Treatment costs are found to vary substantially and systematically within DRGs. Several factors have been shown to contribute to the variation in costs within DRGs. We argue that readmissions might also explain part of the observed variation in costs. A substantial number of all readmissions occur to a different hospital. The change in hospital indicates that a progression of the illness has occurred since the initial hospitalisation. As a result, different-hospital readmissions might be more costly compared to same-hospital admissions. The aim of this paper is twofold. Firstly, to analyse differences in costs between different-hospital readmissions and same-hospital readmissions within the same DRG. Secondly, to investigate whether the effect of different-hospital readmission on costs vary depending of provider type (general versus teaching hospital). We use a rich Danish patient-level administrative data set covering inpatient stays in the period 2008–2010. We exploit the fact that some patients are readmitted within the same DRG and that some of these readmissions occur at different hospitals in a propensity score difference-in-difference design. The estimates are based on a restricted sample of n = 328 patients. Our results show that the costs of different-hospital readmissions are significantly higher relative to the costs of same-hospital readmission (approx. €777). Furthermore, the cost difference is found to be almost twice the size for patients readmitted to a teaching hospital (approx. €1016) (P < 0.10) compared to patients readmitted to a different general hospital (approx. €511) (P < 0.10). The results suggest that hospitals in general face a potential risk by treating different-hospital readmissions, and that the financial consequences are highest among teaching hospitals. If teaching hospitals are not compensated for the additional costs of treating different-hospital readmission patients, they might be unfairly funded under a DRG-based payment scheme.