Genes of the major histocompatibility complex (MHC) are regarded as a potentially important target of mate choice due to the fitness benefits that may be conferred to the offspring. According to the complementary genes hypothesis, females mate with MHC dissimilar males to enhance the immunocompetence of their offspring or to avoid inbreeding depression. Here, we investigate whether selection favours a preference for maximally dissimilar or optimally dissimilar MHC class I types, based on MHC genotypes, average amino acid distances and the functional properties of the antigen-binding sites (MHC supertypes); and whether MHC type dissimilarity predicts relatedness between mates in a wild great tit population. In particular, we explore the role that MHC class I plays in female mate choice decisions while controlling for relatedness and spatial population structure, and examine the reproductive fitness consequences of MHC compatibility between mates. We find no evidence for the hypotheses that females select mates on the basis of either maximal or optimal MHC class I dissimilarity. A weak correlation between MHC allele sharing and relatedness, and between MHC supertype sharing and relatedness suggests that MHC dissimilarity at functional variants may not provide an effective index of relatedness. Moreover the reproductive success of pairs did not vary with MHC dissimilarity. Our results provide no support for the suggestion that selection favours, or that mate choice realises, a preference for complimentary MHC types.