In natural populations, mating between relatives can have important fitness consequences due to the negative effects of reduced heterozygosity. Parental level of inbreeding or heterozygosity has been also found to influence the performance of offspring, via direct and indirect parental effects that are independent of the progeny own level of genetic diversity. In this study, we first analysed the effects of parental heterozygosity and relatedness (i.e. an estimate of offspring genetic diversity) on four traits related to offspring viability in great tits (Parus major) using 15 microsatellite markers. Second, we tested whether significant heterozygosity–fitness correlations (HFCs) were due to ‘local’ (i.e. linkage to genes influencing fitness) and/or ‘general’ (genome-wide heterozygosity) effects. We found a significant negative relationship between parental genetic relatedness and hatching success, and maternal heterozygosity was positively associated with offspring body size. The characteristics of the studied populations (recent admixture, polygynous matings) together with the fact that we found evidence for identity disequilibrium across our set of neutral markers suggest that HFCs may have resulted from genome-wide inbreeding depression. However, one locus (Ase18) had disproportionately large effects on the observed HFCs: heterozygosity at this locus had significant positive effects on hatching success and offspring size. It suggests that this marker may lie near to a functional locus under selection (i.e. a local effect) or, alternatively, heterozygosity at this locus might be correlated to heterozygosity across the genome due to the extensive ID found in our populations (i.e. a general effect). Collectively, our results lend support to both the general and local effect hypotheses and reinforce the view that HFCs lie on a continuum from inbreeding depression to those strictly due to linkage between marker loci and genes under selection.