Abstract-Hands-free devices are often used in a noisy and reverberant environment. Therefore, the received microphone signal does not only contain the desired near-end speech signal but also interferences such as room reverberation that is caused by the near-end source, background noise and a far-end echo signal that results from the acoustic coupling between the loudspeaker and the microphone. These interferences degrade the fidelity and intelligibility of near-end speech. In the last two decades, postfilters have been developed that can be used in conjunction with a single microphone acoustic echo canceller to enhance the near-end speech. In previous works, spectral enhancement techniques have been used to suppress residual echo and background noise for single microphone acoustic echo cancellers. However, dereverberation of the near-end speech was not addressed in this context. Recently, practically feasible spectral enhancement techniques to suppress reverberation have emerged. In this paper, we derive a novel spectral variance estimator for the late reverberation of the near-end speech. Residual echo will be present at the output of the acoustic echo canceller when the acoustic echo path cannot be completely modeled by the adaptive filter. A spectral variance estimator for the so-called late residual echo that results from the deficient length of the adaptive filter is derived. Both estimators are based on a statistical reverberation model. The model parameters depend on the reverberation time of the room, which can be obtained using the estimated acoustic echo path. A novel postfilter is developed which suppresses late reverberation of the near-end speech, residual echo and background noise, and maintains a constant residual background noise level. Experimental results demonstrate the beneficial use of the developed system for reducing reverberation, residual echo, and background noise. S. Gannot is with the School of Engineering, Bar-Ilan University, Ramat-Gan 52900, Israel (e-mail: gannot@eng.biu.ac.il).I. Cohen is with the Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel (e-mail: icohen@ee.technion.ac.il). P. C. W. Sommen is with the Signal Processing