It is argued that from a genuine Leibnizian point of view the well-known thought experiment, call it BTE, involving a possible world with only two exactly similar objects, cannot be used to refute Leibniz’s principle of the identity of indiscernibles (LIdI). If the claim that there are two objects in BTE is based on primitive thisnesses, the Leibnizian objection is that there are no such things; and even if there were, then, quite generally, something true of one object – that it has its primitive thisness – would not be true of the other. Secondly, if the duality claim is based on a primitive, irreducible relation of distinctness, the Leibnizian objection is that there are no irreducible relations. Finally, if it is said that the (putatively) two objects in BTE cannot be separately individuated, then BTE is not a counter-example to LIdI, because if there is no individuation, there are no individuals either, while LIdI presupposes that there are individuals.