Helen Verran uses the term 'relational empiricism' to describe situated empirical inquiry that is attentive to the relations that constitute its objects of study, including the investigator's own practices. Relational empiricism draws on and reconfigures Science and Technology Studies' traditional concerns with reflexivity and relationality, casting empirical inquiry as an important and non-innocent world-making practice. Through a reading of Verran's postcolonial projects in Nigeria and Australia, this article develops a concept of empirical and political 'accountability' to complement her relational empiricism. In Science and an African Logic, Verran provides accounts of the relations that materialize her empirical objects. These accounts work to decompose her original objects, generating new objects that are more promising for the specific postcolonial contexts of her work. The process of decomposition is part of remaining accountable for her research methods and accountable to the worlds she is working in and writing about. This is a practice of narrating relations and learning to tell better technoscientific stories. What counts as better, however, is not given, but is always contextual and at stake. In this way, Verran acts not as participant-observer, but as participant-storyteller, telling stories to facilitate epistemic flourishing within and as part of a historically located community of practice. The understanding of accountability that emerges from this discussion is designed as a contribution, both practical and evocative, to the theoretical toolkit of Science and Technology Studies scholars who are interested in thinking concretely about how we can be more accountable to the worlds we study.