n this work we address the problem of all pole spectral envelope estimation for speech signals. The currently widely used all pole spectral envelope model suffers from well-known systematic errors and more severely from model order mismatch. We will propose a procedure to first establish a band limited interpolation of the observed spectrum using a recently rediscovered true envelope estimator and then using the band limited envelope to derive an all pole envelope model named TE-LPC . The band-limited envelope that is used to derive the all pole envelope model reduces the problem of the unknown all pole model order. For the experimental investigation we propose a new perceptually motivated residual spectral peak flatness measure. The experimental results demonstrate that the proposed method significantly increases the spectral flatness for the perceptually especially important low order harmonics of voiced utterances