Asset indices are widely used, particularly in the analysis of Demographic and Health Surveys, where they have been routinely constructed as “wealth indices.” Such indices have been externally validated in a number of contexts. Nevertheless, we show that they often fail an internal validity test, that is, ranking individuals with “rural” assets below individuals with no assets at all. We consider from first principles what sort of indexes might make sense, given the predominantly dummy variable nature of asset schedules. We show that there is, in fact, a way to construct an asset index which does not violate some basic principles and which also has the virtue that it can be used to construct “asset inequality” measures. However, there is a need to pay careful attention to the components of the index. We show this with South African data.