This paper proposes a method to directly compute controller parameter values in a synchronverter augmented with a so-called damping correction loop, and in so doing, achieve desired transient and steady-state response. The proposed approach is grounded in a reduced third-order system model that captures pertinent dynamic characteristics of the synchronverter active-power loop (APL), particularly those of the dominant mode. This reduced-order model helps to identify and explain a shortcoming in a previous parameter tuning method. Central to the proposed parameter computation method is to express APL parameters of the original system as closed-form functions of the poles of the reduced-order system. Since the reduced-order model retains dominant-mode dynamic behaviors of the original system, APL parameters can be directly computed according to specified APL dominant mode. Time-domain simulations are provided to validate the accuracy of the reduced-order model and the proposed direct-computation parameter tuning method.