This paper presents a system approach to the residual echo suppression (RES) problem in a noisy acoustic environment. We propose a method that takes advantage of our existing robust acoustic echo cancellation system in order to obtain a residual echo estimate that closely resembles the true, noise-free residual echo. To achieve improved RES during strong near-end interference (e.g., double talk), a psychoacoustic postfilter is also used. The simulation results show that our RES based on the system approach outperforms a conventional estimation method. Comparing the postfiltered output to the unprocessed one indicates that our proposed RES approach can raise the PESQ score by more than half a point.