Consumer sleep-tracking devices provide an unobtrusive and affordable way to learn about personal sleep habits. Recent research focused primarily on the information provided by such devices, i.e., whether the information is accurate and meaningful to people. However, little is known about how people judge the credibility of such information, and how the functionality and the design may influence such judgements. Hence, the aim of this research was to examine how consumers assess the credibility of sleep-tracking devices. We conducted a qualitative study with 22 participants who tracked their sleep for 3 nights with three different devices: Fitbit Charge 2, Neuroon EEG, and SleepScope, a medical sleep monitor. Based on semi-structured interviews, we found that people assess the credibility of sleep-tracking devices based not only on the credibility of sleep data per se, but also on device functionality, interface design and physical appearance. People found it difficult to judge credibility, because of the complexities of sleep stages and micro-arousals (sleep fallacy) and the black boxed nature of devices (black box fallacy), and also because of the misalignment between objective sleep measures and subjective sleep quality. We discuss the significance of design and functionality on the credibility of personal health technologies and highlight design challenges and opportunities to enhance their credibility. CCS Concepts: • Human-centered computing → Empirical studies in HCI.