In this paper, we present a new technique for the estimation of short-term linear predictive parameters of speech and noise from noisy data and their subsequent use in waveform enhancement schemes. The method exploits a priori information about speech and noise spectral shapes stored in trained codebooks, parameterized as linear predictive coefficients. The method also uses information about noise statistics estimated from the noisy observation. Maximum-likelihood estimates of the speech and noise short-term predictor parameters are obtained by searching for the combination of codebook entries that optimizes the likelihood. The estimation involves the computation of the excitation variances of the speech and noise auto-regressive models on a frame-by-frame basis, using the a priori information and the noisy observation. The high computational complexity resulting from a full search of the joint speech and noise codebooks is avoided through an iterative optimization procedure. We introduce a classified noise codebook scheme that uses different noise codebooks for different noise types. Experimental results show that the use of a priori information and the calculation of the instantaneous speech and noise excitation variances on a frame-by-frame basis result in good performance in both stationary and nonstationary noise conditions.