The growing popularity of smart-speakers in recent years has led to increased interest in the capacity of Conversational Agents (CAs) to support health and wellbeing. This extends to their potential to engage users in human-like conversations as means of gathering self-reported health data. Prior research has focused on the optimization of CAs for the collection of discrete responses to standardized questionnaires. Less research however, has investigated how a more conversational modality shapes what people recount of their wellbeing nor what they make of the experience. This paper presents the findings of a lab-based random assignment study contrasting 59 participants’ experiences of two distinct designs of a CA named Sofia — each separately enabling discrete or open-ended responses to the World Health Organization-Five Wellbeing Index (WHO-5) questionnaire. Analysis of task completion times, Speech-System Interface Usability (SASSI) scores, and coherence between verbal and paper-based responses suggests that CAs can serve as a feasible means of gathering self-reported health data, although users report finding discrete response options more habitable (i.e. easier to grasp) than an open-ended alternative. We discuss the implications of these findings for the design of CAs to support the self-report of health and wellbeing, and highlight future research directions