Controllable hydraulic vibration-damping support intended to be interposed for purposes of damping between first and second rigid elements (E, BO), this vibration-damping support comprising: - first and second strength members (3,5) intended to be secured to the two rigid elements to be connected, the first strength member having the form of a block and the second strength member being of annular shape centred on a central axis, the first strength member being arranged substantially on said central axis, - an elastomer body which links together the first and second strength members (3,5) and which delimits at least partially a working chamber, the elastomer body having a bell shape, with a top firmly fixed to the first strength member and an annular base firmly fixed to the second strength member, - a deformable compensation chamber which communicates with the working chamber via a constricted passageway, the compensation chamber, the working chamber and the first constricted passageway forming a hydraulic volume filled with liquid, the first constricted passageway having a resonance frequency comprised between 5 and 20 Hz, - an auxiliary chamber, - a decoupling valve comprising an isolating diaphragm made of elastomer, which separates the working chamber and the auxiliary chamber, said decoupling valve being adapted for absorbing vibrations at certain frequencies greater than 20 Hz, - a control device comprising an actuator adapted for selectively locking the isolating diaphragm, wherein the auxiliary chamber and the decoupling valve are arranged in the first strength member, the control device being carried by said first strength member, wherein the first strength member comprises a recess which receives the control device and which extends along the central axis between first and second ends opening respectively into the working chamber and to the open air, the first end being closed by the isolating diaphragm, and the control device is characterized in that it comprises a casing which is fitted into said recess and comprises a base delimiting the auxiliary chamber with the isolating diaphragm. - first and second strength members (3,5) intended to be secured to the two rigid elements to be connected, the first strength member having the form of a block and the second strength member being of annular shape centred on a central axis, the first strength member being arranged substantially on said central axis, - an elastomer body which links together the first and second strength members (3,5) and which delimits at least partially a working chamber, the elastomer body having a bell shape, with a top firmly fixed to the first strength member and an annular base firmly fixed to the second strength member, - a deformable compensation chamber which communicates with the working chamber via a constricted passageway, the compensation chamber, the working chamber and the first constricted passageway forming a hydraulic volume filled with liquid, the first constricted passageway having a resonance frequency comprised between 5 and 20 Hz, - an auxiliary chamber, - a decoupling valve comprising an isolating diaphragm made of elastomer, which separates the working chamber and the auxiliary chamber, said decoupling valve being adapted for absorbing vibrations at certain frequencies greater than 20 Hz, - a control device comprising an actuator adapted for selectively locking the isolating diaphragm,