The distance between the clamps at opposed ends of a shoulder rest bridge adjustable in infinitely fine increments by utilizing a pressure plate which, in an engaged mode, presses a brake member made from an elastomer, particularly soft rubber, against the underside of the bridge body. The pressure plate is actuated by a pivotable latch having a lever and co-operating with a non-rotatable bearing member having a ramp surface complementary in the direction of incline and in pitch with the ramp surface of the pivotable latch. A supplementary camming mechanism provides, upon hand displacement of one of the clamps towards the other into engagement by both with the instrument, an additional motion of the one clamp toward the instrument thus increasing the clamping force holding the shoulder rest to an instrument.