The conceptual distinction between moral cosmopolitanism and political (institutional) cosmopolitanism lies at the heart of many contemporary writings on global justice. The former refers to a belief that all people in the world belong to one all-encompassing moral community and that this should always bear upon considerations about justice. The latter stands for a belief that realization of requirements of justice, as specified by moral cosmopolitanism, should be entrusted to, in essence, a globalised version of the modern state. In order to avoid the controversial idea of a "world-state" while maintaining strong moral convictions, most advocates of cosmopolitan justice claim that the first view does in no way entail the second. Thus, an alternative path to global institutional solutions is said to open, labelled "multi-level governance", "cosmopolitan federalism" and so on. I wish to argue in my paper that this central distinction, as elaborated in the work of B. Barry, D. Moellendorf., T. Pogge, K.C. Tan, S. Caney and others cannot do the job it is supposed to - at least as long as we retain strong moral ideals about global justice (for example, certain comparative principles such as fair equality of opportunity). One reason is that the proposed "moderate" institutional arrangements (Tobin Tax, Global Resource Tax etc.) are nowhere near exhausting the moral content of cosmopolitan justice; another is the issue of real-world enforcement of the given norms. Finally, I will discuss how a somewhat less ambitious approach to the problem founded in basic human rights might be formulated.