Aquatic bladderworts (Utricularia gibba and U. australis) capture zooplankton in mechanically triggered underwater traps. With characteristic dimensions less than 1 mm, the trapping structures are among the smallest known to capture prey by suction, a mechanism that is not effective in the creeping-flow regime where viscous forces prevent the generation of fast and energy-efficient suction flows. To understand what makes suction feeding possible on the small scale of bladderwort traps, we characterised their suction flows experimentally (using particle image velocimetry) and mathematically (using computational fluid dynamics and analytical mathematical models). We show that bladderwort traps avoid the adverse effects of creeping flow by generating strong, fast-onset suction pressures. Our findings suggest that traps use three morphological adaptations: the trap walls' fast release of elastic energy ensures strong and constant suction pressure; the trap door's fast opening ensures effectively instantaneous onset of suction; the short channel leading into the trap ensures undeveloped flow, which maintains a wide effective channel diameter. Bladderwort traps generate much stronger suction flows than larval fish with similar gape sizes because of the traps' considerably stronger suction pressures. However, bladderworts' ability to generate strong suction flows comes at considerable energetic expense.