Links between central counterparties (CCPs) enable participants to clear positions in any linked CCP without needing to maintain multiple CCP memberships. While links enable exposure to be reduced by allowing netting across CCPs, CCPs become exposed to one another through the possibility of a CCP default. The change in system exposure resulting from these two effects has recently been of great interest to policymakers, and we assess this quantitatively using a straightforward extension of the model of Duffie and Zhu. Our model shows that CCP links can reduce overall system exposure in most plausible scenarios. This conclusion is robust to changes in assumptions about the nature of participants and their exposures, as well as to the existence of more than two linked CCPs.