This paper proposes an enhanced method for estimating the a priori Signal-to-Disturbance Ratio (SDR) to be employed in the Acoustic Echo and Noise Suppression (AENS) system for full-duplex hands-free communications. The proposed a priori SDR estimation technique is modified based upon the Two-Step Noise Reduction (TSNR) algorithm to suppress the background noise while preserving speech spectral components. In addition, a practical approach to determine accurately the Echo Spectrum Variance (ESV) is presented based upon the linear relationship assumption between the power spectrum of far-end speech and acoustic echo signals. The ESV estimation technique is then employed to alleviate the acoustic echo problem. The performance of the AENS system that employs these two proposed estimation techniques is evaluated through the Echo Attenuation (EA), Noise Attenuation (NA), and two speech distortion measures. Simulation results based upon real speech signals guarantee that our improved AENS system is able to mitigate efficiently the problem of acoustic echo and background noise, while preserving the speech quality and speech intelligibility.