Sperm competition favours an increase in sperm swimming velocity that maximises the chances that sperm will reach the ova before rival sperm and fertilise. Comparative studies have shown that the increase in sperm swimming speed is associated with an increase in total sperm size. However, it is not known which are the first evolutionary steps that lead to increases in sperm swimming velocity. Using a group of closely related muroid rodents that differ in levels of sperm competition, we here test the hypothesis that subtle changes in sperm design may represent early evolutionary changes that could make sperm swim faster. Our findings show that as sperm competition increases so does sperm swimming speed. Sperm swimming velocity is associated with the size of all sperm components. However, levels of sperm competition are only related to an increase in sperm head area. Such increase is a consequence of an increase in the length of the sperm head, and also of the presence of an apical hook in some of the species studied. These findings suggest that the presence of a hook may modify the sperm head in such a way that would help sperm swim faster and may also be advantageous if sperm with larger heads are better able to attach to the epithelial cells lining the lower isthmus of the oviduct where sperm remain quiescent before the final race to reach the site of fertilisation.