This paper presents a method to iteratively estimate phase information from speech in the cepstrum domain. It assumes that correct markings of pitch periods, which may not correspond to glottal closure instants (GCI), are available and can be used to extract the smooth spectral envelope of speech. By using this information, the minimum-phase cepstrum is derived and used as prior information in a modified version of a previously proposed scheme of complex cepstrum analysis based on the mean squared error. Experiments with an emotional database show that the proposed method achieves better performance in terms of continuous phase spectrum estimation, when compared with approaches that rely on accurate GCI markings and high-resolution phase unwrapping mechanisms. In addition, similar results to the full optimization of the complex cepstrum vector are reached, at a lower computational complexity.