A disk drive head suspension includes a load beam, a flexure for carrying a magnetic head slider, a base mounting structure for coupling the head suspension to a disk drive actuation system, a hinge, and a damping material. The load beam includes a proximal end portion and a distal end portion. The flexure is attached to and supported by the load beam. The hinge is attached to the base mounting structure and to the load beam and includes a constraint layer portion extending toward the distal end portion of the load beam. The damping material is located between and in contact with the constraint layer portion of the hinge and the load beam for damping resonance vibrations in the head suspension.