In this paper we present an original method mixing temporal and spectral processing to reduce the phasiness in the phase vocoder. Phasiness is an inherent artifact of the phase vocoder that appears when a sound is slowed down. The audio is perceived as muffled, reverberant and/or moving away from the microphone. This is due to the loss of coherence between the phases across the bins of the Short-Term Fourier Transform over time. Here the phase vocoder is used almost as usual, except that its phases are regularly reset in order to keep them coherent. Phase reset consists in using a frame from the input signal for synthesis without modifying it. The position of that frame in the output audio is adjusted using cross-correlation, as is done in many temporal time-stretching methods. The method is compared with three state-of-the-art algorithms. The results show a significant improvement over existing processes although some test samples present artifacts.