The dynamic response of under-deck cable-stayed bridges with steel–concrete composite decks under moving loads is presented, and different parameters are considered. The vibrational modes with a strong contribution in the response, the key parameters that control the modal frequencies, and those that reduce the maximum accelerations registered on the deck in a cost-effective manner, are identified. It is found that relatively high accelerations occur and that these can be increased by large load eccentricities. It is also found that maximum accelerations are conditioned by the amplification and cancellation speeds of the loads. Increasing the depth of the deck is determined to be the most effective way to reduce the maximum accelerations. Decks formed by I-beams seem to be quite appropriate from the perspective of dynamic behaviour, while box sections tend to increase the overall cost of the bridge. The findings provide effective strategies to define the most efficient configurations that satisfy the limit state of vibrations, which is critical for this type of bridge.