AbstractLanguage documentation often requires segmenting transcriptions of utterances collected on the field into words and morphemes. While these two tasks are typically performed in succession, we study here Bayesian models for simultaneously segmenting utterances at these two levels. Our aim is twofold: (a) to study the effect of explicitly introducing a hierarchy of units in joint segmentation models; (b) to further assess whether these two levels can be better identified through weak supervision. For this, we first consider a deterministic coupling between independent models; then design and evaluate hierarchical Bayesian models. Experiments with two under-resourced languages (Japhug and Tsez) allow us to better understand the value of various types of weak supervision. In our analysis, we use these results to revisit the distributional hypotheses behind Bayesian segmentation models and evaluate their validity for language documentation data.