The invention relates to a rotatable fairing (1) for a marine riser (2) or other slender marine structure. The fairing (1) is arranged on the riser for reducing watercurrent-induced stresses on said riser (2), said fairing (1) having a tail portion (3) for trailing generally in the downstream direction behind said riser. The fairing (1) is provided with an attenuation unit (8) for counteracting the unstable rotation of said fairing (2) relative to said riser (2), in order to prevent undesired vibrations of said riser (2). The fairing is provided with one or more clamps (10) for attachment to and around a periphery of said riser (2), said clamps (10) arranged with a gear rim (12) for engagement with an actuating cogged wheel (14) of said attenuation unit (8).