The present invention relates to a method and device for releasing into the body from a delivery system a medical prosthesis mounted on the delivery system and held by a constraint in a constrained delivery disposition. The device comprises a first hub for the delivery system, a second hub for an elongate element to connect the device to the prosthesis constraint, a track for the second hub to advance along, from a starting point corresponding to constraint of the prosthesis, to a finishing point corresponding to separation of the prosthesis and constraint, ratchet means to advance the second hub progressively, from the starting point to the finishing point, in a plurality of actuation strokes, and a full stroke actuator to advance the second hub all the way from an intermediate point on the track to a finishing point in one single stroke of the actuator, the intermediate point being selectable by the user within a portion of the track which extends over at least half the length of the track.