A golf club head has a cavity for receiving a face insert. A first face insert, which is disposed in the cavity, has a front surface that is contoured. A second face insert composed of multiple rod elements is disposed in the cavity on top of the first face insert so that the rod elements are supported by the contoured front surface of the first face insert. Because the first face insert supporting the rod elements is contoured, the individual rod elements are of different lengths and, therefore, exhibit different dynamic responses when striking a golf ball, even when the rod elements are made of the same material.