Background With female multiple mating (polyandry), male-male competition extends to after copulation (sperm competition). Males respond to this selective pressure through physiological, morphological and behavioural adaptations. Sperm competitiveness is commonly decreased in heterozygote carriers of male meiotic drivers, selfish genetic elements that manipulate the production of gametes in males. This might give carriers an evolutionary incentive to reduce the risk of sperm competition. Here, we explore this possibility in house mice. Natural populations frequently harbour a well-characterised male driver (t haplotype), which is transmitted to 90 % of heterozygous (+/t) males’ offspring. Previous research demonstrated strong detrimental effects on sperm competitiveness, and suggested that +/t males are particularly disadvantaged against wild type males when first-to-mate. Low paternity success in the first-to-mate role is expected to favour male adaptations that decrease the risk of sperm competition by preventing female remating. Genotype-specific paternity patterns (sperm precedence) could lead to genetically determined alternative reproductive tactics that can spread through gene level selection. Here, we seek confirmation that +/t males are generally disadvantaged when first-to-mate and address whether males of different genotypes differ in reproductive tactics (copulatory and morphological) to maximise individual or driver fitness. Finally, we attempt to explain the mechanistic basis for alternative sperm precedence patterns in this species. Results We confirmed that +/t males are weak sperm competitors when first to mate. When two +/t males competed, the second-to-mate was more successful, which contrasts with first male sperm precedence when wild type males competed. However, we found no differences between male genotypes in reproductive behaviour or morphology that were consistent with alternative reproductive tactics. Sperm of +/+ and +/t males differed with respect to in vitro sperm features. Premature hypermotility in +/t males’ sperm can potentially explain why +/t males are very weak sperm competitors when first-to-mate. Conclusions Our results demonstrate that meiotic drivers can have strong effects on sperm precedence patterns, and may provide a heritable basis for alternative reproductive tactics motivated by reduced sperm competitiveness. We discuss how experimental and evolutionary constraints may help explain why male genotypes did not show the predicted differences.