Benthic invertebrates in streams and rivers face a dominant downstream flow that may impose drift. The mechanisms that allow organisms to maintain their position instead of being swept downstream are not well known. One possible strategy involves active behaviour: Organisms perform small‐scale counter‐current displacements along the streambed. Because these fine‐scale processes are difficult to approach in field studies, evidence for behavioural mechanisms against flow advection has remained scarce. We reconstruct the three‐dimensional trajectories of the widespread cyclopoid copepod Eucyclops serrulatus moving freely in the water column and in the transparent sediment bed of a laboratory flume. In the different experiments, the average flow velocity is 12, 35, and 67 mm/s. We isolate the behavioural component of their motion by subtracting the local flow velocity. We show that copepods stay preferentially within the interstitial space of the sediment bed or close to its surface from which they perform frequent excursions in the water column. We also show that copepods perform active counter‐current swimming to limit downstream drift. The counter‐current swimming effort increases with flow velocity, and therefore, downstream drift remains moderate and does not vary strongly for the different flow rates tested. This active behavioural response to changing flow conditions, combined with frequent stops in the substratum where flow velocity is negligible, may confer lotic copepods the ability to reduce downstream transport. Our results confirm the importance of behaviour in drift avoidance and may evoke further research on taxon‐specific responses to varying hydraulic conditions.