The prospect of central banks issuing digital currency (CBDC) immediately raises the question of how this new form of money should co-exist and interact with existing forms of money. This paper evaluates three different scenarios for the implementation of CBDC in terms of their monetary policy implications. In the ‘money user scenario’ CBDC co-exists with both cash and commercial bank deposits. In the ‘money manager scenario’ cash is abolished and CBDC co-exists only with commercial bank deposits. And in the ‘money maker scenario’ commercial bank deposits are abolished and CBDC co-exist only with cash. The evaluation is based on an adaption of the classical international monetary policy trilemma to a domestic monetary system with multiple forms of money. Our proposition is that a monetary system with two competing money creators, the central bank and the commercial banking sector, can simultaneously only pursue two out of the following three policy objectives: Free convertibility between CBDC and bank money, parity between CBDC and bank money, and central bank monetary sovereignty, which is the use of monetary policy for anything else than support for commercial bank credit creation. This means that the decision on the design of a monetary system with CBDC implies a crucial political decision on the priorities of the central bank.