Jellyfish are a successful and diverse class of animals that swim via jet propulsion, with swimming performance and propulsive efficiency being related to the animal's feeding ecology and body morphology. The Rhizostomeae jellyfish lack tentacles but possess four oral lobes and eight trailing arms at the centre of their bell, giving them a body morphology quite unlike that of other free-swimming medusae. The implications of this body morphology on the mechanisms by which thrust is produced are unknown. Here, we determined the wake structure and propulsive efficiency in the blue-blubber jellyfish Catostylus mosaicus (order: Rhizostomeae). The animal is propelled during both bell contraction and bell relaxation by different thrust-generating mechanisms. During bell contraction, a jet of fluid is expelled from the subumbrellar cavity, which results from the interaction between the counter-rotating stopping (from the preceding contraction cycle) and starting vortices, creating a vortex superstructure and propulsion. This species is also able to utilise passive energy recapture, which increases the animal's swimming velocity towards the end of the bell expansion phase when the bell diameter is constant. The thrust produced during this phase is the result of the flexible bell margin manoeuvring the stopping vortex into the subumbrellar cavity during bell relaxation, enhancing its circulation, and creating a region of high pressure on the inner surface of the bell and, consequently, thrust. These mechanisms of thrust generation result in C. mosaicus having a relatively high propulsive efficiency compared with other swimmers, indicating that economical locomotion could be a contributing factor in the ecological success of these medusan swimmers.