An apparatus (12) by which both tremolo action and string clamping and string intonation adjustment are achieved effectively and in a very small space in a guitar has adjustment screw shanks (42) threaded into bores in the inertia bar (20) or block of the tremolo, and bear against the heads (40) of pull screws (39) that are connected to string clamping saddles (22). The heads (40) of the pull screws (39) are received in recesses (37) in the inertia bar (20); the inertia bar (20) is connected to the bridge plate (13) by several screws (47) that do not interfere with the screw shanks (42). To adjust intonation, the bridge plate (13) is pivoted upwardly and a wrench (46, Fig. 5) is employed to rotate the screw shanks (42) which in turn bear against the heads (40) of the pull screws (39). Furthermore, the pull screws (39) are rotated to release positions while the bridge plate (13) is in its upwardly pivoted position. After intonation is adjusted, the pull screws (39) are rotated to lock the saddles (22) in their desired positions.