Many recent studies report that individual heterozygosity at a handful of apparently neutral microsatellite markers is correlated with key components of fitness, with most studies invoking inbreeding depression as the likely underlying mechanism. The implicit assumption is that an individual's inbreeding coefficient can be estimated reliably using only 10 or so markers, but the validity of this assumption is unclear. Consequently, we have used individual-based simulations to examine the conditions under which heterozygosity and inbreeding are likely to be correlated. Our results indicate that the parameter space in which this occurs is surprisingly narrow, requiring that inbreeding events are both frequent and severe, for example, through selfing, strong population structure and/or high levels of polygyny. Even then, the correlations are strong only when large numbers of loci (~200) can be deployed to estimate heterozygosity. With the handful of markers used in most studies, correlations only become likely under the most extreme scenario we looked at, namely 20 demes of 20 individuals coupled with strong polygyny. This finding is supported by the observation that heterozygosity is only weakly correlated among markers within an individual, even in a dataset comprising 400 markers typed in diverse human populations, some of which favour consanguineous marriages. If heterozygosity and inbreeding coefficient are generally uncorrelated, then heterozygosity-fitness correlations probably have little to do with inbreeding depression. Instead, one would need to invoke chance linkage between the markers used and one or more gene(s) experiencing balancing selection. Unfortunately, both explanations sit somewhat uncomfortably with current understanding. If inbreeding is the dominant mechanism, then our simulations indicate that consanguineous mating would have to be vastly more common than is predicted for most realistic populations. Conversely, if heterosis provides the answer, there need to be many more polymorphisms with major fitness effects and higher levels of linkage disequilibrium than are generally assumed.