According to the first version regarding objects within a given world, PII-Objects, there are no qualitatively indiscernible objects within a single possible world. PII-Objects therefore rules out states of affairs like those suggested in Black (1952) involving qualitatively indiscernible iron spheres. Although PII-Objects ensures that no object has a qualitatively indiscernible worldmate, it is neutral on whether or not there are qualitatively indiscernible worlds, leaving open whether there are distinct yet qualitatively indiscernible worlds.