The evaluation of accurate speech spectral estimates is of importance in many areas such as formant extraction, speaker/speech recognition etc. This work describes an approach based on Dynamic Progamming for the optimal segmentation of speech spectra into Selective Linear Predictive (LP) segments to minimise the discrepancy between real and model spectra and thereby to produce effective spectral estimates of the original signal. A modification of this technique then leads to a novel method for the production of accurate estimates of speech formant positions. This segmentation scheme is implemented for both isolated speech spectra and complete utterances to produce values which are finally incorporated into cascade formant synthesisers. These results are found to offer significant advantages over those available using conventional LP methods.