The haplodiploid sex determining mechanism in Hymenoptera (males are haploid, females are diploid) has played an important role in the evolution of this insect order. In Hymenoptera sex is usually determined by a single locus, heterozygotes are female and hemizygotes are male. Under inbreeding, homozygous diploid and sterile males occur which form a genetic burden for a population. We review life history and genetical traits that may overcome the disadvantages of single locus complementary sex determination (sl-CSD). Behavioural adaptations to avoid matings between relatives include active dispersal from natal patches and mating preferences for non-relatives. In non-social species, temporal and spatial segregation of male and female offspring reduces the burden of sl-CSD. In social species, diploid males are produced at the expense of workers and female reproductives. In some social species, diploid males and diploid male producing queens are killed by workers. Diploid male production may have played a role in the evolution or maintenance of polygyny (multiple queens) and polyandry (multiple mating). Some forms of thelytoky (parthenogenetic female production) increase homozygosity and are therefore incompatible with sl-CSD. We discuss a number of hypothetical adaptations to sl-CSD which should be considered in future studies of this insect order.