Even before their deployment in major economies, one of the concerns that has been voiced about central bank digital currency (CBDC) is that it might be too successful and lead to bank disintermediation, which could intensify further in the case of a banking crisis. Some also argue that CBDC might crowd out private payment solutions beyond what would be desirable from the perspective of the comparative advantages of private and public sector money. This paper discusses success factors for CBDC and how to avoid the risk of crowding out. After examining ways to prevent excessive use as a store of value, the study emphasises the importance of the functional scope of CBDC for the payment functions of money. The paper also recalls the risks that use could be too low if functional scope, convenience or reachability are unattractive for users. Finding an adequate functional scope – neither too broad to crowd out private sector solutions, nor too narrow to be of limited use – is challenging in an industry with network effects, like payments. The role of the incentives offered to private sector service providers involved in distributing, using and processing CBDC (banks, wallet providers, merchants, payment processors, acquirers, etc.) is discussed, including fees and compensation.