In this paper, I critically assess the view that quantum mechanics, and quantum theory more generally, is best interpreted on the basis of an ontology of non-individual objects. I argue that—if one opts for non-individuality at all—one should go for a property- rather than object-based framework. To support this claim, I consider first the role that the Principle of the Identity of the Indiscernibles is supposed to play in this context. Then, I look at more specific facts concerning particle number in quantum field theory and the no-go results that obtain in relativistic quantum field theory. In all these cases, I argue, a theory of non-individual objects falls short of providing a satisfactory explanation, while an ontology of properties fares much better. The necessity follows to provide a precise interpretation of what has been referred to as the Received View of quantum mechanics, and to reassess an ongoing line of research based on the notion of non-individual object.