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Sperm-competition success (SCS) is seen as centrally important for evolutionary change: superior fathers sire superior sons and thereby inherit the traits that make them superior. Additional hypotheses, that phenotypic plasticity in SCS and sperm ageing explain variation in paternity, are less considered. Even though various alleles have individually been shown to be correlated with variation in SCS, few studies have addressed the heritability, or evolvability, of overall SCS. Those studies that have addressed found low or no heritability and have not examined evolvability. They have further not excluded phenotypic plasticity, and temporal effects on SCS, despite their known dramatic effects on sperm function. In Drosophila melanogaster, we found that both standard components of sperm competition, sperm defence and sperm offence, showed nonsignificant heritability across several offspring cohorts. Instead, our analysis revealed, for the first time, the existence of phenotypic plasticity in SCS across an extreme environment (5% CO2), and an influence of sperm ageing. Evolvability of SCS was substantial for sperm defence but weak for sperm offence. Our results suggest that the paradigm of explaining evolution by sperm competition is more complex and will benefit from further experimental work on the heritability or evolvability of SCS, measuring phenotypic plasticity, and separating the effects of sperm competition and sperm ageing.