Controllable hydraulic vibration-damping support comprising a main hydraulic circuit comprising a working chamber, a compensation chamber, and a first constricted passageway, and an auxiliary hydraulic chamber separated from the working chamber by a decoupling valve and communicating with the main hydraulic circuit by means of a second constricted passageway having a resonance frequency of less than 5 Hz. The auxiliary chamber is separated from a pneumatic chamber by a movable wall, and a control device is provided for selectively either connecting the pneumatic chamber to the open air, or bleeding air from the pneumatic chamber.