One of the main concerns about capitation-based reimbursement systems is that tertiary institutions may be underfunded due to insufficient reimbursements of more complicated cases. We test this hypothesis with a data set from New Zealand that, in 2003, introduced a capitation system where public healthcare provider funding is primarily based on the characteristics of the regional population. Investigating the funding for all cases from 2003 to 2011, we find evidence that tertiary providers are at a disadvantage compared with secondary providers. The reasons are that tertiary providers not only attract the most complicated, but also the highest number of cases. Our findings suggest that accurate risk adjustment is crucial to the success of a capitation-based reimbursement system. Copyright © 2017 John Wiley & Sons, Ltd.