This paper proposes to augment the conventional synchronverter control scheme with an auxiliary loop to freely adjust the dynamic response speed. This loop is dubbed as a damping correction loop since its form and function are reminiscent of the damping component in the classical synchronous generatormodel. Central to the proposed auxiliary loop is the creation of an additional tuneable parameter that allows for unrestricted adjustment of the system damping ratio without affecting the steady-state frequency droop characteristic, which is an improvement over the conventional synchronverter design. In the proposed method, relevant parameters are analytically tuned and active-and reactive-power coupling effects are reduced when operating with increased response speed. The dynamic response and robustness of the approach are verified via extensive small-signal analysis. Furthermore, time-domain simulations highlight the advantages of the proposed method over existing ones.