— In this paper, we develop a Bayesian short-time spectral amplitude (STSA) estimator with the purpose of singlechannel speech enhancement in the presence of moderate levels of non-stationary noise. In this regard, we first apply a minimum mean squared error (MMSE) approach for the joint estimation of the short-term predictor (STP) parameters of the speech and noise signals, from the noisy speech observations. This approach is based on using trained codebooks of speech and noise linear predictive (LP) coefficients to model the a priori information needed by the MMSE estimation. Afterwards, the power spectra derived from the estimated STP are passed to the Wβ-SA STSA estimator, where they are used to calculate the enhancement gains applied to the short-term Fourier transform (STFT) coefficients of the noisy speech. When compared to an existing benchmark approach from the literature, the proposed approach combining codebook-based STP estimation with the Wβ-SA method gives rise to ...