Most applied work in health economics accepts, if only implicitly, the axiom of completeness. Preferences over health states or health services are assumed to be well formed. They are effectively 'data' waiting to be collected. An alternative perspective suggests that values are initially incomplete and are constructed rather than just revealed in the process of answering choice-related questions such as willingness to pay or standard gambles. What might appear as measurement error may, therefore, be a more deliberate process of reflection and deliberation. This paper reports on a study that assessed the completeness of health preferences. The results show a mixed pattern. For most of the sample, values were stable over repeat administration, suggesting completeness. However, one-third of participants deliberately changed their answers and suggested that the interview process had forced them to think about their values more deeply. While it is premature to draw conclusions from this small sample, the suggestion is that completeness cannot be taken for granted.