Two challenges stand out in the study of deliberation: the development of appropriate methodological tools and the development of more unified analytical frameworks. On the one hand, analysing deliberative processes is demanding and time-consuming; hence we tend to have only few and non-randomly selected cases at the group or context level. In addition, the real world of deliberation presents us with a complex matrix of nested, cross-classified, and repeated speakers. This article shows that Bayesian multi-level modelling provides an elegant way to tackle these methodological problems. On the other hand, we attempt to enrich comparative institutionalism with individual characteristics and psychologically relevant variables (such as group composition). Focusing on Swiss and German parliamentary debates we show that institutional factors - in particular, consensus systems -, the gender composition of committees and plenary sessions, and age matter for the quality of deliberation. Furthermore, we also show that partisan affiliation - government or opposition status of MPs - affects deliberative quality and can refine institutional arguments. We conclude that a multi-level approach to deliberation focusing on contextual and actor-related characteristics and using Bayesian hierarchical modelling paves the way toward a more advanced understanding - and methodological handling - of deliberative processes.