Modern statistical speech processing frameworks require the speech signals to be translated into feature vectors by means of vocoders. While features representing the amplitude envelope already exist (e.g. MFCC, LSF), parametrizing the phase information is far from straightforward, not only because it is a circular data, but also because it shows an irregular behaviour in noisy time-frequency regions. Thus, many vocoders reconstruct speech by using minimum phases and random phases, relying on a previous voicing decision. In this paper, a phase feature is suggested to represent the randomness of the phase across the full time-frequency plan, in both voiced and unvoiced segments, without voicing decision. esynthesis experiments show that, when integrated into a full-band armonic vocoder, the suggested randomization feature is slightly better, on average, to STRAIGHT's aperiodicity. In HMM-based synthesis, the results show that the suggested vocoder reduces the complexity of the analysis and statistical modelling by removing the voicing decision, while keeping the perceived quality.