Sperm competition is expected to be a driving force in sexual selection. In internally fertilized organisms, it occurs when ejaculates from more than one male are present simultaneously within the female's reproductive tract. It has been suggested that greater sperm size may improve the competitive ability of sperm, but studies provide contradictory results depending on the species. More recently, the role of females in the evolution of sperm morphology has been pointed out. We investigate here the male and female effects that influence sperm precedence in the giant sperm species, Drosophila bifurca Patterson & Wheeler. Females were mated with two successive males, and the paternity outcomes for both males were analyzed after determining sperm transfer and storage. We found very high values of last male sperm precedence, suggesting a strong interaction between rival sperm. However, the data also indicate high frequencies of removal of the sperm of the first male from the female reproductive tract prior to any interaction with the second male. This implies that successful paternity depends mainly on successful sperm storage. Knowing what happens to the sperm within females appears to be a prerequisite for disentangling post-copulatory sexual interactions between males and females.