The ethics of the international monetary system (IMS) can be framed either as a case of background injustice or of structural injustice. Both ideas suggest that due to the background conditions, the interaction of agents, in a context of no rules, can lead to domination and unfairness. Moreover, both ideas emphasise the need to create regulation, or a structure, that prevents domination and unfairness. This article asks how (if at all) do monetary regimes, or each of the three scenarios that stem from the Mundell-Fleming trilemma, raise domination and unfairness. This article identifies domination and unfairness in both regimes with open capital markets: the one with floating exchange rates and the one with fixed exchange rates. Moreover, it offers a principle of non-domination, according to which institutions of the IMS ought to guarantee effective sovereignty of participant states or offer an equal distribution of this value when securing full effective sovereignty for all is not possible. For the last regime, of closed capital markets, this article identifies unfairness but no domination. By identifying domination and unfairness in each regime, this article proposes policies and regulation, or a structure, to prevent and mitigate these issues.