Male copepods must swim to find females, but swimming increases the risk of meeting predators and is expensive in terms of energy expenditure. Here I address the trade-offs between gains and risks and the question of how much and how fast to swim using simple models that optimise the number of lifetime mate encounters. Radically different swimming strategies are predicted for different feeding behaviours, and these predictions are tested experimentally using representative species. In general, male swimming speeds and the difference in swimming speeds between the genders are predicted and observed to increase with increasing conflict between mate searching and feeding. It is high in ambush feeders, where searching (swimming) and feeding are mutually exclusive and low in species, where the matured males do not feed at all. Ambush feeding males alternate between stationary ambush feeding and rapid search swimming. Swimming speed and the fraction of time spent searching increase with food availability, as predicted. This response is different from the pattern in other feeding types. The swimming speeds of non-feeding males are predicted and observed to be independent of the magnitude of their energy storage and to scale with the square root of body length in contrast to the proportionality scaling in feeding copepods. Suspension feeding males may search and feed at the same time, but feeding is more efficient when hovering than when cruising. Therefore, females should mainly be hovering and males cruising, which is confirmed by observations. Differences in swimming behaviour between genders and feeding types imply different mortality rates and predict well the observed patterns in population sex ratios. Sex ratios may become so female-biased that male abundances limit population growth, demonstrating that behaviours that are optimal to the individual may be suboptimal to the population.