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We develop more fully all-pole modeling of speech based on the minimum variance distortionless response (MVDR) spectrum. It is shown that MVDR modeling provides a class of all-pole models that are flexible for tackling a wide variety of speech modeling objectives. In particular the high order MVDR spectrum provides a robust model for all types of speech including voiced speech, unvoiced speech, and mixed spectra. Furthermore, it is simply obtained, and is always superior to the linear prediction (LP) spectrum. With its high quality modeling, the high order MVDR spectrum is suitable for use as a high quality reference spectrum, or for applications like speech recognition. In addition, the MVDR model possesses flexibility for developing low order all-pole models suitable for compression applications. In particular; reduced order MVDR all-pole models are shown to often outperform conventional LP filters in modeling all types of speech spectra. For more accurate modeling of a set of speech spectral samples in the frequency domain, MVDR modeling facilitates the development of superior weighted all-pole filters.