Institutional arrangements of health systems and the incentives they set are increasingly recognized as critical to promote or hinder performance in the health sector. Looking at complex health system interventions from an institutional perspective may contribute to better understanding what are the paths and processes that lead to the results of such interventions. In this article, we propose an analytical framework drawing from new institutional economics. This framework suggests seven dimensions to look at: institutions, enforcement mechanisms, property rights, incentives, interactions between extrinsic and intrinsic sources of motivation, behavioural changes and organizational performance. For illustrative purposes, we then apply the framework to the analysis of the institutional (re)arrangements of two performance-based financing (PBF) schemes in Burundi by carrying out an empirical comparison of case studies. We use mainly qualitative data from primary and secondary sources and analyse them with focus on the seven dimensions of the framework. The analysis of the case studies provides a comparative narrative of the two PBF schemes and highlights the differences in their operational design, the challenges faced during implementation and the adaptations made. From a methodological perspective, this article proposes a tool to analyse complex health system interventions, looking beyond the evaluation of the final effects to focus on the processes through which institutional (re)arrangements affected those results. Its application indicates, at an empirical level, that such analysis could help identify lessons regarding the design of health systems interventions, such as PBF schemes, and the process of reforming institutional arrangements.