which make local public goods essentially private. The body of this paper presents a series of examples, which show that if one tries to generalize the rigorous version of Tiebout's theory in a number of interesting directions, then equilibria may no longer exist or may not be Pareto optimal. The conclusion is that Tiebout's idea does not lead to a satisfactory general theory of local public goods.