Summary: A new approximation for peak transient dynamic displacements is presented. This approximation is based on modal analysis and is valid for general damped structures, which includes the case of actively controlled structures. Intermediate design variable and intermediate response quantity concepts are used to enhance the accuracy of the approximation. When this high-quality approximation is used within the context of the approximation concept approach to design synthesis, the overall efficiency of the process is expected to be improved by reducing the number of complete analyses required for convergence. Numerical results that illustrate the effectiveness of the method are presented.