Little evidence of benefits from female mate choice has been found when males provide no parental care or resources. Yet, good genes models of sexual selection suggest that elaborated male sexual characters are reliable signals of mate quality and that the offspring of males with elaborate sexual ornaments will perform better than those of males with less elaborate ornaments. We used cod (Gadus morhua L.), an externally fertilizing species where males provide nothing but sperm, to examine the potential of optimal mate selection with respect to offspring survival. By applying in vitro fertilizations, we crossed eight females with nine males in all possible combinations and reared each of the 72 sib groups. We found that offspring survival was dependent on which female was mated with which male and that optimal mate selection has the potential to increase mean offspring survival from 31.9 to 55.6% (a 74% increase). However, the size of the male sexual ornaments and sperm quality (i.e. sperm velocity and sperm density) could not predict offspring survival. Thus, even if there may be large fitness benefits of mate selection, we might not yet have identified the male characteristics generating high offspring survival.