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The aim of this article is to resume discussions around the principle of identity of indiscernibles (PIdI) by specifying the type of entities that could derogate from it. I defend the idea that the rejection of PIdI comes from the possibility of three types of doubles: pure replicas, or perfect reproductions, pure doubles, doubles which can not even be distinguished by spatio-temporal relations, and finally pure coincidents. The thesis that I defend is to show that the existence of such entities is not only conceivable, but even, for the first two kinds, physically possible. With regard to the possibility of pure coincidents, the rejection of such entities may be supported by a principle of ontological parsimony based on causal indifference, independently of PIdI.