The paper deals with the problem of adaptive wavelet filtering of speech signals based on Daubechies filters with minimization of errors in finding optimal threshold values. This approach is similar to estimating a speech signal by averaging it using a kernel that is locally adapted to the smoothness of the signal. In this case, a set of coupled mirror filters decomposes the speech signal in a discrete domain according to the orthogonal Daubechies wavelet basis into several frequency bands. Noise removal of speech signals is performed as a complete cutoff of the wavelet transform coefficients based on the assumption that their small amplitude values are noise. Thus, in the Daubechies wavelet basis, where coefficients with large amplitude correspond to abrupt changes in the speech signal, such processing preserves only the intermittent components originating from the input speech signal without adding other components caused by noise. In general, by equating small coefficients to zero, we perform adaptive smoothing that depends on the smoothness of the input speech signal. By keeping the coefficients of large amplitude, we avoid smoothing out sharp drops and preserve local features. Performing this procedure on several scales leads to a gradual reduction of the noise effect on both piecewise smooth and discontinuous parts of the speech signal. In view of this, the main task of the study is to adaptively generate micro-local thresholds, which will reduce the impact of additive noise on the pure form of the speech signal, and preserve significant wavelet coefficients of large amplitude that characterize the local features of the speech signal. Thus, as a result of our work, we have proved the feasibility of developing the presented method of wavelet filtering of speech signals with adaptive thresholds based on Daubechies wavelet analysis, which minimizes the loss of speech intelligibility and allows for noise removal depending on the properties and physical nature of the processed data.