Offspring resulting from mating among close relatives can suffer from impaired fitness through the expression of recessive alleles with deleterious effects. Postcopulatory sperm selection (a prezygotic mechanism of cryptic female choice) has been suggested to be an effective way to avoid inbreeding. To investigate whether postcopulatory female choice allows the avoidance of fertilization by close kin, we performed artificial inseminations in a promiscuous bird, the houbara bustard (Chlamydotis undulata undulata). Females were inseminated with a mix of sperm from triads of males, each constituted of a male genetically unrelated to the female, a first cousin and a half-sibling. When counting the number of eggs sired by unrelated males, cousins or half-siblings, we found a significant deviation from the expected random distribution, with more eggs sired by unrelated males. However, offspring sired by cousins, and especially by half-siblings suffered from high prehatching mortality, suggesting that the observed paternity skew towards unrelated males might reflect differential offspring mortality rather than sperm selection. In agreement with this hypothesis, within-triad siring success was similar for the three parental relatedness categories, but the relationship between siring and hatching success differed across categories. In clutches with high hatching success, unrelated males had the highest success while in clutches with high failure rate, half-siblings had the highest success. Offspring sired by half-siblings also suffered from reduced growth rate during the first three months and higher posthatching mortality. Hence, despite substantial fitness costs associated with fertilization by close relatives, females do not seem to select sperm of unrelated males.