This paper shows that a microcanonical approach to complexity, such as the Microcanonical Multiscale Formalism, provides new insights to analyze non-linear dynamics of speech, specifically in relation to the problem of speech samples classification according to their information content. Central to the approach is the precise computation of Local Predictability Exponents (LPEs) according to a procedure based on the evaluation of the degree of reconstructibility around a given point. We show that LPEs are key quantities related to predictability in the framework of reconstructible systems: it is possible to reconstruct the whole speech signal by applying a reconstruction kernel to a small subset of points selected according to their LPE value. This provides a strong indication of the importance of the Unpredictable Points Manifold(UPM), already demonstrated for other types of complex signals. Experiments show that a UPM containing around 12% of the points providesvery good perceptual reconstruction quality.