The automatic generation of natural internal coordinates is extended to all cases except multiply fused ring systems, i.e., "cages." This is achieved by a relatively simple code; most of the geometrical cases can now be treated by a single subroutine. To handle molecules containing cages we combine the natural internal coordinates with the delocalized coordinates of Baker, Kessi, and Delley. We have also modified the delocalized coordinates to separate modes with strongly different force constants. The new methods show very good convergence properties in geometry optimizations. Our test set of molecules covers a wide range of atoms and of different bonding situations. For such molecules good internal coordinates are particularly important because no reliable initial force constant matrix can be obtained to accelerate convergence.